jumps, cojumps and macro announcements - duke university
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Research Division Federal Reserve Bank of St. Louis Working Paper Series
Jumps, Cojumps and Macro Announcements
Jérôme Lahaye Sébastien Laurent
and Christopher J. Neely
Working Paper 2007-032A http://research.stlouisfed.org/wp/2007/2007-032.pdf
August 2007
FEDERAL RESERVE BANK OF ST. LOUIS Research Division
P.O. Box 442 St. Louis, MO 63166
______________________________________________________________________________________
The views expressed are those of the individual authors and do not necessarily reflect official positions of the Federal Reserve Bank of St. Louis, the Federal Reserve System, or the Board of Governors.
Federal Reserve Bank of St. Louis Working Papers are preliminary materials circulated to stimulate discussion and critical comment. References in publications to Federal Reserve Bank of St. Louis Working Papers (other than an acknowledgment that the writer has had access to unpublished material) should be cleared with the author or authors.
Jumps, Cojumps and Macro Announcements∗
Jerome LAHAYE† Sebastien LAURENT‡ Christopher J. NEELY§
First Version: October 2006
This Version: August 2007
Abstract
We analyze and assess the impact of macroeconomic announcements on the discontinuities in
many assets: stock index futures, bond futures, exchange rates, and gold. We use bi-power variation
and the recently proposed non-parametric techniques of Lee and Mykland (2006) to extract jumps.
Beyond characterizing the jump and cojump dynamics of many assets, we analyze how news arrival
causes jumps and cojumps and estimate limited-dependent-variable models to quantify the impact of
surprises. We confirm previous findings that some surprises create jumps. However, many announce-
ments do not create jumps and many jumps are not related to announcements. The propensity of
surprises to create jumps differs across asset classes, i.e., exchange rates, bonds, stock index. Payroll
announcements are most important on stocks and bonds futures markets. Trade related news often
creates cojumps on exchange rate markets.
Keywords: exchange rate, futures, bonds, realized volatility, bipower variation, jumps, macroeconomic
announcement.
JEL Codes: G14, G15, F31, C22
∗The authors would like to thank participants at the Economic Department Doctoral Workshop (University of Namur,
29th of March 2006), CORE Econometrics Seminar (University of Louvain-la-Neuve, 30th of March 2006), 2nd Research
Day of the METEOR “Money and Banking Group” (University of Maastricht, 28th of June2006), 7th Missouri Economic
Conference (University of Missouri at Columbia, 30th of March 2007), GREQAM summer school/workshop on “New
Microstructure of Financial Markets” (Aix en Provence, 25th to 29th of June 2007) for helpful comments and discussions.
We would like to thank in particular Mardi Dungey, Cumur Ekinci, Woon K. Wong, Jesper Pedersen. This text presents
research results of the Belgian Program on Interuniversity Poles of Attraction initiated by the Belgian State, Prime
Minister’s Office, Science Policy Programming. The scientific responsibility is assumed by the authors.
†CeReFiM, University of Namur and CORE; [email protected] (corresponding author)‡CeReFiM, University of Namur and CORE; [email protected]§Assistant Vice President, Research Department, Federal Reserve Bank of St. Louis; [email protected]
1 Introduction
How markets process information and what determines asset return distributions are central issues
in economics. Our study focuses on two important aspects of financial time series to which the
literature has recently devoted attention: jumps and simultaneous jumps in multiple markets
(cojumps). How big and frequent are jumps across asset classes and over time? Do jumps cluster
in time? Do jumps tend to occur simultaneously on several markets? That is, are there more
“cojumps” than one would expect if asset prices jumped independently? What causes (co)jumps?
Do scheduled macroeconomic announcement create (co)jumps or do these releases affect only the
continuous part of volatility? Our study answers these questions.
We thus re-investigate the central question of how asset prices are related to fundamentals.
Andersen, Bollerslev, Diebold, and Vega (2003, 2007) have studied this issue in great detail but
we focus on discontinuous price changes, not on returns in general. Moreover, as Lee and Myk-
land (2006) and Tauchen and Zhou (2005) explain, characterizing the distribution and causes of
jumps can improve and simplify asset pricing models.1 So—beyond scientific curiosity—we have
a practical interest in understanding how news affects discontinuities. Our paper illuminates the
relations between scheduled macroeconomic news, jumps and cojumps.
We extract jumps and cojumps of many important asset series—exchange rates, stock index
futures, U.S. bond futures and gold prices—and relate them to macroeconomic news. We use the
non-parametric statistic of Lee and Mykland (2006) to estimate jumps on high-frequency data.
The Lee-Mykland estimation technique is simple and parsimonious: Compare returns to a local
volatility measure to find returns that a diffusion is very unlikely to produce—discontinuities. To
measure local volatility, Lee and Mykland (2006) use the jump-robust bi-power variation (RBV)
estimator, defined as the sum of the product intra-daily adjacent returns over the considered
horizon (Barndorff-Nielsen and Shephard, 2004, 2006a).
The Lee-Mykland procedure identifies intraday jumps, which makes it especially useful in
studying if and how announcements cause jumps. We also use this statistic to investigate mul-
tivariate issues and test whether macroeconomic announcements cause cojumps. Though a fully
consistent cojump characterization should compare returns, or a combination of returns to local co-
variation measures, the literature has not yet extended the technique to a multivariate procedure.2
1In general, the impact of jumps on financial management is non-negligible. See for example Duffie, Pan, and
Singleton (2000), Liu, Longstaff, and Pan (2003) , Eraker, Johannes, and Polson (2003), and Piazzesi (2005).2To the best of our knowledge, Barndorff-Nielsen and Shephard (2006b), generalizing their univariate results,
2
It seems very reasonable to assume, however, that highly significant, simultaneous individual jumps
provide insights for understanding cojump processes. This is a conservative approach—analogous
to using OLS rather than SUR to estimate a system of equations—as a multivariate procedure
would surely be more efficient. We show that exchange rate cojumps are relatively frequent and
macroeconomic announcements appear to cause many of them.
Researchers have evaluated the impact of macroeconomic news on assets returns in many
ways.3 The works of Andersen, Bollerslev, Diebold, and Vega (2003, 2007) show that jumps in
exchange rates, stocks and bonds are linked to fundamentals.4 However, recent developments
in jump estimation have revived studies about news and economic events’ impact on financial
markets. The fact that these techniques precisely define jumps enables researchers to analyze such
discontinuites more easily. The recent literature using non-parametric tools to estimate jumps
provides some evidence that news creates jumps. Barndorff-Nielsen and Shephard (2006a) apply
their bipower variation technique on a 10-year exchange rate data set (USD/DEM and USD/JPY),
relating macroeconomic news releases to jump days. Lee and Mykland (2006) also examine the
relation between announcements and jumps on individual equities and the S&P 500 index returns
with three months of high frequency data. They relate jumps to news found with the Factiva
search tool: Jumps on individual equities correspond to scheduled and unscheduled firm level
news while jumps on the S&P index correspond to macroeconomic announcements. Jumps on
individual equities are also much larger and more frequent than those on the stock index. Beine,
Lahaye, Laurent, Neely, and Palm (2007) study the link between central bank interventions and
jumps with the Barndorff-Nielsen and Shephard (2004, 2006a) statistic and find that interventions
can cause rare but especially large discontinuities. To the best of our knowledge, two simultaneous
and building on ideas of Hendry (1995), is the only theoretical paper in the field. While an estimator that accounts
for multivariate behavior is likely to be more efficient in finding jumps, it is very reasonable to define cojumps as
simultaneous individual jumps.3In general, the huge amount of studies in the field are differentiated according to several dimensions: the
moments of the returns’ distribution under study (level or volatility), returns’ frequency (intra-daily or lower
frequency), type of assets (exchange rates, stocks, bonds, ...), type of news (scheduled or unscheduled), etc. For
example, the literature on the effect of news on volatility dates back at least to 1984 and include inter alia Patell
and Wolfson (1984), Harvey and Huang (1991), Ederington and Lee (1993), Andersen and Bollerslev (1998b), Li
and Engle (1998), Jones, Lamont, and Lumsdaine (1998), or Bauwens, Ben Omrane, and Giot (2005). On the other
hand, the literature on the effect of news on the return’s conditional mean includes notably the works of Andersen,
Bollerslev, Diebold, and Vega (2003, 2007), Evans and Lyons (2007), or Veredas (2005).4See Goodhart, Hall, Henry, and Pesaran (1993), Almeida, Goodhart, and Payne (1998), and Dominguez (2003)
about exchange rates.
3
and concurrent papers study the link between non-parametric jumps and news besides the present
paper. Huang (2006) estimates daily jumps with bi-power variation on 10 years of S&P 500 and
U.S. T-bonds 5-minute futures to measure the response of volatility and jumps to macro news.
Analyzing conditional distributions of jumps, and regressing continuous and jump components on
measures of disagreement and uncertainty concerning future macroecnomic states, Huang (2006)
finds a major role for payroll news and a relatively more responsive bond market. This is consistent
with our findings. On the other hand, Dungey, McKenzie, and Smith (2007) focus on the treasury
market, estimating jumps and cojumps using bi-power variation and examining “simultaneous”
jumps across the term structure of interest rates. Dungey, McKenzie, and Smith (2007) find that
the middle of the yield curve often cojumps with one of the ends, while the ends of the curve exhibit
a greater tendency for idiosyncratic jumps. Macro news is strongly associated with cojumps in
the term structure.
Our paper differs from the existing literature in several respects, however:
• We estimate jumps at a very high frequency with the Lee/Mykland technique. These
estimates are better suited than daily (bipower variation) measures of jumps for studying
the link between jumps and scheduled macro news.
• Our approach considers a broad set of financial assets including exchange rates, stocks,
bonds, gold.
• We define simultaneous occurrences of high frequency jumps, which provides precise insights
into cojumping dynamics.
• We estimate Tobit-probit models on the time-series of jumps and cojumps to assess the
impact of surprises on these discontinuities.
The rest of the paper proceeds as follows: After explaining the theory of jump estimation in
Section 2, we characterize (co)jump dynamics and intensity in Section 3. In Section 4, we address
a central issue of asset return distribution: What is the link between macroeconomic news and
(co)jumps? We initially compare jump size distributions on days with and without announcements
and then study what types of announcements cause jumps. We finally evaluate the surprise impact
of news on jumps and cojumps with probit-Tobit models. Finally, Section 5 concludes.
4
2 Theoretical background
This section describes the two estimators used for volatility and jump measurement. We first
describe the more familiar bi-power variation estimator before presenting the Lee and Mykland
(2006) statistic, used throughout this paper.
The idea behind bi-power variation is the following: Realized volatility (RV) is the sum of
squared returns over an interval. This sum consistently estimates the sum of integrated volatility
(the diffusion variance) plus the sum of squared jumps within a period. Bipower variation (BV),
however, is the sum of the products of absolute adjacent returns. This quantity consistently
estimates only integrated volatility even in the presence of jumps. Therefore the difference between
RV and BV consistently estimates the sum of squared jumps within a period.
More formally, let p(t) be a logarithmic asset price at time t. Consider the continuous-time
jump diffusion process defined by the following equation:
dp(t) = µ(t)dt + σ(t)dW (t) + κ(t)dq(t), 0 ≤ t ≤, T (1)
where µ(t) is a continuous and locally bounded variation process, σ(t) is a strictly positive
stochastic volatility process with a sample path that is right continuous and has well defined
limits, W (t) is a standard Brownian motion, and q(t) is a counting process with intensity λ(t)
(P [dq(t) = 1] = λ(t)dt and κ(t) = p(t)− p(t−) is the size of the jump in question). The quadratic
variation for the cumulative process r(t) ≡ p(t)− p(0), denoted [r, r]t, is the integrated volatility
of the continuous sample path component plus the sum of the q(t) squared jumps that occurred
between time 0 and time t:
[r, r]t =∫ t
0
σ2(s)ds +∑
0<s≤t
κ2(s). (2)
The empirical counterpart to daily quadratic variation is daily realized volatility, denoted
RVt+1(∆), which is the sum of the intraday squared returns:
RVt+1(∆) ≡1/∆∑
j=1
r2t+j∆,∆, (3)
where rt,∆ ≡ p(t)− p(t−∆) is the discretely sampled ∆-period return.5
As Andersen, Bollerslev, and Diebold (2006) explain, realized volatility converges uniformly in
probability to the daily increment of the quadratic variation process as the sampling frequency of5We use the same notation as in Andersen, Bollerslev, and Diebold (2006) and normalize the daily time interval
to unity.
5
the returns increases (∆ → 0):6
RVt+1(∆) →∫ t+1
t
σ2(s)ds +∑
t<s≤t+1
κ2(s). (4)
That is, realized volatility consistently estimates integrated volatility plus the sum of the squared
jumps.
In order to disentangle the continuous and the jump component of realized volatility, we need
to consistently estimate the integrated volatility, even in the presence of jumps in the process.
This is done using the asymptotic results of Barndorff-Nielsen and Shephard (2004, 2006a). The
realized bipower variation, denoted BVt+1(∆), is defined as the sum of the product of adjacent
absolute intradaily returns standardized by a constant:
BVt+1(∆) ≡ µ−21
1/∆∑
j=2
|rt+j∆,∆||rt+(j−1)∆,∆|, (5)
where µ1 ≡√
2/π ' 0.79788 is the expected absolute value of a standard normal random variable.
It can be shown that bipower variation converges to integrated volatility, even in the presence of
jumps:
BVt+1(∆) →∫ t+1
t
σ2(s)ds. (6)
Barndorff-Nielsen and Shephard use the difference between realized volatility and bipower
variation to estimate the sum of jumps within a day. This difference does not, however, show how
many jumps there are, their individual size or when they occur within the day. To avoid these
deficiencies, we use the Lee and Mykland (2006) statistics to estimate jumps for each intraday
period.7
To test whether a jump occurred in a small interval, the Lee and Mykland (2006) statistic
quantifies the intuition that a “jump” is too big to come plausibly from a pure diffusion. Because
a “big” price change depends on the volatility conditions prevailing at the time, the Lee and
Mykland (2006) statistic compares the price change to a local robust-to-jumps volatility estimator
6See also, for example, Andersen and Bollerslev (1998a), Andersen, Bollerslev, Diebold, and Labys (2001),
Barndorff-Nielsen and Shephard (2002a), Barndorff-Nielsen and Shephard (2002b), Comte and Renault (1998).7In the Lee-Mykland setting, q(t) is a counting process that may be non homogenous, independent of W (t), and
κ(t) is independent from q(t) and W (t). Moreover, the drift and diffusion coefficients are not allowed to change
dramatically over short period of time. Formally, that is expressed as supj supt+(j−1)∆≤u≤t+j∆ |µ(u)− µ(t + (j −1)∆)| = Op(∆1/2−ε) and supj supt+(j−1)∆≤u≤t+j∆ |σ(u) − σ(t + (j − 1)∆)| = Op(∆1/2−ε), for any ε > 0. That
means that, for any δ > 0, there exists a finite constant Mδ such that the probability that the mentioned supreme
is greater than Mδ∆1/2−ε is smaller than δ.
6
(bipower variation). During periods of “high” volatility, for example, price changes must be even
larger than the average critical value to be considered “jumps.”
The statistic Lµ tests whether a jump occurred between any intradaily time periods t+(j−1)∆
and t+j∆, for an integer j. It is defined as the normalized return—the return, less its local mean,
divided by the local standard deviation:
Lµ(t + j∆) ≡ rt+j∆,∆ − m(t + j∆)σ(t + j∆)
, (7)
where m(t+j∆) is the mean local return and σ(t+j∆) is the realized bipower variation multiplied
by µ21/K−2. They are computed over a K-length window immediately preceding the tested return
and are defined as follows:8
m(t + j∆) =1
K − 1
j−1∑
l=j−K+1
rt+l∆,∆, (8)
σ(t + j∆)2 ≡ 1K − 2
j−1∑
l=j−K+2
|rt+l∆,∆||rt+(l−1)∆,∆|. (9)
Under the null of no jumps at the testing time, the stated assumptions and a suitable choice
of the window size for local volatility K (i.e. we must have K = Op(∆α), with −1 < α < −0.5),
the statistic Lµ asymptotically follows a zero mean normal distribution with variance 1/c2, where
c =√
2/π.
There is a tradeoff in choosing the window size, K. While larger values impose a greater
computational burden, K must be large enough to retain the advantage of bipower variation as
a robust-to-jump estimator. A range of values satisfy the condition for K (K = Op(∆α), with
−1 < α < −0.5). Lee and Mykland (2006) recommend the smallest possible window size within the
range given by α, as their simulations show that greater windows only increase the computational
burden. So K is chosen as ∆−0.5. For example, suppose ∆ = 1252×nobs , nobs being the number
of observations per day, then the integers between 15.87 and 252 are within the required range.
More specifically, they recommend the following window sizes for sampling at frequencies of one
week, one day, one hour, 30 minutes, 15 minutes and 5 minutes: 7, 16, 78, 110, 156, and 270,
respectively.
Finally, Lee and Mykland (2006) propose a rejection region using the distribution of their
statistics’ maximums. Under the stated assumptions and no jumps in (t + (j − 1)∆, t + j∆], then
when ∆ → 0,max |Lµ(t + j∆)| − Cn
Sn→ ψ, (10)
8The term m(t + j∆) reduces to zero in the case of no drift. In that case, the statistic is denoted by L(t + j∆).
7
where ψ has a cumulative distribution function P (ψ ≤ x) = exp(−e−x), Cn = (2 log n)0.5
c −log(π)+log(log n)
2c(2 log n)0.5 and Sn = 1c(2 log n)0.5 , n being the number of observations. So if we choose a signifi-
cance level α = 0.0001, we reject the null of no jump at testing time if |Lµ(t+j∆)|−Cn
Sn> β∗ with the
threshold β∗ such that P (ψ ≤ β∗) = exp(−e−β∗) = 0.9999, i.e. β∗ = −log(−log(0.9999)) = 9.21.
In the remainder of the text, Jt+j∆ denotes significant jumps. It is equal to the tested return
rt+j∆ when the statistic Lµ(t+j∆) detects a significant jump according to the described rejection
region. It is equal to 0 otherwise. Moreover, we use the notation P (jump) for P (Jt+j∆ 6= 0).
We can now move on in the next section to a description of the data used in our analysis before
turning to the empirical results.
3 Data description
3.1 Asset price data
We use a long span of high frequency time series data on 15 assets from 4 asset classes: four
exchange rates involving the dollar (USD/EUR, USD/GBP, JPY/USD, CHF/USD), three stock
index futures (Nasdaq, Dow Jones, S&P 500, for which we use the acronyms ND, DJ, and SP,
respectively), 30-year U.S. Treasury bonds futures (with the acronym US), as well as gold prices
(with acronym XAU). From the four exchange rate series, we recover the implied non-dollar
exchange rates (GBP/EUR, CHF/EUR, JPY/EUR, CHF/GBP, JPY/GBP and CHF/JPY), as-
suming no triangular arbitrage. All the original series were provided at a 5-minute frequency.
We re-sampled them at 15-minute intervals (30-minute for Tobit-probit estimations in Section 4).
Table 1 summarizes information about the series.
Olsen and Associates provide the exchange rate and XAU series. The USD/EUR, USD/GBP
and JPY/USD are sampled using last mid-quotes (average of log bid and log ask) of each 5-
minute interval. The CHF/USD and XAU series are sampled through a linear interpolation of
mid-quotes around 5-minute interval points. The exchange rates series cover about 18 years of
data (1986-2003), while 15 years are available for XAU (1986-2001).
The Dow Jones and 30-year U.S. T-bonds futures contracts series are traded on the Chicago
Board of Trade (CBOT), while the Nasdaq and S&P 500 futures trade on the Chicago Mercantile
Exchange (CME). The futures’ sample ranges vary across series: bond futures data cover about 12
years, the S&P series about 19 years, and 6 years are available for Nasdaq and Dow Jones futures.
8
We construct continuous series by splicing contracts with liquid trading. That is, we roll-over to
another contract 6 business days before maturity (15 business days in the case of U.S. T-bonds).
The currency and XAU markets are decentralized, traded around the clock, and around the
world. A 24 hour trading day is thus divided into 288 5-minute or 96 15-minute intervals. As
standard in the literature, we define trading day t to start at 21.15 GMT on day t − 1 and end
at 21.00 GMT on day t.9 So the first price of trading day t is the last price of the 21.00-21.15
interval (of calendar day t− 1), when prices are sampled at 15-minute. The first return of the day
is a change over the 21.00-21.15 interval.
However, CBOT and CME have limited pit trading hours. We cannot assess whether there
is a jump in the much longer overnight return, because it cannot be directly compared to a local
volatility estimate. Thus, our calculations will omit this return. For the Nasdaq and S&P 500
traded at the CME, we retain the following hours for 15-minute sampled prices: 9.45 - 16.15 EST
for both future contracts, the market opening at 9.30 EST. On these CME markets, the first return
of the day is thus a change over the 9.45-10.00 interval. For the Dow Jones and U.S. T-bonds
futures traded at the CBOT, the market opens at 8.20 EST, and, for 15-minute sampled prices,
we retain 8.25 - 14.55 and 8.25 - 16.10 EST, respectively. So for the CBOT markets, the first
return of the day covers the 8.25-8.40 interval.
We remove week-ends and a set of fixed and irregular holidays, from the intradaily return
series, as well as days where there are too many missing values, constant prices, and/or days with
the longest constant runs activity. The regular holidays removed are December 24 through the
26, December 31 through January 2 and July 4. Irregular holidays include Good Friday, Easter
Monday, Memorial Day, Labor Day, Thanksgiving and the day after. The first two lines of Table
2 report the number of observations and sample days for each asset.
3.2 Jumps and cojumps
In this subsection, we characterize the (co)jumping behavior of financial assets with a sampling
frequency of 15 minutes. Simulation results in Lee and Mykland (2006) show that the test statis-
tic provides excellent results at that frequency. Moreover, though not reported here, volatility
signature plots show that realized volatility starts to stabilize at about 15 minutes. So we expect
our estimates to be free of the noise present in higher frequency returns. We describe jumps
conservatively, analyzing jumps with a very low significance level (α) of 0.0001. We first describe
9This is motivated by the ebb and flow in the daily FX activity patterns. See Bollerslev and Domowitz (1993).
9
individual jumps before focusing on simultaneous jump occurrences.
3.2.1 Jumps
Figure 1 provides a bird’s eye view on the time series of jumps (Jt+j∆, as defined in Section 2),
illustrating that jumping behavior varies by asset class.10 For example, Nasdaq futures, a highly
volatile market11, seem to exhibit fewer but much larger jumps than exchange rates (though one
should not be misled by the different sample length on the X-axis). Moreover, there are big
jumps during major crises as, for example, in October 1987 on the S&P 500 futures.12 When
comparing jumps across series, one should remember that the exchange rate and XAU series have
more trading hours than do the stock index and bonds futures markets. The remainder of this
section contrasts jumps statistics across series.
Table 2 reveals different jump frequencies across series. This table reports the probability that
a day contains at least one jump and the probability that an intra-day return is a jump. For
the latter approach, we also provide information for positive and negative jumps separately. For
example, the first column—labeled “DJ”—shows that the Dow Jones futures series jumped on 25
days, which was 1.43 % of the sample and the expected number of jumps on jump days was 1.04.
Jump days are much less frequent on stock index futures than on U.S. bonds futures (Table
2, second horizontal panel). 5.32% of days have jumps in the US sample, while the DJ, ND
and SP exhibit jumps on only 1.43, 0.70, and 1.70% of days, respectively. Bond futures exhibit
fewer jumps than dollar exchange rates, but about the same proportions as non-dollar exchange
rates. Jumps seem to be very frequent on the XAU series, occurring on 22% of all days. And
the average number of jumps—on jump days—reaches a maximum of 1.36 for the XAU series
(Table 2, second horizontal panel, last line). This heterogeneity in jump frequency is unsurprising
across such different markets. The decentralized 24 hour exchange rate markets, with overlapping
international trading segments, are more likely to produce jumps than a market with limited hours,
such as the futures markets.
When comparing jump probabilities, one should recall that there are more observations per10For clarity, we ignore here the cross exchange rate series recovered under a no-triangular-arbitrage assumption.11Though not reported here, statistics for the daily continuous component of realized volatility show that the
Nasdaq futures market ranks among the most volatile markets.12It is not obvious that “market crashes” create jumps estimated as such. Indeed, the two greatest jumps observed
on the S&P 500 in October 1987 have opposite signs. That means that the S&P 500 lost a great deal of its value
without the negative discontinuities significantly outweighing the positive discontinuities. The jumps identified
during this crisis do not account for a large part of the S&P variation during that period.
10
day on decentralized 24 hours markets. This can be illustrated by comparing jumps per ob-
servation (Table 2, third panel, second line): For example, the bonds future market (column
4, US) exhibits more jumps per observation (P (jump) = 0.2109%) than the USD/EUR market
(column 5) (P (jump) = 0.1630%) but the USD/EUR market exhibits jumps on 13 percent of
days (P (jumpday) = 13.05%) while the bond futures market only jumps on 5 percent of days
(P (jumpday) = 5.32%). The USD/EUR exhibits more jumps per day because it has many more
observations per day but the USD/EUR is less likely to jump on any given observation.
Is there asymmetry in positive and negative jumps? While we analyze jumps rather than re-
turns, previous theoretical and empirical results on returns suggest that markets respond more to
negative surprises in good times. The literature has suggested both behavioral and rational expec-
tations explanations for such asymmetric responses. Barberis, Shleifer, and Vishny (1998) offer
a behavioral approach, while Veronesi (1999) provides a rational expectations model. Moreover,
practitioners commonly accept that markets will strongly respond to bad news in good times,
as explained in Conrad, Bradford, and Landsman (2002) and Andersen, Bollerslev, Diebold, and
Vega (2003). Because surprises are mean zero and most of our sample covers expansions, we might
expect more significant negative jumps, at least for equities.13 The sign of responses to negative
news is less clear in other markets. The number of positive and negative detected jumps (first lines
of fourth and fifth panels of Table 2) bears out that negative jumps are much more frequent than
positive ones on S&P futures. We also observe asymmetry on dollar exchange rates: U.S. dollar
jump depreciations are more common than jump appreciations.14 For example, comparing panels
4 and 5 of Table 2, there were 378 jump depreciations of the USD versus 304 jump appreciations of
the USD. Other markets, i.e. DJ, ND, and US, display no apparent asymmetry between positive
and negative jumps. The SP, however, displays many more negative jumps than positive jumps,
as one might expect from an equity market.
When do jumps usually occur? Figure 2 shows the estimated number of jumps, by time of
day, for each series. Exchange rates, XAU, and the S&P 500 futures have common seasonality,
with lots of jumps between 1200 and 1800. That is, most of the jumps on the 24 hours markets13According to NBER business cycle expansions and contractions dates, only two periods covering about one year
and half of our sample (from July 1990 to March 1991 and from March until November 2001) can be considered as
contractions. These recession periods represent a small fraction of our longest samples that cover about 18 years
of data.14The four dollar exchange rates are USD/EUR, USD/GBP, JPY/USD, and CHF/USD. So a positive jump
means a dollar depreciation for the first two markets and a dollar appreciation for the last two.
11
(exchange rates and XAU) occur after the North-American segment opening at about 1300. Sim-
ilarly, most of the jumps on the U.S. T-bonds futures market occur at the beginning of the U.S.
trading day (returns from 8.25 to 8.40 EST). This is consistent with the idea that macroeconomic
announcements, which are mostly released at 8:30 EST, cause many jumps.
Table 2 and Figure 3 provide further information concerning jump moments and frequencies.
Table 2 (panel 3, 4 and 5, last two lines) provides sample moments for jumps, while Figure 3 is a
scatter plot of mean jump size versus jump frequency. Stock index futures exhibit extremely large
(above 1% in absolute value) but relatively infrequent jumps. Exchange rates (dollar and non-
dollar) and XAU exhibit smaller jumps (between 0.4 and 0.6% in absolute value) than do equities.
Compared with cross rates, dollar exchange rates exhibit more frequent jumps of comparable size.
The bond market stands in the middle in terms of jump size (with an average of about 0.8%
in absolute value) with frequency comparable to those of cross exchange rates, i.e. bond prices
jump less often than do exchange rates and XAU prices. Table 2 shows that jump sizes are highly
variable; the standard deviations for positive and negative jumps often exceed 1% for stock index
futures, lie roughly between 0.2% and 0.35% for bonds and exchange rates, and are about 0.5%
for XAU.
The next section characterizes how markets jump together, or cojump.
3.2.2 Markets interdependence: an analysis of cojumps
This section shows that jumps can occur simultaneously on different markets and characterizes
those cojumps. We denote a cojump on a set of markets M at time t+ j∆ as COJMt+j∆ and define
it as:
COJMt+j∆ =
∏
M
I(Jmi
t+j∆), (11)
where I is the indicator function, Jmi
t+j∆ refers to jumps on market mi in the set M at time t+ j∆.
For clarity in the notations, the superscript referring to markets is omitted. Moreover, we denote
the probability of a cojump P (COJt+j∆ = 1) by P (coj).
Table 3 provides a detailed view on how markets jump together. Table 3 denotes the number
of observations as #obs, the number of cojumps as #coj, the probability of a cojump as P (coj),
and the probability of cojumping under the null that jump processes are independent as P (coj)
if indep. The first (top) horizontal panel of Table 3 shows the likelihood of cojumps on all
combinations between stock index futures and 30-year U.S. T-bonds. For example, the first row
shows that the ND-DJ pair exhibited 4 cojumps over 46548 observations, which produced a jump
12
propensity of 0.0086 percent per observation. The second horizontal panel shows statistics for
cojumps on dollar exchange rates. The third horizontal panel reports results for simultaneous
jumps on pairs of markets with the most liquid exchange rate, the USD/EUR market. The last
horizontal panel shows results for cojumps occurring on all dollar exchange rates plus another
market.
The table allows us to compare the actual probability of cojumping (P (coj)) with the proba-
bility of cojumping under the null of independence P (coj) if indep to assess whether jumps are
independent events. The latter probability is the product of the jump proportions in the respec-
tive markets. The actual proportions of cojumps are overwhelmingly greater than the probability
under the null of independence, indicating that cojumps do not occur by chance. For example, the
observed proportion of cojumps on the ND-DJ markets was 0.0086%, but the expected probability
under the null that the jumps are independent is essentially zero. Formal tests of this hypothesis,
using the properties of the binomial distribution reject the null of independent jumps for all cases
in which there are cojumps.
The data show that cojumps occur frequently on certain markets. But the probability of a
cojump is bounded by the minimum probability of a jump across all the markets considered. For
example, there are only 12 jumps on the ND market; cojumps involving the ND are necessarily
unfrequent. But cojumps might compose a very large proportion of all jumps on some markets.
Therefore we examine the probability of cojumps conditional on jumps in individual markets
(P (coj|jump)). This gives a clearer picture of the dependence of a given market with other
markets. In the third vertical panel of Table 3, the five columns, numbered from 1 to 5, correspond
to individual markets in the order in which they appear on the first column of Table 3. Thus, a
conditional probability on line x and column y gives the probability of a cojump on the markets
considered in line x given that a jump occurred on the market that has the yth position in the
markets of line x. For example, the first conditional probability on the first line of the Table
(33.33%) means that 1/3 of all jumps on the ND market are also cojumps with the DJ prices
(the corresponding line is ND-DJ). Likewise, conditional on a jump in the DJ, the probability of
a cojump on the ND-DJ pair is 15.83%. Column 1 refers to ND; column 2 refers to DJ.
The column labeled “1” under P (coj|jump) in Table 3 shows that when a jump occurs on
the ND market, the probability that it jumps with another market in the group considered here
(stock index and bond futures) is at least 16.67% (ND - US) and can be as high as 41.67% (ND -
SP). That is, many of the infrequent Nasdaq jumps occurred at the same time as jumps on other
13
markets, mainly other stock index futures. For the DJ market, the probability of a cojump, given
a jump on SP, is somewhat smaller than the ND’s. It reaches a maximum of 30.77 % for DJ - US
cojumps. It is even smaller for the SP where the maximum P (coj|jump) is 7.69% for ND-DJ-US
cojumps.
On markets with infrequent jumps, these rare jumps are highly dependent. In particular,
stock index futures and bonds are highly dependent. This is particularly true for the ND market;
when the ND jumps, the SP is also very likely to jump. The probability of a cojump on ND-SP,
conditional on a jump in ND, is 41.67%. Table 3, second panel shows that cojumps are not rare
on dollar exchange rates. There are 391 cojumps on the USD/EUR - CHF/USD market pair,
implying a probability of cojump of about 0.093% (per observation). Because we work with 15-
minute returns, this means that a cojump is expected to occur every 11 days. Cojumps are an
important feature of this market.
Naturally, the number of cojumps declines as the number of markets considered increases.
Nevertheless, the probability of cojump remains substantial even for the four dollar exchange
rates, with P (coj) = 0.0199 %; one expects a cojump in all four USD rates every 52 days. Figure
4 displays the full time series of cojumps for the different dollar exchange rate combinations.
This figure illustrates the frequent cojumps on these markets. Moreover, P (coj|jump) estimates
are also very high. The conditional probabilities show that when a jump occurs on any dollar
exchange rates, the chance of a cojump on all four USD exchange rates exceeds 10% (see the last
row of the second horizontal panel of Table 3). The maximum P (coj|jump) estimates are found
for USD/EUR - CHF/USD cojumps. When a jump occurs on one of these markets, a cojump
occurs on both with probability above 50%. We can conclude that cojumps are common on dollar
exchange rates, and that jumps on these markets are strongly dependent.
The third horizontal panel shows strong linkages between USD/EUR and several assets: Trea-
sury bonds (US), stock index futures (DJ) and EUR/JPY. The probability of cojumps on these
market pairs can be very high (see Table 3, third horizontal panel). For example, it reaches 0.045%
for USD/EUR - US cojumps. This implies an expected cojump every 23 days. Conditional cojump
probabilities can also be very high. For example, more than one in five (21.08%) Treasury bond
futures (US) jumps are also USD/EUR cojumps. And almost one in two (42.95%) EUR/JPY
jumps are USD/EUR - EUR/JPY cojumps.
The fourth horizontal panel of Table 3 shows statistics on cojumps on the four USD markets
plus another. Jumps across these five markets are much less likely; both P (coj) and P (coj|jump)
14
are relatively low, compared to other market combinations. The largest such P (coj) is 0.0091,
with the US.
At what time do cojumps usually occur? This question is of primary interest as one of our
goals is to understand whether macroeconomic releases cause cojumps. The arrival time for
macroeconomic news is almost always known in advance and is most often at 8:30 U.S. Eastern
Time (12.30 or 13.30 GMT), for the news considered in our study. Figure 5 shows histograms for
cojumps arrival, where we focus our attention on dollar exchange rates combinations. It displays
the count of cojumps per intra-day period, as in Figure 2 for jumps. The cojumps clearly occur
near the opening of the North American markets and the release of macro announcements. This
period also coincides with the overlap of the London - New York markets.
The next subsection describes our macroeconomic announcement data, before we go on to
analyze how (co)jumps relate to macro news.
3.3 Macroeconomic announcements
As is standard in the literature, we use the International Money Market Service data on surveyed
and realized macroeconomic fundamentals. Table 4 provides summary information on these data.
As in Balduzzi, Elton, and Green (2001) or Andersen, Bollerslev, Diebold, and Vega (2003), we
standardize surprises to easily compare coefficients across surprises and series. The standardized
surprise for announcement i at time t is defined by Nit = Rit−Eit
σi, where Rit is the realization
of announcement i at time t, Eit is its survey expectation and σi its standard deviation. These
macro news are scheduled at a monthly frequency. Balduzzi, Elton, and Green (2001) have shown
that the expected value of macro news predicts the announcement in an approximately unbiased
manner.
4 Macroeconomic announcements, jumps and cojumps: em-
pirical analysis
In this section, we analyze the impact of U.S. macroeconomic announcements on (co)jumps.
We first describe the data before moving on to estimate limited dependent variable models for
(co)jumps. We drop from the analysis markets that open after news arrival, i.e. SP and ND
futures. Indeed, these markets open at 9.30 EST (see Table 1) while most announcements are
15
scheduled at 8.30 EST.
4.1 Descriptive analysis
4.1.1 The distribution of jumps conditional on macroeconomic announcement
Table 5 presents conditional jump moments for days without any news and days with at least one
announcement. We provide statistics for all jumps in absolute value, as well as for positive and
negative jumps (with significance level α = 0.0001). The provided descriptive statistics are the
number of observations, jump probabilities, and the first two moments.
Every one of the assets displays a higher proportion of jumps on U.S. announcement days. This
suggests that announcements indeed create jumps. Under the null that jump probabilities are equal
in the announcement sample and in the non-announcement sample, the difference between the
probabilities in the two samples follows a normal distribution with mean zero and variance equal
to Pnews(1−Pnews)Nnews
+ Pnonews(1−Pnonews)Nnonews
, where Pnews (Pnonews) denotes the jump probability in the
announcement (non-announcement) sample, and Nnews (Nnonews) the number of observations in
the announcement (non-announcement) sample. This simple test of proportions equality rejects
the null of equal means, for most markets. The mean absolute value of jumps on announcement
days is significantly larger than jumps on non-announcement days for all the USD exchange rates,
all the futures markets, the JPY/EUR, the CHF/JPY and (at the 10 percent level) the XAU. Both
positive and negative jumps are often significantly more frequent in the announcement sample,
although the tests sometimes fail to reject because of lower power with fewer observations (Table
5). To sum up, jumps are more frequent on announcement days.
Are jump means different on announcement days? A simple test of the null of no difference
between jump means in the news and the no-news samples reveals different mean jump sizes in
four cases: US, JPY/USD, CHF/USD and CHF/JPY (see means in Table 5). The signs of the
differences are inconsistent, however. In two cases, absolute jumps are larger on announcement
days and in two cases they are smaller (Table 5). There is no evidence that jumps are larger on
announcement days.
We observed in Table 2 that jump USD depreciations were more frequent than jump USD
appreciations. Table 5 confirms this phenomenon: jump USD depreciations are more numerous
than jump USD appreciations on announcement days. Moreover, there are more positive jumps
in U.S. bond futures prices than negative ones (63 positive against 43 negative jumps), suggesting
16
some asymmetry in reactions to news. As positive jumps indicate rises in bond prices—a large
fall in yields—it appears that bond prices could be more sensitive to negative news about long
run economic activity or inflation.
In the next section, we investigate how macro news releases match jumps, and what types of
releases are most influential.
4.1.2 Matching jumps and macroeconomic announcement
Do jumps on financial markets closely match announcements? What sorts of news are most likely
to produce discontinuities? This subsection answers these questions.
Figures 6 and 7 present time histograms of jump occurrences on days without and with an-
nouncements, respectively. Jumps tend to cluster around announcement times on announcement
days, on most markets. Moreover, these figures show that, though jumps are more concentrated
around announcement time on news days, many jumps occur before 12.30 GMT or 13.30 GMT on
these days. This illustrates the necessity to study intraday data to understand what causes jumps
and avoid spuriously associating jumps with surprises.
Let us analyze the jump-announcement relationship in greater detail. The upper panel of Table
6 shows how announcements match jumps, while the lower panel details results across announce-
ments. We report in the upper panel the number of sample days (# days) and observations (#
obs.), the number of jumps and announcement days (# jumps and # news days), the count of
jumps matching announcements (# Jump-news match, where we count a match if a jump occurs
within one hour after the announcement), the probability of a news (P (news)), the probability of a
jump given a news (P (jump|news)), the probability of a news given a jump (P (news|jump)), and
finally the probability of observing a day where news and jumps match exactly (P (jump, news)).
When a generic announcement occurs, there is a 10.85% chance of a USD/EUR jump (see Table
6, upper panel, P (jump|news)). In general, the propensity of news to cause jumps is highest for
bond futures, USD exchange rates and XAU series where between 6% and 11% of announcements
generate a jump in prices. This ratio is much lower on non-dollar exchange rates (between 1.04%
and 3.28%) and DJ futures (0.75 %). The higher probability of jumps, conditional on news, for
the USD exchange rates, U.S. bonds and XAU seems sensible. Non-dollar exchange rates surely
respond less to U.S. announcements than dollar exchange rates. And the stock index futures
markets are not open during times of announcements. The high probability that news will induce
jumps in the bond market is also unsurprising given that researchers have long found Treasury
17
markets to be sensitive to macro news announcements (Ederington and Lee, 1993; Fleming and
Remolona, 1997; 1999).
How many jumps are caused by news? If a high proportion of jumps are caused by news, then
P (news|jump) will be high compared to P (news). In fact, it appears that news causes many
jumps, at least on some markets. The probability of an announcement, conditional on a jump,
can reach 48.19%, for bond futures (see Table 6, upper panel, P (news|jump)). This is relatively
high compared to the unconditional news probability on the bond market, which is equal to 1.15%
(Table 6, upper panel, P (news)). The row labeled P (news|jump), in the upper panel of Table
6, suggests that announcements create about 15 % to 20% of USD jumps, roughly 4% to 13% of
non-dollar exchange rate jumps and 9.91% of XAU jumps. The unconditional probability of a
news is about 0.3% for most markets.
What news announcements are the most likely to create surprises that lead to jumps? The
second horizontal panel of Table 6 decomposes results per news. It shows that the employment
report (nonfarm payroll employment and unemployment) and trade balance news are outstanding
in terms of jump association. The employment report is particulary important for DJ, US and
USD exchange rates. The trade balance report is important for exchange rates. For example, as
much as one payroll news in four (27.67%) and one trade balance news in five (20.28%) cause
jumps on the USD/EUR market (see P (jump|news)). The proportion of jumps associated with
these news is also relatively high. For example, we see in Table 6 (lower panel, P (news|jump))
that 33.57% of U.S. bond jumps are associated with payroll news. Price level (PPI, CPI) surprises
are important for bonds and USD exchange rates. The probability of a jump in the bond market
(US) conditional on a CPI news release, is 10.64% and the probability of news release, conditional
on a jump in bond futures is 8.82 %. The probability of a jump on the CHF/USD market, given
a durable goods announcement, is 6.82%.
The relative response of foreign exchange and bond markets to PPI and CPI shocks is consistent
with standard intuition about how (non)tradeables inflation should influence those markets. Jumps
in foreign exchange markets appear to respond better to PPI announcements, while jumps in
bond prices appear to respond more strongly to CPI news. This is sensible because exchange
rates should be more sensitive to tradeable goods prices—which the PPI better reflects—while the
bond market should respond to a broader price index, such as the CPI. The fact that cross-rates
are more sensitive to PPI shocks (reflecting international tradeables prices) also supports this
explanation.
18
The next subsection describes how cojumps match announcements.
4.1.3 Cojumps and macroeconomic announcements
The last column of Table 3 provides insights into cojump dynamics with respect to news arrival.
Our cojump indicator equals one when jumps occur simultaneously on different markets. So
working at a 15-minute frequency, we very precisely estimate cojump timing. Many cojumps
occur right after news arrival. For example, 67 of the 243 cojumps found on the USD/EUR -
USD/GBP markets match exactly news arrival (Table 3, # coj. matching news).
Moreover, the greater the number of market considered, the greater the proportion of cojumps
associated with news. Indeed, about half of the cojumps detected on the four dollar exchange
rates markets match perfectly news arrival. Besides cojumps on dollar exchange rates markets,
the combinations of markets where the probability of a cojump is relatively high are USD/EUR
- US, USD/EUR - XAU, and USD/EUR - EUR/JPY, where we detect 35, 34, and 134 cojumps,
respectively (see Table 3, # coj.). Again, many of these cojumps exactly match news arrival.
The proportion of cojumps matching exactly news is about 2/3, 1/3 and 1/5 of all cojumps on
USD/EUR - US, USD/EUR - XAU, and USD/EUR - EUR/JPY, respectively. For example,
USD/EUR - US had 35 cojumps (# coj.), of which 23 (# coj. matching news) exactly matched
news releases.
This descriptive subsection has characterized how (co)jumps relate to a set of macroeconomic
announcements. There are more jumps on days of macro announcements. Moreover, on some
markets, we detect asymmetry between positive and negative jumps on announcement days, sug-
gesting that news might have asymmetric effects. Matching news and jumps closely, we find
that between 0.75% and 10.85% of announcements create jumps (P (jump|news)), while between
5.79% (CHF/EUR) and 48.19% (US) of jumps match perfectly announcements (P (news|jump)).
Employment reports, trade balance releases and price level news are most likely to create jumps.
Finally, macro announcements appear to produce many of the cojumps.
It is necessary, however, to model (co)jumps formally so that proper inference can be made
about the link between (co)jumps and macro surprises. The next and final subsection models the
effects of surprises on the absolute value of jumps and on the probability of cojumps.
19
4.2 Modeling jumps and cojumps in Tobit-probit framework
In this subsection, we use Tobit and probit models to formally study the link between (co)jumps
and macro news. We focus on the series where (co)jumps are the most frequent, and where the
link with macro news is likely to be strongest. For jumps, the regression analysis includes dollar
exchange rates, XAU, U.S. T-bonds and Dow Jones futures. For cojumps, we focus on dollar
exchange rates.
4.2.1 Modeling jumps to assess the impact of macro announcements
We estimate the impact of macroeconomic announcements on jumps with a Tobit model (Table
7) to estimate the determinants of absolute jumps, which have a limited distribution.
|J∗t+j∆| = xt+j∆ + εt+j∆, (12)
xt+j∆ = µ + αt+j∆ + µt+j∆ + ξt+j∆,
|Jt+j∆| =
|J∗t+j∆| if |J∗t+j∆| > 0,
c if |J∗t+j∆| ≤ 0
where εt+j∆|xt+j∆ is N(0, σ20). The time index is denoted as before and refers to high frequency
points in time: t + j∆, where ∆ is the sampling interval, t refers to days, while j is an integer.
|Jt+j∆| represents significant jumps in absolute value, as defined by the Lee and Mykland (2006)
technique (see Section 2), while |J∗t+j∆| is its latent counterpart. αt+j∆ and µt+j∆ are defined as
linear combinations of day-of-the-week dummies and U.S. announcements, respectively:
αt+j∆ = α1TUESDAYt+j∆ +α2WEDNESDAYt+j∆ +α3THURSDAYt+j∆ +α4FRIDAYt+j∆,
(13)
where TUESDAYt+j∆, WEDNESDAYt+j∆, THURSDAYt+j∆ and FRIDAYt+j∆, are day-of-
the-week dummies, α1 to α4 are parameters to estimate and µt+j∆ describes the impact of U.S.
20
news.15
µt+j∆ =β1CPIt+j∆ + β2PPIt+j∆ + β3TRADEBALt+j∆ + β4DURABLEt+j∆ (14)
β5LEADINGIt+j∆ + β6HOUSINGt+j∆ + β7NFPAY ROLt+j∆,
where β’s are parameters to be estimated and the explanatory variables are the standardized
surprises magnitudes.16
We have tested a specification for µt+j∆ that permits surprises to influence jumps asymmetri-
cally. That is, where positive and negative surprises enter the equation with separate coefficients.
To evaluate whether surprises did influence jumps asymmetrically, we performed simple Wald tests
for the equality of the parameters of positive and negative surprises and were usually unable to
reject symmetry. For this reason, we only report results for µt+j∆ containing surprises in absolute
value, which enforces a symmetric response to positive and negative shocks. Because a coefficient
is unidentified unless there is a non-zero value for the regressor that is coincident with a jump,
only regressors that have at least one contemporaneous match with the dependent variable are
included in the estimations.
All models are estimated at an intra-day level. This raises some issues due to the nature of the
data in question. First of all, the huge number of observations and the high level of censoring of
the jump series imposes substantial computational demands in maximum likelihood estimation.
To conserve memory to permit maximization of the likelihood function, we reduce the sampling
frequency (∆) to 30 minutes. The second issue is that, as shown in Figure 2, intraday jumps
may have a seasonal component, separate from effects caused by announcements. To control for
potential impact of volatility seasonal components on jumps, we include regressors based on a
flexible fourier form that captures seasonality. That is, we include
ξt+j∆ = γ1trendt+j∆ + γ2trend2t+j∆ +
p∑
i=1
(γ2+i cos κi(t+j∆) + γ2+p+i sin κi(t+j∆)), (15)
where trend is a trend component across intra-day periods, κi(t+j∆) = 2π∆× i× trendt+j∆, and
15In a previous version of the paper, we have tested the effect of some European announcements on RV and its
continuous and jump components, using BNS statistics. Some news were found to affect the continuous component
of realized volatility but not jumps. Moreover, we have also tested a specification accounting for business cycles,
allowing for different impact of news on recession times compared to expansions. Probably given the small recession
period of the sample, we could not find any model improvement by including interaction terms between macro news
and a dummy indicating recession.16Export-import and unemployment news are not included in the regressors set because they are highly correlated
with trade balance and non-farm payroll news, respectively.
21
p is fixed at a conservative level of 4 or 5 terms (depending on the series), such that the fitted
seasonal component follows closely the intra-day seasonality pattern. Except for the DJ series,
this seasonal component significantly improves the likelihood of the models.
Table 7 (upper panel) presents estimation results for the impact of U.S. macro news on the
retained series. We find that, as reported by other studies in the context of news impact on returns
or volatility, payroll and trade balance announcements strongly predict jumps in financial markets,
particularly on foreign exchange markets. The remainder of this Section details the results by asset
type.
Exchange Rates Table 7 shows that some announcements affect jumps in all dollar ex-
change rate series. Indeed, absolute PPI (but not CPI) surprises have a significant positive effects
on foreign exchange jumps. Payroll and trade balance announcements both produce consistent
and important effects. The estimated coefficients for these surprises are highly significant every-
where. Durable good orders are significant on two exchange rate markets markets (USD/EUR
and CHF/USD).
XAU The determinants of XAU jumps are similar to those of exchange rates. Unlike for
some exchange rate markets, durables surprises are insignificant in the model for XAU, while
housing news have a significant—but perverse—effect. That is, large shocks to housing starts
actually reduce the predicted jumps in the gold market. But similarly to exchange rate markets,
PPI (and not CPI), payroll and trade balance news are significant predictors in the tobit model
for XAU jumps.
U.S. T-bonds futures The U.S. bonds market is usually thought as being very sensitive to
public news due to the nature of bond pricing. Announcements do cause jumps, to a statistically
significant degree. CPI and payroll surprises are significant. The coeffcient on PPI is much smaller
than that on CPI shocks and only marginally significant. Trade balance news are also significant,
but are wrongly signed, however. That is, a surprise announcement of a larger trade deficit in
absolute value significantly reduces jumps in the bond market.
Dow Jones futures The only announcement that is identified in the Dow-Jones futures
data is the payroll announcement. These payroll surprise shocks significantly explain size and
occurrence jumps in 30-minute data.
22
We note that the index of leading indicators is the only variable that never produces statistically
significant effects. This is not surprising as market participants can predict this index very well
from public information, prior to its release.
Finally, we report the McKelvey-Zavoina R2, that provides an estimate of the fitted latent
variable variance over the total variance. We obtain values between 6% and 17%, while the U.S.
bond futures model estimation yields a surprising 99%. This is consistent with the fact that most
of the jumps occur at the same time on this market. Jumps are indeed concentrated at 8.30
EST (see Figure 2). The strong ability of macro announcements to predict jumps in bond prices
is consistent with Fleming and Remolona (1997, 1999). Thus, it appears that macro surprises
together with regressors capturing seasonality allow to explain a great deal of variation in the
latent variable.
4.2.2 Modeling cojumps
Table 7 (lower panel) presents evidence on the link between macro news and cojumps with a
probit model. We use probit estimation with a qualitative indicator for cojumps because there is
no unambiguous way to attach a single magnitude to cojumps.
COJ∗t+j∆ = xt+j∆ + εt+j∆, (16)
xt+j∆ = µ + αt+j∆ + µt+j∆ + ξt+j∆,
COJt+j∆ =
1 if COJ∗t+j∆ > 0
0 if COJ∗t+j∆ ≤ 0,
where εt+j∆ is NID(0, 1). COJt+j∆ is the cojump indicator (see Equation 11), while COJ∗t+j∆ is
the associated latent variable. The remaining variables are defined as above, in the Tobit model:
αt+j∆ controls weekly seasonality; µt+j∆ includes macro surprises in absolute value; ξt+j∆ controls
for intradaily seasonality.
The seasonal component significantly improves the models’ likelihood, as it does for the Tobit
models. Moreover, we also tested for the presence of asymmetric response of markets in terms of
cojumps, specifying µt+j∆ such that surprises influence jumps asymmetrically (as explained for
the Tobit models). We could not find evidence of asymmetry, as in Tobit models. Consequently,
only results for surprises in absolute value are presented in Table 7.
23
Payroll and trade balance news produce the most significant effects. Across all combinations of
two dollar exchange rates, these news announcements always have significant impacts on cojumps.
While PPI news are significant at the two-sided 5% level in all exchange rates’ Tobit models, they
seem to have slightly less significant effects in probit models for pairs of exchange rate cojumps
(significance is found at the two-sided 10% level, on most market combinations). On the other
hand, they are much more important and consistent determinants of exchange rate cojumps than
shocks to CPI.
We obtain McFadden R2s of 14% to 27 % for the exchange rate cojumping variables. U.S.
announcements explain a substantial portion of exchange rate cojumps.
5 Conclusion
This paper has extended the previous literature studying jumps and the reactions of financial
markets to macroeconomic announcements in several ways. We apply the Lee and Mykland (2006)
statistic to characterize the timing and size of intraday jumps in a variety of markets, USD and
cross exchange rates, U.S. Treasury bond futures, U.S. equity futures and gold futures. Because
we can (almost) exactly determine jump times, we can more precisely associate them with macro
announcements. Precise timing also permits us to characterize the propensity of “cojumps”—
simultaneous jumps on multiple markets—and their association with macro announcements.
We first informally describe the data, finding that jumps are more frequent on announcement
days but that there is no evidence that jumps are consistently larger on announcement days.
Some markets (e.g. the bond market) display evidence of asymmetry in jump frequency. There
are more negative bond jumps than positive bond jumps. A precisely comparison of the timing of
announcements and jumps indicates that announcements create about 15% to 20% of USD jumps,
roughly 4% to 13% of non-dollar exchange rate jumps and 9.91% of XAU jumps.
When we compare the probabilities of jumps, conditional on macro surprises, we find that
jumps and cojumps in foreign exchange markets appear to respond better to PPI announcements,
while jumps in bond prices appear to respond more strongly to CPI news. This is consistent
with foreign exchange markets responding more strongly to tradeables inflation (better proxied
by PPI) and bond markets should react more strongly to overall inflation (better proxied by the
CPI). Consistent with this, cross-exchange rates react to PPI, which better reflects international
commodity prices, but not CPI.
24
We follow our data description by estimating Tobit models of jumps and probit models of
cojumps. Because the data generally rejected formal tests of asymmetry in either Tobit or probit
models of jump reaction to news (that is, negative suprises are usually no more or less likely to
produce cojumps than are positive surprises), we report the impact of absolute value surprises on
(co)jumps. Of all the surprises that we investigate, payroll and trade balance news consistently
significantly create jumps and cojumps. Price level shocks and surprises to durable goods orders
also often produce jumps. The index of leading indicators and housing starts do not significantly
explain jumps.
25
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29
Table 1: Description of the raw original series used in the study
Asset Source Freq Trading Hours Period available
NASDAQ 100 Futures (ND) CME 5-min 9.30-16.15 EST 07/01/1998 - 01/22/2005
S&P 500 Futures (SP) CME 5-min 9.30-16.15 EST 01/02/1986 - 07/22/2005
US Treasury bonds (US) CBOT 5-min 8.20-15.00 EST 01/04/1993 - 11/29/2004
Dow Jones Futures (DJ) CBOT 5-min 8.20-16.15 EST 06/11/1998 - 07/22/2005
USD/EUR O&A 5-min 24 hours a day 01/02/1987 - 10/01/2004
USD/GBP O&A 5-min 24 hours a day 02/01/1986 - 10/01/2004
JPY/USD O&A 5-min 24 hours a day 06/26/1986 - 10/01/2004
CHF/USD O&A 5-min 24 hours a day 02/02/1986 - 09/30/2004
Gold (XAU) O&A 5-min 24 hours a day 02/03/1986 - 09/07/2001
30
Tab
le2:
Jum
pses
tim
ated
usin
gLee
-Myk
land
test
stat
isti
cD
JN
DSP
US
USD
/EU
RU
SD
/G
BP
JPY
/U
SD
CH
F/U
SD
EU
R/C
HF
EU
R/G
BP
EU
R/JPY
GBP/C
HF
GBP/JPY
JPY
/C
HF
XA
U
#obs.
56096
46602
130572
78705
418464
435648
429120
446688
420384
418080
419232
435552
426432
429120
373728
#days
1753
1726
4836
2915
4359
4538
4470
4653
4379
4355
4367
4537
4442
4470
3893
Jum
pday
(day
wit
hat
least
one
jum
p)
frequency
#ju
mp
days
25
12
82
155
569
502
467
574
188
217
282
210
260
247
858
P(j
um
pd
ay)
(%)
1.4
30.7
01.7
05.3
213.0
511.0
610.4
512.3
44.2
94.9
86.4
64.6
35.8
55.5
322.0
4
E(#
ju
mp|j
um
pd
ay)
1.0
41.0
01.1
61.0
71.2
01.2
01.1
81.2
11.2
91.1
61.1
11.1
41.1
31.1
61.3
6
All
jum
ps
(abso
lute
valu
e)
#ju
mps
26
12
95
166
682
601
551
695
242
251
312
239
294
286
1171
P(j
um
p)
(%)
0.0
463
0.0
257
0.0
728
0.2
109
0.1
630
0.1
380
0.1
284
0.1
556
0.0
576
0.0
600
0.0
744
0.0
549
0.0
689
0.0
666
0.3
133
E(|
ju
mp
siz
e||
ju
mp)
1.3
72.9
81.6
20.7
40.5
20.4
60.5
40.5
20.4
10.5
10.6
10.5
10.6
30.6
20.5
5√
Va
r(|
ju
mp
siz
e||
ju
mp)
0.8
42.2
71.7
40.3
20.2
70.2
20.3
20.2
20.2
30.2
80.3
40.2
10.3
30.2
90.5
0
Posi
tive
jum
ps
#ju
mps>
013
624
82
378
319
250
308
107
124
151
111
143
149
576
P(j
um
p>
0)
(%)
0.0
232
0.0
129
0.0
184
0.1
042
0.0
903
0.0
732
0.0
583
0.0
690
0.0
255
0.0
297
0.0
360
0.0
255
0.0
335
0.0
347
0.1
541
E(j
um
ps
iz
e|j
um
p>
0)
1.5
93.2
72.2
30.7
50.5
20.4
50.5
60.5
20.4
20.5
10.6
20.5
30.6
30.6
10.5
3√
Va
r(j
um
ps
iz
e|j
um
p>
0)
1.0
52.9
52.6
80.3
00.2
70.2
10.3
30.2
40.2
90.2
90.3
80.2
30.3
50.2
90.4
8
Negati
ve
jum
ps
#ju
mps<
013
671
84
304
282
301
387
135
127
161
128
151
137
595
P(j
um
p<
0)
(%)
0.0
232
0.0
129
0.0
544
0.1
067
0.0
726
0.0
647
0.0
701
0.0
866
0.0
321
0.0
304
0.0
384
0.0
294
0.0
354
0.0
319
0.1
592
E(j
um
ps
iz
e|j
um
p<
0)
-1.1
4-2
.68
-1.4
1-0
.72
-0.5
3-0
.47
-0.5
3-0
.52
-0.3
9-0
.51
-0.6
0-0
.50
-0.6
3-0
.64
-0.5
7√
Va
r(j
um
ps
iz
e|j
um
p<
0)
0.4
61.2
11.2
00.3
40.2
70.2
40.3
00.2
10.1
70.2
60.3
00.1
90.3
10.3
00.5
2
Note
:T
he
table
dis
pla
ys,
from
top
tobott
om
the
num
ber
of
sam
ple
poin
ts(#
obs
.)and
sam
ple
days
(#d
ay
s),
the
tota
lnum
ber
of
jum
pdays
(#ju
mp
da
ys,i.e.
days
wit
hat
least
one
jum
p),
the
pro
bability
(in
%)
of
aju
mp
day
(P(j
um
pd
ay)
=100(#
ju
mp
da
ys
/#
da
ys))
,and
the
num
ber
ofju
mps
per
jum
pday
(E(#
ju
mp|j
um
pd
ay)
=#
ju
mp
/#
ju
mp
da
ys).
We
furt
her
giv
eth
eto
talnum
ber
jum
ps
(#ju
mp
s),
their
pro
port
ion
(in
%)
over
sam
ple
obse
rvati
ons
(P(j
um
p)
=100(#
ju
mp
s/#
obs
.)),
as
well
as
their
abso
lute
mean
size
and
standard
devia
tion
(E(|
ju
mp
siz
e||
ju
mp)
and
√V
ar(|
ju
mp
siz
e||
ju
mp))
.Fin
ally,th
ela
sttw
opanels
split
the
jum
ps
intw
ose
ts:
posi
tive
and
negati
ve
jum
ps.
Pro
port
ions
(P(j
um
p>
0)
and
P(j
um
p<
0))
,m
ean
(E(j
um
ps
iz
e|j
um
p>
0)
and
E(j
um
ps
iz
e|j
um
p<
0)
)and
std.
dev.
(√V
ar(j
um
ps
iz
e|j
um
p>
0)
and
√V
ar(j
um
ps
iz
e|j
um
p<
0))
are
report
ed,
as
for
the
full
set
ofju
mps
inabso
lute
valu
e.
The
chose
nsi
gnific
ance
levelfo
rju
mps
est
imati
on
isα
=0
.0001.
The
sam
pling
frequency
is15
min
ute
.
31
Tab
le3:
Coj
umps
ondi
ffere
ntm
arke
tco
mbi
nati
ons
#obs.
#coj.
P(c
oj)
(%)
P(c
oj)
(%)
P(c
oj|j
um
p)
(%)
#coj.
ifin
dep.
12
34
5m
atc
hin
gnew
s
ND
-D
J46548
40.0
086
0.0
000
33.3
315.3
80
ND
-SP
46575
50.0
107
0.0
000
41.6
75.2
60
ND
-U
S34122
20.0
059
0.0
001
16.6
71.2
00
DJ
-SP
47142
60.0
127
0.0
000
23.0
86.3
20
DJ
-U
S42444
80.0
188
0.0
001
30.7
74.8
23
SP
-U
S64108
70.0
109
0.0
002
7.3
74.2
20
ND
-D
J-
SP
46521
40.0
086
0.0
000
33.3
315.3
84.2
10
ND
-D
J-
US
34078
20.0
059
0.0
000
16.6
77.6
91.2
00
DJ
-SP
-U
S34584
30.0
087
0.0
000
11.5
43.1
61.8
10
ND
-SP
-U
S34122
20.0
059
0.0
000
16.6
72.1
11.2
00
ND
-D
J-
SP
-U
S34078
20.0
059
0.0
000
16.6
77.6
92.1
11.2
00
USD
/EU
R-
USD
/G
BP
418080
243
0.0
581
0.0
002
35.6
340.4
367
USD
/EU
R-
JPY
/U
SD
419232
134
0.0
320
0.0
002
19.6
524.3
255
USD
/EU
R-
CH
F/U
SD
420384
391
0.0
930
0.0
003
57.3
356.2
694
USD
/G
BP
-JPY
/U
SD
426432
95
0.0
223
0.0
002
15.8
117.2
444
USD
/G
BP
-C
HF/U
SD
435552
220
0.0
505
0.0
002
36.6
131.6
568
JPY
/U
SD
-C
HF/U
SD
429120
130
0.0
303
0.0
002
23.5
918.7
155
USD
/EU
R-
USD
/G
BP
-JPY
/U
SD
417312
88
0.0
211
0.0
000
12.9
014.6
415.9
743
USD
/G
BP
-JPY
/U
SD
-C
HF/U
SD
426432
85
0.0
199
0.0
000
14.1
415.4
312.2
344
USD
/EU
R-
USD
/G
BP
-C
HF/U
SD
418080
193
0.0
462
0.0
000
28.3
032.1
127.7
764
USD
/EU
R-
JPY
/U
SD
-C
HF/U
SD
419232
114
0.0
272
0.0
000
16.7
220.6
916.4
053
USD
/EU
R-
USD
/G
BP
-JPY
/U
SD
-C
HF/U
SD
417312
83
0.0
199
0.0
000
12.1
713.8
115.0
611.9
443
USD
/EU
R-
US
77517
35
0.0
452
0.0
003
5.1
321.0
823
USD
/EU
R-
ND
41067
10.0
024
0.0
000
0.1
58.3
30
USD
/EU
R-
SP
117180
30.0
026
0.0
001
0.4
43.1
60
USD
/EU
R-
DJ
49536
80.0
161
0.0
001
1.1
730.7
73
USD
/EU
R-
XA
U347328
34
0.0
098
0.0
005
4.9
92.9
013
USD
/EU
R-
EU
R/JPY
419232
134
0.0
320
0.0
001
19.6
542.9
530
USD
/EU
R-
USD
/G
BP
-JPY
/U
SD
-C
HF/U
SD
-X
AU
344352
90.0
026
0.0
000
1.3
21.5
01.6
31.2
90.7
76
USD
/EU
R-
USD
/G
BP
-JPY
/U
SD
-C
HF/U
SD
-N
D40905
00.0
000
0.0
000
0.0
00.0
00.0
00.0
00.0
00
USD
/EU
R-
USD
/G
BP
-JPY
/U
SD
-C
HF/U
SD
-SP
116370
00.0
000
0.0
000
0.0
00.0
00.0
00.0
00.0
00
USD
/EU
R-
USD
/G
BP
-JPY
/U
SD
-C
HF/U
SD
-U
S77301
70.0
091
0.0
000
1.0
31.1
61.2
71.0
14.2
26
Note
:C
oju
mps
are
defined
as
an
indic
ato
rvari
able
equal
toone
when
signific
ant
jum
ps
(at
α=
0.0
001
and
a15-m
inute
frequency)
occur
exactl
yat
the
sam
eti
me
on
diffe
rent
mark
ets
.T
he
table
dis
pla
ys,
the
num
ber
of
obse
rvati
ons,
the
num
ber
of
coju
mps,
the
coju
mp
pro
bability
(P(c
oj),
in%
),th
ecoju
mp
pro
bability
under
independence
of
the
jum
ppro
cess
es
(pro
duct
of
jum
ppro
port
ions,
in%
).C
olu
mns
6to
10
(P(c
oj|j
um
p)
in%
,num
bere
d1
to5)
report
the
pro
bability
of
acoju
mp
on
the
mark
ets
giv
en
on
aline
giv
en
aju
mp
on
am
ark
et
giv
en
by
the
num
ber
ofth
ecolu
mn
(1to
5).
This
num
ber
refe
rsto
the
ord
er
ofth
em
ark
ets
inw
hic
hth
ey
appear
on
the
firs
tcolu
mn.
The
last
colu
mn
report
sth
enum
ber
ofcoju
mps
matc
hin
gexactl
ynew
sarr
ival.
32
Table 4: Scheduled macroeconomic announcement
Announcement Variable Name Range Unit Day of the week
Labor market
Employees on Payrolls NFPAYROL 1985-2005 change in 1000 Friday
Prices
Producer Price Index PPI 1980-2005 %change Thursday or Friday
Consumer Price Index CPI 1980-2005 %change Tuesday to Friday
Business cycle conditions
Durable Good Orders DURABLE 1980-2005 %change Tuesday to Friday
Housing Starts HOUSING 1980-2005 millions Tuesday to Friday
Leading Indicators LEADINGI 1980-2005 %change Monday to Friday
Trade Balance TRADEBAL 1980-2005 $ billion Tuesday to Friday
U.S. Exports USX 1988-2005 $ billion Tuesday to Friday
U.S. Imports USI 1988-2005 $ billion Tuesday to Friday
33
Tab
le5:
Jum
ppr
obab
iliti
esan
dm
omen
tsco
ndit
iona
lon
anno
unce
men
ts
No
announcem
ent
days
Announcem
ent
days
No
announcem
ent
days
Announcem
ent
days
Jum
ps
(abs.
val)
Jum
ps>
0Jum
ps<
0Jum
ps
(abs.
val)
Jum
ps>
0Jum
ps<
0Jum
ps
(abs.
val)
Jum
ps>
0Jum
ps<
0Jum
ps
(abs.
val)
Jum
ps>
0Jum
ps<
0
Dow
-Jones
CH
F/EU
R
P(j
um
p)
(%)
0.0
307
0.0
154
0.0
154
0.0
822**
0.0
411
0.0
411
0.0
556
0.0
254
0.0
302
0.0
621
0.0
256
0.0
365
#ju
mps
12
66
14
77
162
74
88
80
33
47
Mean
1.3
01.5
2-1
.09
1.4
21.6
6-1
.19
0.4
20.4
4-0
.40
0.3
80.4
0-0
.38
St.
Dev.
0.9
31.1
90.4
60.7
50.9
10.4
50.2
60.3
30.1
90.1
60.1
90.1
4
U.S
.T
-bonds
GBP/EU
R
P(j
um
p)
(%)
0.1
107
0.0
350
0.0
756
0.4
328
***
0.2
573***
0.1
756***
0.0
576
0.0
269
0.0
307
0.0
656
0.0
359
0.0
297
#ju
mps
60
19
41
106
63
43
167
78
89
84
46
38
Mean
0.6
50.6
6-0
.65
0.7
8***
0.7
7*
-0.7
9**
0.5
10.5
3-0
.50
0.5
00.4
8-0
.54
St.
Dev.
0.2
00.2
00.2
00.3
60.3
20.4
20.2
40.2
90.2
00.3
40.3
00.3
7
USD
/EU
RJPY
/EU
R
P(j
um
p)
(%)
0.1
240
0.0
641
0.0
600
0.2
511***
0.1
497***
0.1
014***
0.0
657
0.0
303
0.0
354
0.0
941***
0.0
490***
0.0
451
#ju
mps
360
186
174
322
192
130
191
88
103
121
63
58
Mean
0.5
10.5
1-0
.51
0.5
30.5
2-0
.56
0.6
30.6
5-0
.62
0.5
70.5
7-0
.56
St.
Dev.
0.2
70.2
90.2
50.2
60.2
40.2
90.3
80.4
50.3
20.2
60.2
50.2
6
USD
/G
BP
CH
F/G
BP
P(j
um
p)
(%)
0.1
128
0.0
605
0.0
523
0.1
950***
0.1
020
0.0
930***
0.0
526
0.0
251
0.0
275
0.0
600
0.0
262
0.0
337
#ju
mps
341
183
158
260
136
124
159
76
83
80
35
45
Mean
0.4
50.4
4-0
.45
0.4
80.4
6-0
.49
0.5
20.5
2-0
.52
0.5
00.5
4-0
.48
St.
Dev.
0.1
90.1
80.1
90.2
60.2
40.2
80.1
80.1
80.1
80.2
50.3
10.1
9
JPY
/U
SD
JPY
/G
BP
P(j
um
p)
(%)
0.1
061
0.0
480
0.0
581
0.1
789***
0.0
815***
0.0
975***
0.0
648
0.0
321
0.0
328
0.0
783
0.0
368
0.0
415
#ju
mps
316
143
173
235
107
128
192
95
97
102
48
54
Mean
0.5
70.5
9-0
.55
0.5
1**
0.5
2*
-0.5
10.6
50.6
5-0
.65
0.6
10.6
1-0
.61
St.
Dev.
0.3
50.3
70.3
30.2
70.2
80.2
60.3
40.3
50.3
30.3
10.3
50.2
8
CH
F/U
SD
CH
F/JPY
P(j
um
p)
(%)
0.1
283
0.0
585
0.0
698
0.2
182***
0.0
929***
0.1
253***
0.0
571
0.0
299
0.0
272
0.0
883***
0.0
457**
0.0
426**
#ju
mps
399
182
217
296
126
170
170
89
81
116
60
56
Mean
0.4
90.4
9-0
.49
0.5
5***
0.5
6***
-0.5
5***
0.6
60.6
4-0
.68
0.5
7***
0.5
7*
-0.5
8**
St.
Dev.
0.2
10.2
30.1
90.2
40.2
40.2
30.3
30.3
10.3
40.2
20.2
30.2
0
XA
U
P(j
um
p)
(%)
0.3
027
0.1
500
0.1
527
0.3
373*
0.1
634
0.1
739
#ju
mps
785
389
396
386
187
199
Mean
0.5
50.5
2-0
.57
0.5
60.5
6-0
.56
St.
Dev.
0.5
40.5
20.5
60.4
00.3
90.4
1
Note
:Jum
ppro
port
ions(P
(ju
mp),
in%
)and
mom
ents
(mean
and
standard
devia
tion
ofju
mpsin
abso
lute
valu
e,posi
tive
and
negati
ve)fo
rdaysw
ithoutannouncem
entand
daysw
ith
atle
ast
one
announcem
ent.
The
num
ber
ofju
mps
(com
pute
dat
a15-m
inute
frequency
wit
ha
signific
ance
level
α=
0.0
001)
isals
ore
port
ed
(#ju
mps)
.Sta
rson
the
announcem
ent
sam
ple
means
and
pro
port
ions
indic
ate
wheth
er
they
are
stati
stic
ally
diffe
rent
from
those
inth
eno-a
nnouncem
ent
sam
ple
.O
ne,tw
oand
thre
est
ars
corr
esp
ond
tosi
gnific
ance
at
1%
,5%
,and
10%
level,
resp
ecti
vely
.
34
Tab
le6:
Jum
pan
dan
noun
cem
ent
prob
abili
ties
DJ
US
USD
/EU
RU
SD
/G
BP
JPY
/U
SD
CH
F/U
SD
XA
UC
HF/EU
RG
BP/EU
RJPY
/EU
RC
HF/G
BP
JPY
/G
BP
CH
F/JPY
Overall
result
s
#days
1753
2915
4359
4538
4470
4653
3893
4379
4355
4367
4537
4442
4470
#obs.
56096
78705
418464
435648
429120
446688
373728
420384
418080
419232
435552
426432
429120
#ju
mps
26
166
682
601
551
695
1171
242
251
312
239
294
286
#new
sdays
532
907
1336
1389
1368
1413
1192
1342
1333
1340
1389
1357
1368
#Jum
p-n
ew
sm
atc
h4
80
145
110
94
139
116
14
19
44
24
25
37
P(n
ew
s)
(%)
0.9
51.1
50.3
20.3
20.3
20.3
20.3
20.3
20.3
20.3
20.3
20.3
20.3
2
P(j
um
p|n
ew
s)
(%)
0.7
58.8
210.8
57.9
26.8
79.8
49.7
31.0
41.4
33.2
81.7
31.8
42.7
0
P(n
ew
s|j
um
p)
(%)
15.3
848.1
921.2
618.3
017.0
620.0
09.9
15.7
97.5
714.1
010.0
48.5
012.9
4
P(j
um
p,
ne
ws)
(%)
0.2
32.7
43.3
32.4
22.1
02.9
92.9
80.3
20.4
41.0
10.5
30.5
60.8
3
Result
sdetailed
per
announcem
ents
P(j
um
p|n
ew
s)
(%)
PPI
0.0
08.5
110.4
89.6
37.5
19.9
513.9
81.4
31.9
04.2
92.7
52.8
23.7
6
CPI
0.0
010.6
46.1
93.6
22.7
83.5
98.6
00.0
00.4
80.0
00.4
50.0
00.9
3
NFPAY
RO
L,U
NEM
PLO
Y3.5
733.5
727.6
720.1
814.6
223.6
413.0
41.9
24.8
38.2
13.6
72.8
47.5
5
DU
RA
BLE
0.0
02.8
87.2
51.8
54.2
56.8
25.9
51.4
40.4
91.9
30.4
60.9
51.4
2
LEA
DIN
GI
1.1
81.4
32.4
31.9
01.4
01.8
33.8
30.4
80.4
90.4
80.4
70.0
00.4
7
HO
USIN
G0.0
01.4
22.4
03.6
51.4
03.1
57.5
70.4
80.0
01.9
20.9
11.4
11.4
0
TR
AD
EBA
L,U
SI,
USX
0.0
00.7
020.2
814.2
916.8
219.8
216.2
22.3
62.3
76.6
04.1
55.1
64.2
1
P(n
ew
s|j
um
p)
(%)
PPI
0.0
07.2
33.2
33.4
92.9
03.1
72.2
21.2
41.5
92.8
82.5
12.0
42.8
0
CPI
0.0
09.0
41.9
11.3
31.0
91.1
51.3
70.0
00.4
00.0
00.4
20.0
00.7
0
NFPAY
RO
L,U
NEM
PLO
Y11.5
428.3
18.3
67.3
25.6
37.4
82.0
51.6
53.9
85.4
53.3
52.0
45.5
9
DU
RA
BLE
0.0
02.4
12.2
00.6
71.6
32.1
60.9
41.2
40.4
01.2
80.4
20.6
81.0
5
LEA
DIN
GI
3.8
51.2
00.7
30.6
70.5
40.5
80.6
00.4
10.4
00.3
20.4
20.0
00.3
5
HO
USIN
G0.0
01.2
00.7
31.3
30.5
41.0
11.2
00.4
10.0
01.2
80.8
41.0
21.0
5
TR
AD
EBA
L,U
SI,
USX
0.0
00.6
06.3
05.1
66.5
36.3
32.5
62.0
71.9
94.4
93.7
73.7
43.1
5
Note
:T
he
table
giv
es
the
overa
llm
atc
hin
gbetw
een
new
sand
jum
ps
com
pute
dat
a15-m
inute
frequency
wit
ha
signific
ance
level
α=
0.0
001
(upper
panel)
and
deta
iled
resu
lts
per
announcem
ent
(lower
panel)
.T
he
table
show
s,fr
om
top
tobott
om
,th
enum
ber
of
sam
ple
days
(#days)
,th
enum
ber
of
obse
rvati
ons
(#obs.
),th
enum
ber
of
jum
ps
and
the
num
ber
of
announcem
ent
days
(#ju
mps
and
#new
sdays)
,th
enum
ber
of
jum
ps
occurr
ing
wit
hin
one
hour
aft
er
new
sarr
ival(#
Jum
p-n
ew
sm
atc
h),
the
uncondit
ionalpro
bability
(in
%)
of
anew
s
(P(n
ew
s)
=100(#
new
sdays
/#
obs.
)),th
epro
bability
(in
%)
ofa
jum
pgiv
en
anew
s(P
(ju
mp|n
ew
s)
=100(#
Jum
p-n
ew
sm
atc
h/
#new
sdays)
),th
epro
bability
(in
%)
ofa
new
sgiv
en
a
jum
p(P
(ne
ws|j
um
p)
=100(#
Jum
p-n
ew
sm
atc
h/
#ju
mps)
),th
epro
bability
(in
%)
ofa
new
sand
aju
mp
(P(j
um
p,
ne
ws)
=100(#
Jum
p-n
ew
sm
atc
h/
#days)
).T
he
lower
paneldeta
ils
resu
lts
for
each
new
sand
dis
pla
ys
P(j
um
p|n
ew
s)
and
P(n
ew
s|j
um
p).
Note
that
labor
mark
et
new
s(N
FPAY
RO
Land
UN
EM
PLO
Y)
and
trade
rela
ted
new
s(T
RA
DEBA
L,U
SI,
USX
)are
pre
sente
dre
specti
vely
on
asi
ngle
line
because
they
are
part
ofa
single
report
.
35
Tab
le7:
Tob
itm
odel
sfo
rju
mps
and
prob
itm
odel
sfo
rco
jum
ps
Tobit
models
for
jum
ps
USD
/EU
RJPY
/U
SD
USD
/G
BP
CH
F/U
SD
XA
UU
SD
J
Est
.t-
stat.
Est
.t-
stat.
Est
.t-
stat.
Est
.t-
stat.
Est
.t-
stat.
Est
.t-
stat.
Est
.t-
stat.
VPPI
0.5
82.2
10.7
32.3
50.5
62.4
50.6
02.3
00.9
12.2
90.5
01.8
4-
-
VC
PI
0.4
71.0
50.8
21.7
90.3
30.6
80.6
21.5
10.7
21.4
01.3
54.0
0-
-
VN
FPAY
RO
L1.9
96.7
11.6
05.3
31.5
66.1
32.0
07.0
41.0
13.2
01.7
26.5
96.6
54.5
4
VD
UR
ABLE
1.0
34.7
40.5
61.7
20.4
41.3
90.7
72.4
8-0
.18
-0.6
8-0
.92
-0.9
5-
-
VLEA
DIN
GI
--
--
-4.4
8-1
.85
0.1
10.1
5-0
.70
-0.9
0-0
.71
-0.7
5-
-
VH
OU
SIN
G-0
.68
-0.9
1-
--
--
--2
.92
-2.0
9-1
.22
-1.1
9-
-
VT
RA
DEBA
L2.1
98.0
32.5
48.2
62.1
07.6
02.2
38.2
81.3
33.6
0-8
.86
-2.0
7-
-
Const
-12.2
0-1
2.8
5-5
.42
-2.4
6-7
.07
-15.3
3-7
.43
-9.8
1-1
9.0
7-7
.20
-777.7
9-2
05.0
2-1
6.1
7-1
.56
sigm
a2.0
630.7
72.2
413.5
41.9
030.6
62.1
230.9
32.4
219.6
12.0
514.2
66.8
19.6
1
VLLF
-2669.9
0-2
532.4
8-2
216.5
9-2
611.3
8-4
335.9
2-6
34.2
4-1
70.4
3
obs
210192
214560
217824
223344
186864
40810
28048
R2 M
Z0.1
20.0
60.1
30.1
10.1
70.9
90.0
8
Probit
models
for
coju
mps
USD
/EU
R-
USD
/G
BP
USD
/EU
R-
JPY
/U
SD
USD
/EU
R-
CH
F/U
SD
USD
/G
BP
-JPY
/U
SD
USD
/G
BP
-C
HF/U
SD
JPY
/U
SD
-C
HF/U
SD
Est
.t-
stat.
Est
.t-
stat.
Est
.t-
stat.
Est
.t-
stat.
Est
.t-
stat.
Est
.t-
stat.
VPPI
0.2
41.8
70.2
61.9
10.2
51.9
70.2
51.8
50.2
51.6
00.2
71.9
9
VC
PI
-0.8
0-1
.62
--
0.1
40.4
60.2
80.9
70.2
30.8
30.3
21.1
3
VN
FPAY
RO
L0.8
65.7
80.7
74.9
91.0
06.2
40.6
74.9
50.8
52.5
20.7
95.4
7
VD
UR
ABLE
0.2
91.8
10.3
32.1
70.0
90.4
20.2
21.1
00.1
40.6
20.2
61.3
7
VT
RA
DEBA
L1.2
08.0
71.2
68.6
01.1
48.1
01.2
78.6
01.1
33.7
61.2
58.6
0
Const
13.3
11.2
2-7
.90
-5.6
9-3
5.8
8-1
2.3
0-4
6.3
8-2
.98
52.0
71.1
6-1
7.6
3-3
.69
VLLF
-933.9
8-5
89.5
4-1
545.8
4-4
62.1
6-7
93.0
4-5
21.3
6
obs
208992
209568
210192
213216
217776
214560
McFadden
R2
0.2
00.2
10.1
40.2
70.2
20.2
2
Note
:The
upper
panelre
ports
Tobit
est
imate
s:|J∗ t+
j∆|=
µ+
αt+
j∆
+µ
t+
j∆
+ξ
t+
j∆
+ε
t+
j∆
,w
here|J
t+
j∆|=|J∗ t+
j∆|i
f|J∗ t+
j∆|
>0
and|J
t+
j∆|=
0if|J∗ t+
j∆|≤
0,
εt+
j∆|x
t+
j∆
isN
(0,
σ2 0),
and
the
sequence{J
t+
j∆
,x
t+
j∆}
isiid.|J
t+
j∆|re
pre
sents
signific
ant
jum
ps
as
defined
inth
eth
eore
ticalpart
.The
lower
panelre
ports
pro
bit
est
imate
s:
CO
J∗ t+
j∆
=µ
+α
t+
j∆
+µ
t+
j∆
+ξ
t+
j∆
+ε
t+
j∆
,
where
CO
Jt+
j∆
=1
ifC
OJ∗ t+
j∆
>0
and
CO
Jt+
j∆
=0
ifC
OJ∗ t+
j∆≤
0.
εt+
j∆
isN
ID
(0,1).
CO
Jt+
j∆
isth
ecoju
mp
indic
ato
r(s
ee
Equati
on
11).
Inbo
thTobit
and
pro
bit
models,
αt+
j∆
contr
ols
for
day
ofth
eweek
effects
(not
report
ed)
and
µt+
j∆
inclu
des
surp
rise
sconcern
ing
macro
announcem
ents
.For
each
seri
es,
we
regre
ssju
mps
inabso
lute
valu
e(c
oju
mp
indic
ato
rin
the
case
ofpro
bit
models
)on
surp
rise
sin
abso
lute
valu
e.
ξt+
j∆
contr
ols
for
intr
adaily
seaso
nality
(not
report
ed).
Est
imate
sand
robust
t-st
ati
stic
sare
report
ed
for
each
surp
rise
coeffic
ient,
the
const
ant
and
the
err
or
standard
devia
tion
sigm
afo
rTobit
models
.R
egre
ssors
wit
hno
conte
mpora
neous
matc
hw
ith
signific
ant
jum
ps
(coju
mp
indic
ato
rin
the
case
ofpro
bit
models
)are
exclu
ded
from
the
model.
We
furt
her
report
the
maxim
ized
log-lik
elihood
functi
on
valu
e(V
LLF),
the
num
ber
ofobse
rvati
ons
(Obs)
,as
well
as
agoodness
offit
measu
re,th
eM
cK
elv
ey-Z
avoin
aR
2(R
2 MZ
)fo
rTobit
models
,th
at
pro
vid
es
an
est
imate
ofth
efitt
ed
late
nt
vari
able
vari
ance
over
the
tota
lvari
ance,i.e.
Va
r(J∗ )
Va
r(J∗ )
+σ2
.For
pro
bit
models
,th
egoodness
offit
measu
reis
the
McFadden
R2.
36
Figure 1: Time series of significant jumps
-6
-4
-2
0
2
4
6
8
10
1998 1999 2000 2001 2002 2003 2004 2005 2006
Jum
ps
Intra-day periods
ND
-3
-2
-1
0
1
2
3
4
1998 1999 2000 2001 2002 2003 2004 2005 2006Ju
mps
Intra-day periods
DJ
-10
-5
0
5
10
15
1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006
Jum
ps
Intra-day periods
SP
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005
Jum
ps
Intra-day periods
US
-3
-2
-1
0
1
2
3
4
1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006
Jum
ps
Intra-day periods
USD/EUR
-3
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006
Jum
ps
Intra-day periods
USD/GBP
-4
-3
-2
-1
0
1
2
3
4
1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006
Jum
ps
Intra-day periods
JPY/USD
-1.5
-1
-0.5
0
0.5
1
1.5
2
1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006
Jum
ps
Intra-day periods
CHF/USD
-8
-6
-4
-2
0
2
4
6
8
1986 1988 1990 1992 1994 1996 1998 2000 2002
Jum
ps
Intra-day periods
XAU
Note: jumps estimated with Lee-Mykland statistic (Jt+j∆, as defined in Section 2). The chosen
significance level is α = 0.0001. The sampling frequency is 15 minute. The X-axis displays
intradaily periods over the whole sample, while the Y-axis displays returns (%) identified as
jumps, Jt+j∆.
37
Figure 2: Histograms of significant jump occurrences
0
0.5
1
1.5
2
09 10 11 12 13 14 15 16 17
Count of ju
mps
Intra-Day Periods over one day (EST)
ND
0
1
2
3
4
5
6
08 09 10 11 12 13 14 15 16 17C
ount of ju
mps
Intra-Day Periods over one day (EST)
DJ
0
2
4
6
8
10
12
09 10 11 12 13 14 15 16 17
Count of ju
mps
Intra-Day Periods over one day (EST)
SP
0
10
20
30
40
50
60
70
80
90
100
08 09 10 11 12 13 14 15
Count of ju
mps
Intra-Day Periods over one day (EST)
US
0
20
40
60
80
100
20 22 00 02 04 06 08 10 12 14 16 18 20 22
Count of ju
mps
Intra-Day Periods over one day (GMT)
USD/EUR
0
10
20
30
40
50
60
70
20 22 00 02 04 06 08 10 12 14 16 18 20 22
Count of ju
mps
Intra-Day Periods over one day (GMT)
USD/GBP
0
10
20
30
40
50
60
70
20 22 00 02 04 06 08 10 12 14 16 18 20 22
Count of ju
mps
Intra-Day Periods over one day (GMT)
JPY/USD
0
10
20
30
40
50
60
70
80
90
100
20 22 00 02 04 06 08 10 12 14 16 18 20 22
Count of ju
mps
Intra-Day Periods over one day (GMT)
CHF/USD
0
10
20
30
40
50
60
20 22 00 02 04 06 08 10 12 14 16 18 20 22
Count of ju
mps
Intra-Day Periods over one day (GMT)
XAU
Note: count of Lee-Mykland jumps per intradaily period, α = 0.0001, 15-min. frequency.
38
Figure 3: Scatter plot: mean jumps against jump frequency
0.50 0.75 1.00 1.25 1.50 1.75 2.00 2.25 2.50 2.75 3.00
0.1
0.2
0.3
Fre
quen
cy
All jumps in absolute value
XAU
U.S. Bonds Dow SP500 Nasdaq
Dollar Exchange rates
Non−dollar exchange rates
0.50 0.75 1.00 1.25 1.50 1.75 2.00 2.25 2.50 2.75 3.00 3.25
0.05
0.1
0.15
Fre
quen
cy XAU
NasdaqSP500DowU.S. Bonds
Dollar Exchange rates
Non−dollar exchange ratesPositive jumps
−2.6 −2.4 −2.2 −2.0 −1.8 −1.6 −1.4 −1.2 −1.0 −0.8 −0.6 −0.4
0.05
0.1
0.15
Jump mean
Fre
quen
cy
XAU
Nasdaq SP500 Dow U.S. Bonds
Dollar Exchange rates
Non−dollar exchange rates
Negative jumps
39
Figure 4: Time series of cojump indicator
1990 1995 2000 2005
0.5
1 EUR − GBP
coju
mps
1990 1995 2000 2005
0.5
1 EUR − JPY
coju
mps
1990 1995 2000 2005
0.5
1 EUR − CHF
coju
mps
1990 1995 2000 2005
0.5
1 GBP − JPY
coju
mps
1990 1995 2000 2005
0.5
1 GBP − CHF
coju
mps
1990 1995 2000 2005
0.5
1 JPY − CHF
coju
mps
1990 1995 2000 2005
0.5
1 EUR − GBP − JPY
coju
mps
1990 1995 2000 2005
0.5
1 GBP − JPY − CHF
coju
mps
1990 1995 2000 2005
0.5
1 EUR − GBP − CHF
coju
mps
1990 1995 2000 2005
0.5
1 EUR − JPY − CHF
coju
mps
1990 1995 2000 2005
0.5
1 EUR − GBP − JPY − CHF
Intra−day periods
coju
mps
Note: the graphs display the time series of cojump indicator for different exchange rates
combinations. The X-axis displays intra-day periods for the sample length.
40
Figure 5: Histogram of cojump occurrences
0
10
20
30
40
50
60
20 22 00 02 04 06 08 10 12 14 16 18 20 22
coun
t of c
ojum
ps
Intra-day periods
USD/EUR - USD/GBP
coj hist
0 5
10 15 20 25 30 35 40 45 50
20 22 00 02 04 06 08 10 12 14 16 18 20 22
coun
t of c
ojum
ps
Intra-day periods
USD/EUR - JPY/USD
0
10
20
30
40
50
60
70
80
20 22 00 02 04 06 08 10 12 14 16 18 20 22
coun
t of c
ojum
ps
Intra-day periods
USD/EUR - CHF/USD
0
5
10
15
20
25
30
35
40
20 22 00 02 04 06 08 10 12 14 16 18 20 22
coun
t of c
ojum
ps
Intra-day periods
USD/GBP - JPY/USD
0
10
20
30
40
50
60
20 22 00 02 04 06 08 10 12 14 16 18 20 22
coun
t of c
ojum
ps
Intra-day periods
USD/GBP - CHF/USD
0 5
10 15 20 25 30 35 40 45 50
20 22 00 02 04 06 08 10 12 14 16 18 20 22
coun
t of c
ojum
ps
Intra-day periods
JPY/USD - CHF/USD
0
5
10
15
20
25
30
35
40
20 22 00 02 04 06 08 10 12 14 16 18 20 22
coun
t of c
ojum
ps
Intra-day periods
USD/EUR - USD/GBP - JPY/USD
0
5
10
15
20
25
30
35
40
20 22 00 02 04 06 08 10 12 14 16 18 20 22
coun
t of c
ojum
ps
Intra-day periods
USD/GBP - JPY/USD - CHF/USD
0
10
20
30
40
50
60
20 22 00 02 04 06 08 10 12 14 16 18 20 22
coun
t of c
ojum
ps
Intra-day periods
USD/EUR - USD/GBP - CHF/USD
0
5
10
15
20
25
30
35
40
45
20 22 00 02 04 06 08 10 12 14 16 18 20 22
coun
t of c
ojum
ps
Intra-day periods
USD/EUR - JPY/USD - CHF/USD
0
5
10
15
20
25
30
35
40
20 22 00 02 04 06 08 10 12 14 16 18 20 22
coun
t of c
ojum
ps
Intra-day periods
USD/EUR - USD/GBP - JPY/USD - CHF/USD
Note: the graphs display histograms of cojump occurrences for different exchange rates
combinations. The X-axis displays intra-day periods over 24 hours in GMT time.
41
Figure 6: Histogram of jump occurrences on days without announcements
0
0.5
1
1.5
2
2.5
3
08 09 10 11 12 13 14 15 16 17
Cou
nt o
f jum
ps
Intra-Day Periods over one day (EST)
DJ
0
2
4
6
8
10
12
14
16
18
20
08 09 10 11 12 13 14 15
Cou
nt o
f jum
ps
Intra-Day Periods over one day (EST)
US
0
5
10
15
20
20 22 00 02 04 06 08 10 12 14 16 18 20 22
Cou
nt o
f jum
ps
Intra-Day Periods over one day (GMT)
USD/EUR
0
2
4
6
8
10
12
14
20 22 00 02 04 06 08 10 12 14 16 18 20 22
Cou
nt o
f jum
ps
Intra-Day Periods over one day (GMT)
USD/GBP
0
2
4
6
8
10
12
14
20 22 00 02 04 06 08 10 12 14 16 18 20 22
Cou
nt o
f jum
ps
Intra-Day Periods over one day (GMT)
JPY/USD
0
5
10
15
20
25
20 22 00 02 04 06 08 10 12 14 16 18 20 22
Cou
nt o
f jum
ps
Intra-Day Periods over one day (GMT)
CHF/USD
0
5
10
15
20
25
30
35
40
45
20 22 00 02 04 06 08 10 12 14 16 18 20 22
Cou
nt o
f jum
ps
Intra-Day Periods over one day (GMT)
XAU
0
1
2
3
4
5
6
7
20 22 00 02 04 06 08 10 12 14 16 18 20 22
Cou
nt o
f jum
ps
Intra-Day Periods over one day (GMT)
CHF/EUR
0
2
4
6
8
10
12
14
16
20 22 00 02 04 06 08 10 12 14 16 18 20 22
Cou
nt o
f jum
ps
Intra-Day Periods over one day (GMT)
GBP/EUR
0
1
2
3
4
5
6
7
20 22 00 02 04 06 08 10 12 14 16 18 20 22
Cou
nt o
f jum
ps
Intra-Day Periods over one day (GMT)
JPY/EUR
0
2
4
6
8
10
20 22 00 02 04 06 08 10 12 14 16 18 20 22
Cou
nt o
f jum
ps
Intra-Day Periods over one day (GMT)
CHF/GBP
0
1
2
3
4
5
6
7
20 22 00 02 04 06 08 10 12 14 16 18 20 22
Cou
nt o
f jum
ps
Intra-Day Periods over one day (GMT)
JPY/GBP
0
1
2
3
4
5
6
7
20 22 00 02 04 06 08 10 12 14 16 18 20 22
Cou
nt o
f jum
ps
Intra-Day Periods over one day (GMT)
CHF/JPY
42
Figure 7: Histogram of jump occurrences on announcement days
0
0.5
1
1.5
2
2.5
3
3.5
4
08 09 10 11 12 13 14 15 16 17
Cou
nt o
f jum
ps
Intra-Day Periods over one day (EST)
DJ
0
10
20
30
40
50
60
70
80
08 09 10 11 12 13 14 15
Cou
nt o
f jum
ps
Intra-Day Periods over one day (EST)
US
0
10
20
30
40
50
60
70
80
90
20 22 00 02 04 06 08 10 12 14 16 18 20 22
Cou
nt o
f jum
ps
Intra-Day Periods over one day (GMT)
USD/EUR
0
10
20
30
40
50
60
20 22 00 02 04 06 08 10 12 14 16 18 20 22
Cou
nt o
f jum
ps
Intra-Day Periods over one day (GMT)
USD/GBP
0
5
10
15
20
25
30
35
40
45
50
20 22 00 02 04 06 08 10 12 14 16 18 20 22
Cou
nt o
f jum
ps
Intra-Day Periods over one day (GMT)
JPY/USD
0
10
20
30
40
50
60
70
80
20 22 00 02 04 06 08 10 12 14 16 18 20 22
Cou
nt o
f jum
ps
Intra-Day Periods over one day (GMT)
CHF/USD
0
5
10
15
20
25
30
20 22 00 02 04 06 08 10 12 14 16 18 20 22
Cou
nt o
f jum
ps
Intra-Day Periods over one day (GMT)
XAU
0
1
2
3
4
5
20 22 00 02 04 06 08 10 12 14 16 18 20 22
Cou
nt o
f jum
ps
Intra-Day Periods over one day (GMT)
CHF/EUR
0
2
4
6
8
10
12
14
20 22 00 02 04 06 08 10 12 14 16 18 20 22
Cou
nt o
f jum
ps
Intra-Day Periods over one day (GMT)
GBP/EUR
0
5
10
15
20
25
20 22 00 02 04 06 08 10 12 14 16 18 20 22
Cou
nt o
f jum
ps
Intra-Day Periods over one day (GMT)
JPY/EUR
0
2
4
6
8
10
12
20 22 00 02 04 06 08 10 12 14 16 18 20 22
Cou
nt o
f jum
ps
Intra-Day Periods over one day (GMT)
CHF/GBP
0
1
2
3
4
5
6
7
8
9
20 22 00 02 04 06 08 10 12 14 16 18 20 22
Cou
nt o
f jum
ps
Intra-Day Periods over one day (GMT)
JPY/GBP
0
2
4
6
8
10
12
14
16
18
20 22 00 02 04 06 08 10 12 14 16 18 20 22
Cou
nt o
f jum
ps
Intra-Day Periods over one day (GMT)
CHF/JPY
43