exposure conditional on default: a fast structural approach · exposure conditional on default: a...

Exposure Conditional On Default:A Fast Structural Approach

Global Derivatives Trading & Risk Management

Amsterdam, May 2015

Vladimir Chorniy, BNP ParibasErdem Ultanir

Agenda

■ Capturing counterparty risk in the evolving world

■ WWR, conditionality on default

■ Conditionality on default/WWR – portfolio exposures or market

risk factors

■ Fast and structural approach

■ Modelling dependence – credit only

■ Using Merton as foundation for common drivers

■ Extending approach to cross asset – long-term credit and equity

link

■ Conditional simulation

■ Problem with simple multi-step: correlation washout

■ Backward simulation as better fast approximation

■ Path dependency with and without default

■ Short-term links

2

Counterparty risk today

■ The way we look at counterparty risk is changing

■ Increased role of clearing and margining (EMIR, Dodd-Frank)

■ Central Counterparties (CCPs)

■ Tails become more important, but specific requirements result in

zooming in on different areas

■ Still need “classical” counterparty risk calculations: expectation for regulatory capital and CVA, and 90th or 99th percentile exposures

■ With more trades collateralised and cleared, banks focus on higher percentiles over typical slippage / no-control periods for residual risk

■ Long-term stability of the financial system would require extreme events over long horizons to be assessed

■ Cross-asset dependence can become crucial in many of these cases

3

CCP and Margining

■ CCP

■ Client accounts: clearing is segment specific, but close-out is across all segments

■ CCP: rulebook and legal entity specific (e.g., LCH SA vs. LCH Ltd)

■ Cross-asset netting – may be; portfolio effect – definitely

■ Extreme events are expected to be propagating through majority of markets

■ Margining (EMIR)

■ Margins (both VM & IM) must be exchanged between counterparties when they are both either Financial Counterparties (FC) or Non-Financial Counterparties above the clearing threshold (NFC+) according to EMIR definitions.

■ Transactions between counterparties where one of them is neither FC nor NFC+ are exempt

■ Legacy – pre-EMIR, but also pre-EBA RTS implementation

■ Shifting credit cost to funding cost

■ Need to cover existing risk scope and address new elements

4

Counterparty risk: what needs to be measured and why

Percentile/Horizon Short (10d) Medium Long (2y+)

Lower (Expectation;

90 - 99%)

Collateralised

legacy; NFC-; IM

calculation /

verification –

CCPs/FC, NFC+

Legacy trades

and NFC-

(“classical”);

IM stability –

CCPs/FC,

NFC+; CCP

Legacy trades

and NFC-

(“classical”)

Higher (above 99%) Risk above IM

covered level

CCP/FC, NFC+

Same Systems stability

- stress tests;

Regulators; All

positions

■ WWR or conditionality on default now need to be modelled for all part of

distribution including extreme tails - mean, 90-99% and well above 99%

■ How confident are we in tail modelling with WWR? Use structural models?

5

WWR modeling approaches

■ What is ideal WWR method?

■ Easy to calibrate [to event not yet observed - default of counterparty]

■ Fast to calculate

■ Cheap to integrate into existing infrastructure (risk systems and

methodology)

■ Satisfy needs of all players:

■ CVA and other xVAs

■ Regulatory Capital (and EC if still used)

■ Risk (limit management) - PFE as percentile now, and/or ES in post-EMIR world

■ Backtesting and risk model validation (usually at both exposure and market risk factor level)

■ WWR vs. EAD (exposure at default) as exposure conditional on

default is required if WWR is to be recognised at limit level

■ Question. If ideal cannot be reached should we correlate c/p credit

risk to c/p exposure or underlying market risk factors (MRFs)?

6

Exposure based WWR (I)

■ Exposure based WWR*: attempt to create fast method preserving existing

(pre-WWR) infrastructure

■ Exposure sampling approach

■ Sokol (2010); Cespedes et al (2010); Rosen, Saunders (2012)■ Exposure Sampling: pre-compute unconditional exposures, calculate structural or reduced form

credit model factor(s); and introduce copula or compute the historical correlation; draw from pre-computed set based on such correlation or link

■ Parametric dependency

■ Hull, White (2012)■ Credit factor is linked to exposure through a hazard rate equation dependent on exposure values

■ Redon (2006), Turlakov (2013) (based on tail risk stress scenarios)

7

* Some methods on this slide give as an alternative or a generalisation the use of

correlation with “main” risk factor, with exposure as a function of such factor, thus Ruiz

(2015) could be listed here or Redon (2006) later.

Authors often concentrate on how to correlate (copula, parametric, etc.) rather what to

correlate. See Böcker, Brunnbauer (2014) for analysis of correlation methods difference

or equivalence.

Exposure based WWR (II)

■ Exposure based WWR: the good and the bad (or just ugly).

■ Preserving existing (pre-WWR) infrastructure –”Yes”, but

■ “No” - calibration may require expensive new infrastructure (more than Basel 3 WWR benchmark portfolios) – revaluing today’s portfolio in the past. That assumes we have market data – remember discussion stressed VAR proxies for Basel 2.5?

■ “Yes” - good for CVA and IT department, “No” - not helpful to Risk (EAD does not represent WWR)

■ Calibration made easy and transparent? Opposite opinions: Sokol says “Yes”, but we say “No”. Why?

“Yes”, [following Sokol (2014)]:

■ There are many correlations needed for all MRFs, but only one for exposure of given counterparty. One correlation is clear to users and simplifies stress tests.

■ Exposure sampling - multiple WWR assumptions can be run without re-running

exposure simulation

■ Correlation between credit spread and other MRFs is unstable.

■ The correlation which drives WWR is one with exposure, so direct estimate of correlation with exposure is better than indirect one via correlation with MRFs

8

Exposure based or marker risk factor based WWR (I)

■ Exposure based WWR. Calibration (continued)

Objections - “No”:

■ One correlation. Yes, but there are thousands of counterparties.

■ Stability? Aggregate correlation does not guarantee stability. It may magnify model error during regime shift/market stress period.

■ Transparent? One number is easy to see, but how something which has no fundamental underpinning should be interpreted or trusted in during market stress? How to stress what we do not understand?

■ Model risk is high and hard to test (e.g. choice of copula). Ability to capture relationship in the tails with no structural, fundamental underpinning – unproven.

■ And finally - what about new counterparties?

■ So - should we use correlation with market risk factors?

9

Exposure based or marker risk factor based WWR (II)

■ So - should we use correlation with market risk factors?

■ For Risk Management we would prefer simulating risk factors for

WWR:

■ Calibration is done on risk factor level, thus we do not require exposure history or assumption static traded assets and sizes in portfolios

■ Users are on familiar territory – they have intuition what the correlations mean, how they are expected to behave, how to stress them to reflect various market circumstances

■ Fundamental relationship can be captured explicitly between different assets. We have choice to use structural approach to model (like Merton). Approximation and model risk is better understood.

■ Structural models extend into event/tail risk: for extreme events we are outside of backtesting, but in principle we know which risks are in and which are out.

■ Any “Noes”?

10

MC approach based on risk factors

■ Infrastructure: Number of required paths in brute force MC

■ CCC one year default probability is 21.12%, AA is 0.01% (Moody’s). Only 1 path out of 10000 paths default for AA. In order to get the same variance reduction versus unconditional paths x10000 paths should be generated per each counterparty

■ Need methodology to simulate only conditional paths or convert

unconditional into conditional in a simple way

■ Structural models (Merton) are difficult to link to risk neutral calibration. If

CVA is a price…

■ What is available?

11

Market risk factor based WWR

■ Risk factor based WWR

■ Simulate underlying risk factors of exposure and credit together. Credit risk can be modeled structural or through reduced form while market risk factors (including CDS spreads) are linked to underlying factors of exposure

■ Chorniy, Wilkens (2009); Buckley, Wilkens, Chorniy (2011). Credit scenarios are simulated conditional on the counterparty’s default. Credit-credit link based on Merton asset/liability model

■ Finger (2000) demonstrated parametric fitting currencies and credit, follows Levin, Levy [JPMorgan] (1999), which also relates jumps type FX devaluation model: jump at counterparty default for FX markets, e.g. overview in Hulme(2013)

■ Ruiz (2015) introduces parametric relationships between default probabilities, equity, FX, and commodities. In spirit follows Finger (2000), but with parametric view extends Hull-White (2012) to dominant underlying risk factor(s) -exposures are linked, but unconditional at default

12

How to generate conditional simulations (I)

■ Before discussing mathematics of original model and its cross-asset

extension let us outline the basic ideas – what we try to achieve and what

are the compromises

■ Chorniy, Wilkens (2009) “Capturing credit correlation between counterparty

and underlying” is based on two basic requirements:

■ Counterparty credit evolution (default) should be easy to simulate and calibrate

■ Conditionality impact on unconditional path should be easy to transmit, without joint simulation of market scenario and counterparty evolution – need a simple transformation of unconditional distribution

■ Translate these two requirements into two steps. Our choice:

1. Find the process which captures counterparty (c/p) – MRFs correlation and “easy” to calibrate. Merton is an obvious candidate. Simplified Merton – single step normal distribution with thresholds calibrated to migration matrix is easiest to deliver

2. Impose results via “moment matching” – shift to mean and variance of original c/p asset distribution. Both shifts could be analytically pre-calculated and stored as tuples (e.g. 18x18 rating per time step) or fitted with parametric function. Easy to stress and override

■ In principle, both steps 1 and 2 could be replaced with a different process and coupling

13

How to generate conditional simulations (II)

■ Compared to Sokol or Hull our approach achieve most of the objectives:

simple model; stable and easy to calibrate; no need to re-simulate risk

factors; clear stress test application

■ Immediate shortcoming are mostly results of particular choice – discrete

single step version of Merton results in correlation wash-out and limitation

on path dependency (both for exposure and MRFs), but this is can be

improved ( will be discussed later in this presentation).

■ The model is Basel 2 and 3 approved, live for credit since 2011, and shows

stable calibration and performance.

■ If the model is so good why it is not an industry standard?

If you are so clever, why aren’t you rich?*

■ The problem is that model comes with pre-conditions.

14

*A slightly daft question to ask at a quants’ conference. Our apologies.

How to generate conditional simulations (III)

■ Model comes with pre-conditions:

“If you like me – then you must also like my parents, like my

cousin, like my eccentric uncle, like my dog, like my turtle…”

■ Whatever “signal” is chosen to carry information about counterparty state, it

needs to propagate through models of all market risk factors – any type that

we need to make conditional

■ Easy for credit derivatives – same Merton is used to evolve credit spread

over long time (and/or generate event risk)

■ Spread-to-rating mapping is an established tool – well-known in application of both counterparty IMM and market IMM for IRC/CRM*

■ The stochastic credit spread could be “bolted” on top of Merton to describe shorter term/market evolution (again regulator and Basel 2.5 approved)

■ Other assets – not easy, e.g. equity. There is no “price to rating” mapping for

equity

■ Equity model driver by Merton model via rating transition need to be developed. Similar preconditions for other asset classes if WWR to be covered there

■ Extra incentive for such “equity by Merton” – if CDS is based on Merton and if cross-

asset model required to include defaults across same equity-credit names as MRFs then such extension is needed anyway

15*IRC/CRM material in References

Conditional simulations – initial model recap (I)

■ “Capturing credit correlation between counterparty and underlying” -

reminder.

■ For transparency reasons and to allow simple closed-form expressions slides show one-step model where the counterparty can default at any time between time zero and t, see Buckley, Wilkens, Chorniy (2011) for multistep solution

■ Structural credit equations are written which incorporate counterparty

correlation/conditionality on default – two-asset case

■ Correlated (systematic) asset returns ZCP and ZAsset at time t in a one-factor

model:

(ε, φ: standard Gaussian deviates; ρ: correlation)

■ Focus on exposure conditional on counterparty default , i.e., scenarios

where ZCP(t) < TCP, with TCP (t; RCP,0) as the threshold to go from the initial

counterparty rating RCP,0 to default at time t

16

■ Generate asset simulations where first two moments match the

conditional simulations

Conditional simulations – initial model recap (II)

17

Conditional simulations – initial model recap (III)

■ This provides mean and variance of the distribution of ZAsset

conditional on ZCP < TCP:

reducing to the appropriate limits (mean: 0, variance: 1) as

■ Transformation of the unconditional distribution of asset returns to

the conditional distribution:

Notably, this does not modify the correlation between two different

assets

18

Conditional simulations – initial model recap (IV)

Shift in first two moments of asset return distribution depending on

counterparty credit quality (1 year horizon)

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

-5.0 -4.0 -3.0 -2.0 -1.0 0.0 1.0 2.0 3.0 4.0 5.0

PD

F

Unconditional CP: Well-rated hedge fund

CP: Major financial institution CP: Country like Germany/France

19

■ Influence of counterparty-asset correlation: ρ = 30%

Conditional simulations – initial model recap (V)

■ Illustration of the approach in practice:

20

Conditional simulations – initial model recap (VI)

■ No need to simulate the whole path, model does a direct jump to default at

pricing time point.

■ Model is good for CDS exposures where one does not need to know how

credit risk evolved to price CDS at future: knowing credit state at valuation

point is enough to get present value of CDS

■ The setup as discussed shows a too strong counterparty conditionality at

the short term

■ For example, if an AA-rated entity defaults in two years it is likely that the overall economic conditions have led to a significant deterioration in economy-wide asset values, thus increasing the default probability

■ In the short term: Default of a (well-rated) counterparty has most likely a rather low correlation with the development of overall market conditions and is therefore more of idiosyncratic nature

■ Solutions within the model:

■ Term structure of correlation. Start with zero, or short term can reflect market jump - “Lehman jump” at short term (in effect WWR floor). This depends whether c/p is large (systemic or not)

■ Direct adjustment of the first and second-order shifts

21

New: Conditional equity path simulations

■ Not only credit-credit, but also cross-asset modeling can follow a similar

approach

■ CDSs are not path dependent on instrument level

■ Portfolio has limited path dependency due to non-zero MTA under CSA

■ Portfolio has strong dependency during margin period of risk only (e.g. last 10 days) –generally much shorter then instrument tenor.

■ Equity is different. Many derivatives (knock-in/out) require path dependent

pricing with cross asset links. Thus not only the equity level conditional on

counterparty default at the exposure time point, but the conditional path of

equity should be determined. Path dependent pricing link with conditionality

is explicitly created in our approach

■ Sokol and Hull solutions implicitly can create a path dependence. Explicit

dependence enables simulating the portfolio that can exhibit extreme events

- default of company underlying the trade before the exposure time. In

addition not only mean of the paths, but percentile measures can be

calculated including such defaults.

22

Overview of cross asset equity-credit link approach

■ Path dependent equity trades need underlying credit path

conditional on counterparty’s default

■ Rating paths are integrated with rating dependent equity long term

model

■ Developed a new approach to simulate conditional rating paths

efficiently

■ Default time simulation approach is introduced to identify default point of

a company linked to trade

■ Credit dependent equity long term model (Chorniy, Greenberg,

Moran (2014) “Credit-Equity Model Building Blocks”, WBS Fixed

Income) is precondition. A short summary:

23

Credit dependent equity long term model

■ Share price dynamics around rating migrations exhibits long term

impacts in the price levels suggesting structural shifts

■ Investigate dynamics that result in 1 notch changes

1 notch downgrade 1 notch upgrade

24

Share price dynamics around rating migrations

■ Downgraded names – “hockey

stick” pattern: negative drift before,

stable after

■ Starts approximately 9 months

before the event

■ Upgraded names: smaller upward

drift before, largely stable after

■ Timing less clear, possibly a slower

and/or weaker effect

■ “Risk-return” pattern after the event

decreases if “de-systematised” per

rating band* “De-syst” means that market average has been subtracted

25

CDS spread dynamics around rating migrations

■ Downgraded names – “hat”

pattern: spreads rise before, drop

after

■ Post-downgrade level higher,

reflecting increased credit risk

■ Upgraded names: less clear, some

hybrid of “hockey stick” and “hat”

patterns

■ Signal weaker overall

26

Symmetry: definition and model advantages

■ Structural shifts in prices takes over at long horizons…

■ Just established: +1 -1 = -1 +1 on average

■ What about 0 +2 = +1 +1 etc.? Approximately, yes (within error margin)

■ Why are these two “yeses” important?

■ Allows to construct a single “share price-to-rating” map.

■ Recall that “spread-to-rating” maps are well known in IRC/CRM modelling and allow construction

of “simple” models on Lego principles

■ Instead of mapping ratings to levels (as for spreads), consider mapping from rating transition to ratio of share prices (after and before the event).

■ More formally, the questions to ask:

■ Initial rating dependence: moving from rating a to rating a+k vs. from rating b to rating b+k

■ Path dependence: intermediate steps in moving from rating a to rating b

■ Direction dependence: from a to b vs. from b to a. (Can be subset of path dependence)

■ Excluded time dimension:

■ Is speed (drift) different between up- and downgrades only or are there other dependencies, e.g., investment/non-investment grade, high/low volatility bands etc.? There is some differentiation see Chorniy-Greenberg-Moran (2014) “Credit-Equity Model Building Blocks”, but these are secondary effects to model

■ Graphical visualisation: introducing “tree branches”, “needles and “twigs”…

27

“Tree branches”, “needles” and “twigs”… (I)

■ Introducing the toolkit – look at single transition only at first:

■ Cumulative equity drift of migrated names vs. drifts of those names that did not migrate

■ In each rating category, take average growth rate of the names that stayed in this rating over the

whole 5 year period as “base”; calculate average excess drift of equity log-returns for the names that

migrated out of this rating

■ Assume that consecutive migrations lead to adding up [log] drifts, plot the cumulative drift as a

function of rating, increasing for consecutive upgrades or decreasing for downgrades: “spine curve”

■ Consider “spine curve” as the “path” of cumulative equity drift from consecutive upgrades. For each

rating category on the upgrade drift “path”, estimate excess drift averaged over observed single-

notch downgrades from this rating and draw a line on top of “spine curve” (left-hand panel) – this is

the extra “needle” or “twig”.

■ If upgrade and downgrade effects were completely symmetric, no “needles” or “twigs” would

exist

Rating n S&P

2 [C-CCC]

3 B-

4 B

…………………..

17 AA+

18 AAA

28

“Tree branches” , “needles” and “twigs”… (II)

29

Conditional equity simulations

■ Brute force simulations in discrete systems

■ Costly, it takes several hundred thousands paths to observe defaults in

investment grade ratings

■ Correlation wash-out. Discrete steps credit process do not follow a

continuous asset level.

■ Continuous asset processes are proposed to avoid correlation

wash-out

■ Continuous asset processes do not integrate well with the Markov

assumption of rating migration matrix

■ Number of rating migrations observed in such simulations is very different to what is observed in empirical data

■ Issues with paths where the counterparty rating goes into default before the exposure horizon point. Eliminating these paths disturbs standard normal distribution assumption of paths at any given exposure horizon

30

Correlation wash-out

■ At each step only the terminal ratings of the previous step is used to

determine the start point of bilateral asset processes underlying the ratings.

At two separate simulation paths, asset returns that fall in the same rating

band will start from the same point in the next simulation step regardless of

their previous asset returns

31

0 100 200 300 400 500 600 700 800-0.05

0

0.05

0.1

0.15

0.2Counterparty 7->10, Asset 7->10 Joint Probability, Corr=30%

%

days

Analytical

ForwardCorr 30%

Is continuous asset process a solution?

■ Asset process is replaced by GBM, ratings are defined when asset

process passes rating threshold curves

32

0 50 100 150 200 250 300 350 400 450 500-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

days

asset

level

Continuous asset process and rating thresholds

Continuous Process

Resetting Process

Continuous process, defaulted paths?

■ Defaulting steps - should we bounce or absorb

■ Bouncing■ Asset defaults, equity price drops to zero. What is equity price after rating recovers from

default?

■ Absorbing defaults■ Left out paths no longer Gaussian distribution

33

-5 -4 -3 -2 -1 0 1 2 3 4 50

0.1

0.2

0.3

0.4

0.5

0.6

0.7

PD

F

asset return

Bouncing From Default

Absorbing Defaults

Adjust correlation to mitigate correlation wash-out impact?

■ Increase correlation to correct the correlation wash-out

■ Requires a different correlation for each set of exposure horizons and starting rating combinations. Concentrating on downgrades allows this approximation, but is rather basic.

34

0 100 200 300 400 500 600 700 8000

0.1

0.2

0.3

0.4

0.5

0.6

0.7


%

days

Analytical

ForwardCorr 30%

ForwardCorr 80%

ForwardCorr 60%

0 100 200 300 400 500 600 700 8000

0.05

0.1

0.15

0.2

0.25

0.3

0.35


%

days

Analytical

ForwardCorr 30%

ForwardCorr 80%

ForwardCorr 60%

■ Instead of forward simulation, do a backward simulation where

ratings are pinned at the beginning and at exposure horizon

■ Do a single step jump to exposure horizon

■ Simulate backward from the exposure horizon conditional on the ratings of counterparty and asset underlying the trade at initial and exposure points

Alternative: conditional backward simulation

0 100 200 300 400 500 600 700 8000

0.1

0.2

0.3

0.4

0.5

0.6


%

Analytical

Backward

Forward

0 100 200 300 400 500 600 700 8000

0.05

0.1

0.15

0.2

0.25

0.3


%

Analytical

Backward

Forward

35

Conditional backward simulation

■ Further improvements in methodology

■ Construct the path from large time steps instead small steps

■ One large jump to end, then do a backward jump to the middle of

exposure horizon, and continue bisection

36

0 100 200 300 400 500 600 700 8000

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4


%

days

Analytical

Backward

Forward

0 100 200 300 400 500 600 700 8000

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4


%

days

Analytical

Backward

Forward

Backward with bisection

Simulated conditional equity paths (I)

■ Now we have a solution to simulate conditional credit paths avoiding

correlation wash-out

■ How do conditional credit paths look like? Can we approximate them

through slight modifications on unconditional paths?

37

0 100 200 300 400 500 600 700 8000.8

0.9

1

1.1

1.2Equity Levels

0 100 200 300 400 500 600 700 8006

6.5

7Ratings

conditional

unconditional

proxy

BB-

BB

• Initial ratings: Counterparty BB,

Company linked to trade BB

• Proxy is equally distributing the

rating implied shift through time

days

Simulated conditional equity paths (II)

■ The rating difference between unconditional and conditional paths is equally distributed to appear between initial and exposure time point

■ For extreme differences (>=3 ratings) there is a sudden jump at the final rating point

38

Gets worse conditionally

-2 -1 0 1 2 3 4 5 6 7 80

5

10

15

20

25

30

35

40

45

50

%

Percentage of Final Delta Rating Observations

Unconditional - Conditional Rating at the end , Counterparty: 7, Asset: 7

0 100 200 300 400 500 600 700 8000

0.5

1

1.5

2Unconditional - Conditional Rating evolution, Counterparty: 7, Asset: 7, Final Delta: 1

0 100 200 300 400 500 600 700 800-1

0

1


0 100 200 300 400 500 600 700 800-2

0

2


1%

10%

50%

90%

99%

mean

1%

10%

50%

90%

99%

mean

1%

10%

50%

90%

99%

mean

Initial Ratings BB

Final Delta = 3

Final Delta = 2

Final Delta = 1

Simulated conditional equity paths (III)

■ Conditionality can also improve the rating if counterparty is speculative grade, thus counterparty need to survive till the exposure time point

■ Again most paths suggest that rating impact can be equally distributed along the time horizon

39

-6 -5 -4 -3 -2 -1 0 1 2 3 40

5

10

15

20

25

30

35

40

%

Percentage of Final Delta Rating Observations

Unconditional - Conditional Rating at the end , Counterparty: 2, Asset: 7

0 500 1000 1500 2000 2500 3000 3500 4000-1

-0.8

-0.6

-0.4

-0.2


1%

10%

50%

90%

99%

mean

0 500 1000 1500 2000 2500 3000 3500 4000-3

-2

-1

0

1Unconditional - Conditional Rating evolution, Counterparty: 2, Asset: 7, Final Delta: -1

1%

10%

50%

90%

99%

mean

0 500 1000 1500 2000 2500 3000 3500 4000-3

-2

-1

0

1Unconditional - Conditional Rating evolution, Counterparty: 2, Asset: 7, Final Delta: -2

1%

10%

50%

90%

99%

mean

Final Delta = -2

Final Delta = -1

Final Delta = 0

Unconditional – Conditional Ratings Initial Ratings Counterparty C, Trade company BB

What if underlying defaults before exposure time point?

■ We know the company is in default at the exposure point, but for path

dependent trades we need to know when exactly it has defaulted

■ P1 ,…, Pk denote the conditional probabilities of the conditional default of the

underlying happening in the interval (t0, t1], …, (tk-1, tk],

■ Simulate uniform random variable U to determine default step

40

Equity and credit short-term correlations (I)

■ Equity and credit long-term behaviour is linked to ratings

■ What about short-term correlations between credit (CDS) and equity

levels? (Short-term process can stay unconditional)

41

-1

-0.5

0

0.5

1

10D 1M 1D

Correlation between cds and equity of same name

-1

-0.5

0

0.5

1

10D 1M 1D

Correlation between cds and equity of all universe

■ Correlations between same name are stronger than correlations between equity and credit of different names

■ Factor model will capture the idiosyncratic correlation while also linking the credit and equity of different names

Equity and credit short-term correlations (II)

■ For individual names, some dependence on credit quality may transpire

■ Median correlation between equity and spread returns of the same name is -41%

■ Poorly rated names show stronger link:

■ Short term relationship is rating dependent through same name correlations

42

Conclusions

■ Exposure conditional on default – market risk factor

based WWR model was presented. Extended model is

cross asset and covers path dependent instruments

■ Potential advantages:■ Fast

■ Re-use unconditional infrastructure

■ Use structural approach and capture rare events (migrations, defaults)

■ Stable calibration on readily available data

■ Modular

■ Transparent for stress tests

■ The presented version of the model is oriented towards

real world simulation (Risk as primary user)

■ The model restricts unconditional simulation to the use of

matching structural approach

43

■ Thanks to Jean-Baptiste Brunac, Andrei Greenberg, Vera Minina, Mirela

Predescu, Sascha Wilkens for their input at various stages of this work.

Acknowledgements

44

References

Sokol (2010), “A Practical Guide to Monte Carlo CVA” in Lessons from the Financial Crisis: Insights from the

Defining Economic Event of our Lifetime, ed. A. Berd, (London, Risk Books) ;

Cespedes et al (2010), “Effective modeling of wrong way risk, counterparty credit risk capital, and alpha in

Basel II”, The Journal of Risk Model Validation, Vol 4 No 1;

Rosen, Saunders (2012), “CVA the wrong way”, Journal of Risk Management in Financial Institutions, Vol 5 No

3;

Hull, White (2012), “CVA and Wrong Way Risk”; Financial Analysts Journal, Vol 68, No 5;

Redon (2006), “Wrong Way Risk Modelling”, Risk, April;

Turlakov (2013), “Wrong-Way Risk, Credit and Funding”, Risk, March;

Böcker, Brunnbauer (2014), “Path-consistent wrong-way risk”, Risk, November;

Sokol (2014) “Long Term Portfolio Simulation”, (London, Risk Books);

Chorniy, Wilkens (2009) “Capturing credit correlation between counterparty and underlying”, Quant Congress

Europe;

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