economic scenario generation: some · pdf file3 my experience of stochastic models...
TRANSCRIPT
Economic Scenario Generation:
Some practicalities
David GrundyOctober 2010
2
my perspective
• as an empiricist rather than a theoretician
• as stochastic model owner and user
All my comments today are my own views.
These may differ from the view of my employer.
3
My experience of stochastic models
• Economic scenario generatorsToy ESGs – interest rate, equity, credit spreadGeneSISTSM *
• Projection modelsTraditional Prophet (A, L, S, G)LifeDFA (design phase)Spreadsheet projection models
• Application to ALM
• Interpretation of results
4
Agenda
• Reminder of Market-Consistent valuation philosophy
• Focus on market-consistentNominal Interest Rate (“NIR”) model
Market dataBasic tests of model:market fitModel selection
• Getting started
5
What kind of model?
• Why?pricing guarantees MCMCEV MCunderstand the range of outcomes RWcapital requirement depends
• Popular assetscash NIR modelgovernment bonds NIR modelequity equity risk modelcorporate credit spreads
defaults
6
Calculation of the value of guarantees
• Value on stochastic basisGenerate 1,000 economic sims(‘market-consistent’ basis)For each sim calculate the PVIFTake the average PVIF over all simulations
• Value on deterministic basisSingle projection
Discount profitsat the Risk Free Rate
PVIF
Valuemany simulations
t Set of1000
results
mean
ValueValue
MC valuedeterministic
Time Value of
Guarantees
7
Rationale for Market-Consistent calibration
• If our model can calculate correct values for many different kinds of assets …
• … and we use the same model to calculate the value of our business cashflows …
• … then maybe the model can calculate the correct value for our business.
8
Market-consistent values:calibration and extrapolation
Life Insurance Business
VeryHard !
Time horizon
Complexity
Formulasor sims
Use sims tovalue these
Hard
Easy Equity optionsRisk-free bonds
SwaptionsCorporate bonds
9
Risk-neutral sims vs Real-World sims
• different samples from the same underlying set of possible outcomes
t
RW
Future assetsPossible market outcomes
RN
Discounted value
Discount @ RDRDiscount @ RFR
10
Easy data sourcesfor Market-Consistent calibration
Model Market data Sources• Interest rates
level yield curve BBG, central banksvolatility swaption volatility BBG, ibanks
• equity returnsvolatility implied volatility BBG, ibanks
• credit spreadslevel swap rates BBG
corp bond yields BBGvolatility ??? ???
• credit lossesignore this for now
11
NIR model – rough conceptual framework
• initial yield curvein MC sims, this determines average future ratescan be observed directly
• stochastic model of changes in short ratesmathematical formulation & parameterisationcan be fitted to swaption data
• calculation of full yield curve at each time stepbased on the mathematical model
12
NIR model: Initial yield curve
• The yield curve sets future average returns (MC)
• Derivatives are priced from swap ratesno market-implied prices for govt bond volatility
• Most companies hold govt bondsswap rates usually overstate risk-free returns available
• The govt bond yield curve will not reproduce your bond portfolio value
• Data is hard to interpret in stressed markets
13
NIR model data problems
• Yield curvesnot straightforward
• Interest rate derivativesno caplets for most Asian marketsswaption data is messy
14
NIR model data: Bloomberg yield curve
• Example: USD 2009.12.31
15
Bloomberg yields summary
• Example: USD 2009.12.31
• 1-year rate is 0.445%
16
Underlying bond yield data
• The reference bond is not quite 1 year
• By interpolation we could estimate the 1-year rate as about 0.5% at that time.
17
More underlying data
• USD Govt curve at 2009YE (all issues)
0.0%
0.5%
1.0%
1.5%
2.0%
2.5%
3.0%
3.5%
4.0%
4.5%
5.0%
0 5 10 15 20 25 30 35
All bondsReference
18
Forwards (fitted to the reference rates)
• Example: Forward curve is a step functionreproduces all the reference spot prices exactly
• Adding the “off”points fits betterbut is less smooth.
• An alternative is tofit a smooth curveto all the data.
• But ... no smooth curve fits all the data.
0%
1%
2%
3%
4%
5%
6%
7%
0 10 20 30
UST Actives FwdUST On/Off the run FwdUST Actives Spot (ZCB)UST On/Off the run Spot (ZCB)
19
A stressed curve
• USD Govt curve at 2008YE
0.0%
0.5%
1.0%
1.5%
2.0%
2.5%
3.0%
3.5%
0 5 10 15 20 25 30 35
All bondsReference
20
Is the interest rate model market-consistent?1. Bond price test
• Cashflow of $100 in 10 years from now.
• Market pricePrice = Amount I need to invest to have $100 in 10 years
= $100 * 1-year ZCB price= $100 * (say) 0.80= $80
• Model pricedifferent in each simdepends on cash accumulation over 10 yearstake the average
21
Bond price test illustration
• 10-year bond price
• 5% flat yield curve
• 10 simulations
• Error measure:Absolute or proportional?
Situation at simulation year 10Sim Cash
AccumDiscount
factor1 1.462 0.68422 1.471 0.67983 1.693 0.59054 1.718 0.58205 1.650 0.60606 1.601 0.62487 1.701 0.58798 1.641 0.60959 1.674 0.597210 1.543 0.6481
Bond price testTarget 0.607Sim average 1.615 0.621Discrepancy in bond price
absolute 1.4%proportional 2.4%
Rough 95% confidence intervallower 0.597upper 0.645
22
Model vs target: bond price test example
Ratio of model price to market price(and model confidence limits)
0.990
0.995
1.000
1.005
1.010
0 10 20 30 40 50Year
ExpectedAverageLower limitUpper limit
Illustration only, not a model of USD2009.12.31
23
Average interest rate vs initial forward curve
• Unexpected implications of the bond price testYear: 0 1 2
Initial forward curveForward rate throughout the year 5% 5%ZCB Bond Price 1 0.9524 0.9070
= Value today of a future $1 after T years
Bond price test:Average valuation factor should agree with the original bond price
Version 1 Version 2Asset Measure Sim Year: 0 1 2 0 1 2
Cash Return 1 4% 3% 4% 3%2 6% 7% 6.02% 7.12%Average 5.00% 5.00% 5.01% 5.06%
Discount factor (from cash) 1 1 0.9615 0.9335 1 0.9615 0.93352 1 0.9434 0.8817 1 0.9432 0.8805Average 1.00 0.9525 0.9076 1.00 0.9524 0.9070
Return backed out from average DF 4.99% 4.94% 5.00% 5.00%
24
NIR model – dynamics(volatility, mean reversion, etc?)
• data sources – “deep and liquid markets”swaption volatilitiescaplets (if available)
• swaptions vs caplets
• “swaption volatility”depends on yield curvedepends on interest rate volatility characteristics
25
USD swaption data
• USD swaptions (Bloomberg VOLM, 2009.12.31)USD Swap term
Expiry 1 YR 2 YR 3 YR 4 YR 5 YR 6 YR 7 YR 8 YR 9 YR 10 YR 12 YR 15 YR 20 YR 25 YR 30 YR
1 YR 60.2% 48.3% 41.9% 38.4% 36.4% 34.7% 32.8% 31.2% 30.5% 30.3% 29.7% 26.0% 25.2% 24.9% 24.7%
2 YR 43.7% 38.9% 34.9% 33.2% 31.6% 30.9% 29.6% 28.4% 27.9% 27.9% 27.6% 24.6% 24.7% 24.0% 24.0%
3 YR 34.0% 31.8% 30.3% 28.8% 28.2% 27.6% 26.9% 26.0% 25.5% 25.5% 24.7% 23.0% 22.7% 22.4% 22.2%
4 YR 29.1% 28.5% 26.9% 26.5% 25.8% 25.5% 24.6% 24.2% 23.9% 23.6% 23.7% 21.6% 21.8% 21.0% 21.2%
5 YR 27.6% 25.7% 25.3% 24.7% 23.8% 23.8% 22.9% 22.4% 22.1% 22.0% 22.2% 20.7% 20.1% 20.1% 19.9%
6 YR 24.7% 24.2% 23.7% 23.2% 22.6% 22.2% 21.7% 21.9% 21.1% 20.8% 20.3% 19.4% 19.1% 19.1% 19.1%
7 YR 24.3% 23.3% 22.0% 21.4% 20.7% 20.9% 20.3% 20.0% 19.8% 19.9% 20.1% 18.6% 18.5% 18.0% 18.1%
8 YR 22.7% 21.3% 20.7% 20.3% 19.4% 19.3% 19.2% 19.1% 19.0% 19.1% 18.6% 17.9% 17.6% 17.4% 17.3%
9 YR 21.2% 20.0% 19.2% 18.8% 18.3% 18.2% 18.1% 18.0% 18.0% 17.9% 17.7% 17.3% 17.0% 16.7% 16.5%
10 YR 19.4% 18.7% 18.6% 18.1% 17.6% 17.8% 17.6% 17.4% 17.3% 17.3% 17.4% 16.2% 15.9% 15.6% 15.6%
12 YR 18.5% 18.1% 17.9% 17.5% 17.1% 17.2% 17.0% 16.8% 16.6% 16.6% 16.5% 15.6% 15.1% 14.8% 14.8%
15 YR 16.7% 16.6% 16.5% 16.2% 16.1% 15.9% 15.9% 15.7% 15.5% 15.5% 15.1% 14.5% 13.9% 13.6% 13.5%
20 YR 15.9% 15.6% 15.4% 15.1% 14.7% 14.6% 14.5% 14.0% 13.9% 13.8% 13.4% 12.9% 12.4% 12.2% 12.1%
25 YR 14.8% 15.2% 14.9% 14.2% 14.2% 14.1% 13.6% 13.5% 13.7% 13.6% 13.2% 12.6% 12.0% 11.8% 11.7%
30 YR 14.5% 14.3% 14.2% 14.0% 13.7% 13.6% 13.2% 13.2% 13.1% 13.1% 12.9% 12.7% 11.8% 11.4% 11.3%
26
HKD Swap term
Expiry 1 YR 2 YR 3 YR 4 YR 5 YR 6 YR 7 YR 8 YR 9 YR 10 YR 12 YR 15 YR 20 YR 25 YR 30 YR
1 YR 62.0% 48.5% 40.8% 36.0% 33.2% 32.5% 31.8% 30.6% 29.5% 28.4% 28.4% 28.4% 28.4% 28.4% 28.4%
2 YR 41.7% 35.6% 32.0% 29.9% 28.6% 28.4% 28.3% 27.6% 26.9% 26.2% 26.2% 26.2% 26.2% 26.2% 26.2%
3 YR 33.2% 29.5% 28.1% 27.0% 25.8% 25.4% 25.0% 25.0% 25.1% 25.2% 25.2% 25.2% 25.2% 25.2% 25.2%
4 YR 28.0% 26.9% 26.0% 25.3% 24.4% 24.0% 23.7% 23.9% 24.1% 24.4% 24.4% 24.4% 24.4% 24.4% 24.4%
5 YR 26.7% 25.4% 24.4% 23.8% 23.6% 23.2% 22.7% 23.1% 23.4% 23.8% 23.8% 23.8% 23.8% 23.8% 23.8%
6 YR 25.4% 23.9% 23.5% 22.4% 21.8% 22.1% 22.5% 22.9% 23.3% 23.7% 23.7% 23.7% 23.7% 23.7% 23.7%
7 YR 24.2% 22.3% 22.6% 21.1% 19.9% 21.1% 22.3% 22.7% 23.2% 23.6% 23.6% 23.6% 23.6% 23.6% 23.6%
8 YR 25.8% 22.5% 22.8% 21.5% 20.5% 21.6% 22.7% 23.1% 23.6% 24.0% 24.0% 24.0% 24.0% 24.0% 24.0%
9 YR 27.3% 22.7% 23.0% 22.0% 21.0% 22.1% 23.2% 23.6% 23.9% 24.4% 24.4% 24.3% 24.3% 24.3% 24.3%
10 YR 28.9% 22.8% 23.1% 22.4% 21.6% 22.6% 23.6% 24.0% 24.3% 24.7% 24.7% 24.7% 24.7% 24.7% 24.7%
12 YR 29.0% 22.9% 23.2% 22.4% 21.6% 22.6% 23.6% 24.0% 24.4% 24.7% 24.7% 24.7% 24.7% 24.7% 24.7%
15 YR 29.2% 23.1% 23.3% 22.5% 21.6% 22.6% 23.7% 24.0% 24.4% 24.7% 24.7% 24.7% 24.7% 24.7% 24.7%
20 YR 29.2% 23.1% 23.3% 22.5% 21.6% 22.6% 23.7% 24.0% 24.4% 24.7% 24.7% 24.7% 24.7% 24.7% 24.7%
25 YR 29.2% 23.1% 23.3% 22.5% 21.6% 22.6% 23.7% 24.0% 24.4% 24.7% 24.7% 24.7% 24.7% 24.7% 24.7%
30 YR 29.2% 23.1% 23.3% 22.5% 21.6% 22.6% 23.7% 24.0% 24.4% 24.7% 24.7% 24.7% 24.7% 24.7% 24.7%
HKD swaption data
• HKD swaptions (Bloomberg VOLM, 2009.12.31)
27
HK Swaption vol surface (VOLM 2009.12.31)
1 YR
6 YR
12 YR
1 Y
R
3 Y
R
5 Y
R
7 Y
R
9 Y
R
12 Y
R
20 Y
R
30 Y
R0.0%
10.0%
20.0%
30.0%
40.0%
50.0%
60.0%
70.0%
60.0%-70.0%50.0%-60.0%40.0%-50.0%30.0%-40.0%20.0%-30.0%10.0%-20.0%0.0%-10.0%
Swap termOption term
28
Data from specific swaptions
• Different from the VOLM figures ...
• Multiple sources available
• Is it better to fit to Bloomberg’s smoothed data?Or to fit to a set of underlying prices?
HKD Differences (Underlying - model)Swap term
Expiry 1 YR 2 YR 3 YR 4 YR 5 YR 6 YR 7 YR 8 YR 9 YR 10 YR 12 YR 15 YR 20 YR 25 YR 30 YR1 YR 7.1% 2.8% 3.0% 4.5% 3.2% 4.9% n/a n/a n/a n/a n/a2 YR 1.1% 3.3% 3.6% 4.7% 3.4% 4.4% n/a n/a n/a n/a n/a3 YR 1.9% 3.3% 4.1% 4.5% 5.4% 4.9% n/a n/a n/a n/a n/a4 YR 4.3% 4.4% 3.4% 4.1% 4.4% 4.8% n/a n/a n/a n/a n/a5 YR 3.8% 4.1% 5.8% 2.9% 4.1% 3.1% n/a n/a n/a n/a n/a6 YR n/a n/a n/a n/a n/a7 YR 2.6% 3.6% 2.2% 4.5% 2.9% 1.4% n/a n/a n/a n/a n/a8 YR n/a n/a n/a n/a n/a9 YR n/a n/a n/a n/a n/a10 YR -3.8% 1.9% 1.9% 3.0% 1.2% -0.5% n/a n/a n/a n/a n/a12 YR n/a n/a n/a n/a n/a n/a n/a n/a n/a n/a n/a n/a n/a n/a n/a15 YR n/a n/a n/a n/a n/a n/a n/a n/a n/a n/a n/a n/a n/a n/a n/a20 YR n/a n/a n/a n/a n/a n/a n/a n/a n/a n/a n/a n/a n/a n/a n/a25 YR n/a n/a n/a n/a n/a n/a n/a n/a n/a n/a n/a n/a n/a n/a n/a30 YR n/a n/a n/a n/a n/a n/a n/a n/a n/a n/a n/a n/a n/a n/a n/a
29
KRW swaptions: less “deep and liquid”
Some terms are missingMany quotes appear to be inactive
Option Swap Ticker 01 02 03 04 07 08 09 10 11 14 15 16 17 18 21 22 23 24 25 28 29 30 311 1 KWSV011 CMPL Index 23.3 23.3 23.3 23.3 23 23.3 23.7 24.2 24.2 23.4 24.2 23.5 23.5 23.7 24.2 24.2 24.2 24.2 24.2 24.2 24.2 22.2 22.22 1 KWSV021 CMPL Index 20.7 20.7 20.7 20.7 20.7 20.7 20.8 20.6 20.6 20.4 20.6 20.6 20.6 20.6 20.6 20.2 20.6 20.6 20.6 20.2 20.1 20.63 1 KWSV031 CMPL Index 18.8 18.8 18.8 18.8 18.7 18.7 18.8 19 19 18.7 19 19 18.6 19 19 19 19 19 19 18.2 18.5 18.3 17.94 1 KWSV041 CMPL Index 17.6 17.6 17.6 17.6 17.4 17.4 17.4 17.9 17.9 17.6 17.9 17.9 17.9 17.9 17.9 17.9 17.9 17.9 17.9 17.1 17.5 17.1 175 1 KWSV051 CMPL Index 17.1 17.6 17.1 17.1 16.8 16.8 16.8 17.1 17.3 17.3 17.3 17.3 17.3 17.3 17.3 17.3 17.3 17.3 17.3 16.9 17 16.4 16.66 1 KWSV061 CMPL Index #N/A N/A7 1 KWSV071 CMPL Index 15.6 15.6 15.6 15.6 16.4 16 15.6 15.9 15.9 16.5 15.9 15.9 15.9 15.9 15.9 15.9 15.9 15.9 15.9 16 15.9 15.2 15.28 1 KWSV081 CMPL Index #N/A N/A9 1 KWSV091 CMPL Index #N/A N/A
10 1 KWSV101 CMPL Index 15.2 15.2 15.2 15.2 15.8 15.2 15.2 15.6 15.6 15.9 15.6 15.6 15.6 15.6 15.6 15.5 15.7 15.6 15.6 15.5 15.4 15.1 15.312 1 KWSV121 CMPL Index #N/A Invalid Security1 2 KWSV012 CMPL Index 21.5 21.5 21.1 21.5 21.5 21.3 21.6 21.5 21.5 21.3 21.5 21.5 21.5 21.5 21.5 21.1 21.5 21.5 21.5 21.1 21 20.9 20.32 2 KWSV022 CMPL Index 18.9 18.9 19.3 18.7 19.3 19.3 19.3 19.4 19.4 19 19.4 19.4 19.4 19.4 19.4 19 19.4 19.4 19.4 18.9 18.3 18.7 18.23 2 KWSV032 CMPL Index 17.6 17.6 17.6 17.6 17.4 17.6 17.9 17.8 17.8 18.2 17.8 17.8 17.8 17.8 17.8 17.8 17.8 17.8 17.8 17.7 17.7 17.1 17.54 2 KWSV042 CMPL Index 16.4 16.4 16.4 16.4 16.5 16.4 16.4 16.8 17 17 17 17 17 17 17 17 17 17 17 16.5 16.7 16.2 16.35 2 KWSV052 CMPL Index 15.7 15.7 15.7 15.7 15.7 15.7 15.7 16.3 16.3 16.5 16.3 16.3 16.3 16.3 16.3 16.3 16.3 16.3 16.3 16 16.1 15.5 15.86 2 KWSV062 CMPL Index #N/A N/A7 2 KWSV072 CMPL Index 14.8 14.8 14.8 14.8 14.8 14.8 14.8 15 15 15.5 15 15 15 15 15 15 15 15 15 15 15 14.4 14.88 2 KWSV082 CMPL Index #N/A N/A9 2 KWSV092 CMPL Index #N/A N/A
10 2 KWSV102 CMPL Index 14.7 14.7 14.7 14.7 14.7 14.7 14.7 14.9 14.9 15.4 14.9 14.9 14.9 14.9 14.9 15.1 15.2 15.1 14.9 15 14.9 14.4 14.812 2 KWSV122 CMPL Index #N/A Invalid Security1 3 KWSV013 CMPL Index 20 20 20 20 19.7 20 20 20.1 20.4 20.2 20.4 20.4 20.4 20.4 20.4 20.4 20.4 20.4 20.4 19.6 19.9 19.9 19.32 3 KWSV023 CMPL Index 18 18 17.6 18 17.7 17.7 18.2 18.3 18.3 18.4 18.3 18.4 18.4 18.4 18.4 18.4 18.4 18.4 18.4 17.8 18.1 17.6 17.63 3 KWSV033 CMPL Index 16.5 16.5 16.5 16.5 16.6 16.5 16.8 16.8 16.8 17.5 16.8 16.8 16.8 16.8 16.8 16.8 16.8 16.8 16.8 16.8 16.7 16.2 16.64 3 KWSV043 CMPL Index 15.4 15.4 15.4 15.4 15.5 15.4 15.4 15.8 16 16.4 16 16 16 16 16 16 16 16 16 15.9 15.9 15.3 15.75 3 KWSV053 CMPL Index 14.7 14.7 14.7 14.7 15 14.8 14.8 15.1 15.3 15.7 15.3 15.3 15.3 15.3 15.3 15.3 15.3 15.3 15.3 15.3 15.3 14.7 156 3 KWSV063 CMPL Index #N/A N/A7 3 KWSV073 CMPL Index 14.1 14.1 14.1 14.1 14 14.1 14.1 14.2 14.2 14.8 14.2 14.2 14.2 14.2 14.2 14.3 14.4 14.2 14.2 14.3 14.2 13.9 14.18 3 KWSV083 CMPL Index #N/A N/A9 3 KWSV093 CMPL Index #N/A N/A
10 3 KWSV103 CMPL Index 14.2 14.2 14.2 14.2 14 14.2 14.2 14.2 14.2 14.6 14.2 14.2 14.2 14.2 14.2 14.3 14.4 14.4 14.2 14.3 14.2 13.9 14.112 3 KWSV123 CMPL Index #N/A Invalid Security
30
KRW swaptions from Bloomberg VOLM
no gaps ...KRW Swap term
Expiry 1 YR 2 YR 3 YR 4 YR 5 YR 6 YR 7 YR 8 YR 9 YR 10 YR 12 YR 15 YR 20 YR 25 YR 30 YR
1 YR 22.2% 20.7% 19.6% 18.8% 18.0% 17.4% 16.9% 16.6% 16.4% 16.3% 16.3% 16.3% 16.3% 16.3% 16.3%
2 YR 19.6% 18.5% 17.6% 16.7% 15.8% 15.2% 14.7% 14.5% 14.2% 14.0% 14.0% 14.0% 14.0% 14.0% 14.0%
3 YR 18.1% 17.3% 16.4% 15.5% 14.7% 14.0% 13.4% 13.3% 13.1% 13.0% 13.0% 13.0% 13.0% 13.0% 13.0%
4 YR 17.3% 16.5% 15.6% 14.8% 14.0% 13.5% 13.0% 12.7% 12.6% 12.4% 12.4% 12.4% 12.4% 12.4% 12.4%
5 YR 16.5% 15.7% 14.7% 14.0% 13.3% 12.9% 12.5% 12.3% 12.0% 11.8% 11.8% 11.8% 11.8% 11.8% 11.8%
6 YR 16.5% 15.7% 14.7% 14.0% 13.3% 12.9% 12.5% 12.3% 12.0% 11.8% 11.8% 11.8% 11.8% 11.8% 11.8%
7 YR 16.5% 15.7% 14.7% 14.0% 13.3% 12.9% 12.5% 12.3% 12.0% 11.8% 11.8% 11.8% 11.8% 11.8% 11.8%
8 YR 16.5% 15.7% 14.7% 14.0% 13.3% 12.9% 12.5% 12.3% 12.0% 11.8% 11.8% 11.8% 11.8% 11.8% 11.8%
9 YR 16.5% 15.7% 14.7% 14.0% 13.3% 12.9% 12.5% 12.3% 12.1% 11.8% 11.8% 11.8% 11.8% 11.8% 11.8%
10 YR 16.5% 15.7% 14.7% 14.0% 13.3% 12.9% 12.5% 12.3% 12.1% 11.9% 11.9% 11.9% 11.8% 11.8% 11.8%
12 YR 16.5% 15.7% 14.7% 14.0% 13.3% 13.0% 12.6% 12.4% 12.2% 12.0% 12.0% 11.9% 11.9% 11.9% 11.9%
15 YR 16.5% 15.7% 14.9% 14.2% 13.6% 13.2% 12.8% 12.6% 12.4% 12.2% 12.1% 12.1% 12.0% 12.0% 11.9%
20 YR 16.8% 16.0% 15.1% 14.5% 13.8% 13.4% 13.0% 12.8% 12.6% 12.3% 12.3% 12.2% 12.1% 12.0% 12.0%
25 YR 16.8% 16.0% 15.1% 14.5% 13.8% 13.4% 13.0% 12.8% 12.6% 12.3% 12.3% 12.2% 12.1% 12.0% 12.0%
30 YR 16.8% 16.0% 15.1% 14.5% 13.8% 13.4% 13.0% 12.8% 12.6% 12.3% 12.3% 12.2% 12.1% 12.0% 12.0%
31
Model vs target: swaption volsMarket vs Model Swaption Vols for Swap term 10
0%
2%
4%
6%
8%
10%
12%
14%
16%
18%
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75Time ( Yrs)
Swa
ptio
n vo
latil
ity
Lower LimitAverage
Upper LimitMarket Swaption Volat ilit ies
Illustration only, not a model of HKD2009.12.31
32
How do I know my simulations are good?
• Real world:averages, std deviations, other tests
• Risk neutral:martingale tests, other tests
• MC = Risk Neutral + fit to market values(bond price test, other market prices)
33
Martingale test illustration
• 10-year bond price
• 5% flat yield curve
• 10 simulations
Situation at simulation year 10Sim Cash
AccumDiscount
factorBond Index Value today of
$1 investmentin bonds
1 1.462 0.6842 1.641 1.1232 1.471 0.6798 1.184 0.8053 1.693 0.5905 1.634 0.9654 1.718 0.5820 1.934 1.1265 1.650 0.6060 1.802 1.0926 1.601 0.6248 1.376 0.8607 1.701 0.5879 1.954 1.1498 1.641 0.6095 2.319 1.4139 1.674 0.5972 2.064 1.23210 1.543 0.6481 1.419 0.920
Bond price test Martingale testTarget 0.607 1.000Sim average 1.615 0.621 1.733 1.069Discrepancy in bond price
absolute 1.4% 0.069proportional 2.4%
Rough 95% confidence intervallower 0.597 0.952upper 0.645 1.185
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Average asset class return vs cash return
• Unexpected implications of the martingale testAsset Measure Sim Year: 0 1 2
Cash returnsCash Return 1 4% 3%
2 6% 7%Average 5.00% 5.00%
Cash Discount factor 1 1 0.96 0.932 1 0.94 0.88Average 1.00 0.95 0.91
Version 1 Version 2Bond portfolio returns Year: 0 1 2 0 1 2Bond Return 1 15% 12% 15% 12%
2 -5% -2% -5.21% -4.56%Average 5% 5% 4.89% 3.72%
Bond Index 1 1 1.15 1.29 1 1.15 1.292 1 0.95 0.93 1 0.95 0.90Average 1.05 1.11 1.05 1.10
Martingale testBond Discounted FV 1 1 1.11 1.20 1.00 1.11 1.20
2 1 0.90 0.82 1.00 0.89 0.80Average 1.000 1.001 1.012 1.000 1.000 1.000
Martingale test discrepancy 0.000 0.001 0.012 0.000 0.000 0.000
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Getting started
• who will do the work?platform: in-house or outsourcedproduction: in-house or outsourcedvalidation: in-house or outsourced
• selection of the models
• calibration
• validation
• uses of the model
• interpretation of the results
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Outsource or build?
Three decisions
• platform
• production
• validation
Some considerations
• Initial development
• Future developmentstaffingstaying up to date
• Availability of expertisemodel validationinternal educationproblem-solvingstatus of the company
• Continuity
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Model selection (focus on NIR model)
• Many NIR models availableReading suggestion ... Brigo and Mercurio:Interest Rate Models – Theory and Practice
• Be aware of weaknesses of the model
• Different models for different purposes?
• A simple model may be enough
• I prefer ...to model forward rates rather than spot ratesmodels with fewer parametersparameters which can be interpreted intuitivelymodels which can be calibrated consistently for varying timesteps
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Model selection – RW vs RN
noyescan incorporate an investment viewyes (*)noeasy to calculate market pricesyesmaybeinternally consistentyesmaybemathematically tractablemaybeyesplausible interest rate dynamicsmaybeyesplausible distribution
Risk-Neutral
Real World
(*) needed for calibration
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Interest rate dynamics
• What we expect :Longer rates are less volatile than short ratesExtreme long rates don’t change muchRates at different terms are correlatedInterest rate volatility may be less when rates are low
• Implications of some modelsCox-Ingersoll-Ross modelHull-White modelBlack-Karasinsky modelLIBOR Market Model
• Empirical evidence
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Empirical interest rate volatility – HK(empirical measure related to vol)
Country: HK View: +ve and -ve changes Interval: 2 % Min # data points: 20
0
0.5
1
1.5
2
2.5
3
3.5
-2.00 0.00 2.00 4.00 6.00 8.00 10.00Interest Rate (%)
Del
ta
HK0.0833HK0.25HK0.5HK01HK02HK03HK05HK07HK10#N/A#N/A#N/A#N/A#N/A#N/A#N/A#N/A
0
50
100
150
-2.00 0.00 2.00 4.00 6.00 8.00 10.00Interest Rate (%)
Num
ber o
f Poi
nts
41
Empirical interest rate volatility – US(empirical measure related to vol)
Country: US View: +ve and -ve changes Interval: 2 % Min # data points: 20
0
0.5
1
1.5
2
2.5
0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.00Interest Rate (%)
Del
ta
US0.0833US0.25US0.5US02US03US05US10US30#N/A#N/A#N/A#N/A#N/A#N/A#N/A#N/A#N/A
050
100
150200
250
0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.00Interest Rate (%)
Num
ber o
f Poi
nts
42
Empirical relative vol of 3-month rate(empirical measure related to vol)
Term: 0.25 View: +ve and -ve changes Interval: 2 % Min # data points: 20
0
0.5
1
1.5
2
2.5
3
-2.00 0.00 2.00 4.00 6.00 8.00 10.00Interest Rate (%)
Del
ta
US0.25UK0.25JP0.25CN0.25HK0.25ID0.25MY0.25NZ0.25PH0.25SG0.25KR0.25#N/A#N/A#N/A#N/A#N/A#N/A
0
50
100
150
200
-2.00 0.00 2.00 4.00 6.00 8.00 10.00Interest Rate (%)
Num
ber o
f Poi
nts
43
Empirical relative vol of 10-year rate(empirical measure related to vol)
Term: 10 View: +ve and -ve changes Interval: 2 % Min # data points: 20
0
0.5
1
1.5
2
2.5
3
0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.00Interest Rate (%)
Del
ta
US10EU10UK10JP10AU10SH10HK10IN10ID10MY10NZ10PH10SG10KR10TW10TH10#N/A
050
100
150200
250
0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.00Interest Rate (%)
Num
ber o
f Poi
nts
44
Calibration
• Market-consistent modelcalibrate to market instrumentsextrapolate
• Real-worldparameters reflect our assumptions about the market
• Risk-neutral but not market consistentwhen is this appropriate?can choose parametersbut ... average market-consistent parameters are different from best-estimate parameters
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Basic validation
• Sampling error vs bias
• Correcting one bias may introduce other hidden biastake care if sims have been adjusted
• Market consistentbond price testmatch market prices of other instrumentsmartingale tests for various bond termsmartingale tests for other asset classes
• Real worldaverage returnsuncertainty of returns and rates
46
Use and interpretation :Application to asset strategy
• RW vs RN
• investment views
• Measures of value / return / utility
• Measures of risk
• Are the results reliable?
47
Communicating the meaning
• people don’t understand risk
• summarising the distribution
• risk/return is simplistic
• limitations of the model
48
Final thought
• We don’t have a very good understanding of market dynamics. So we should not be too sure that our models are a good representation of the market.