economic scenario generation: some · pdf file3 my experience of stochastic models...

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

34

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

35

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

36

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

37

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

38

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

39

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

40

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

45

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.