Economic Scenario Generation: Some practicalities. David Grundy October 2010

Transcription

1 Economic Scenario Generation: Some practicalities David Grundy October 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. 2

3 My experience of stochastic models Economic scenario generators Toy ESGs interest rate, equity, credit spread GeneSIS TSM * Projection models Traditional Prophet (A, L, S, G) LifeDFA (design phase) Spreadsheet projection models Application to ALM Interpretation of results 3

4 Agenda Reminder of Market-Consistent valuation philosophy Focus on market-consistent Nominal Interest Rate ( NIR ) model Market data Basic tests of model:market fit Model selection Getting started 4

5 What kind of model? Why? pricing guarantees MCEV understand the range of outcomes capital requirement MC MC RW depends Popular assets cash government bonds equity corporate credit NIR model NIR model equity risk model spreads defaults 5

6 Calculation of the value of guarantees Value on stochastic basis Generate 1,000 economic sims ( market-consistent basis) For each sim calculate the PVIF Take the average PVIF over all simulations Value on deterministic basis Single projection Discount profits at the Risk Free Rate PVIF Value many simulations Value Value mean deterministic MC value Time Value of Guarantees t Set of 1000 results 6

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. 7

8 Market-consistent values: calibration and extrapolation Complexity Very Hard! Life Insurance Business Use sims to value these Hard Easy Corporate bonds Swaptions Equity options Risk-free bonds Formulas or sims Time horizon 8

9 Risk-neutral sims vs Real-World sims different samples from the same underlying set of possible outcomes Possible market outcomes Future assets Discounted value RW RN RDR RFR t 9

10 Easy data sources for Market-Consistent calibration Model Market data Sources Interest rates level yield curve BBG, central banks volatility swaption volatility BBG, ibanks equity returns volatility implied volatility BBG, ibanks credit spreads level swap rates corp bond yields BBG BBG volatility?????? credit losses ignore this for now 10

11 NIR model rough conceptual framework initial yield curve in MC sims, this determines average future rates can be observed directly stochastic model of changes in short rates mathematical formulation & parameterisation can be fitted to swaption data calculation of full yield curve at each time step based on the mathematical model 11

12 NIR model: Initial yield curve The yield curve sets future average returns (MC) Derivatives are priced from swap rates no market-implied prices for govt bond volatility Most companies hold govt bonds swap 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 12

13 NIR model data problems Yield curves not straightforward Interest rate derivatives no caplets for most Asian markets swaption data is messy 13

14 NIR model data: Bloomberg yield curve Example: USD

15 Bloomberg yields summary Example: USD year rate is 0.445% 15

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. 16

17 More underlying data USD Govt curve at 2009YE (all issues) 5.0% 4.5% 4.0% 3.5% 3.0% 2.5% 2.0% 1.5% All bonds Reference 1.0% 0.5% 0.0%

18 Forwards (fitted to the reference rates) Example: Forward curve is a step function reproduces all the reference spot prices exactly Adding the off points fits better but is less smooth. 7% 6% 5% 4% An alternative is to fit a smooth curve to all the data. But... no smooth curve fits all the data. 3% 2% 1% 0% UST Actives Fwd UST On/Off the run Fwd UST Actives Spot (ZCB) UST On/Off the run Spot (ZCB)

19 A stressed curve USD Govt curve at 2008YE 3.5% 3.0% 2.5% 2.0% 1.5% 1.0% All bonds Reference 0.5% 0.0%

20 Is the interest rate model market-consistent? 1. Bond price test Cashflow of $100 in 10 years from now. Market price Price = Amount I need to invest to have $100 in 10 years = $100 * 1-year ZCB price = $100 * (say) 0.80 = $80 Model price different in each sim depends on cash accumulation over 10 years take the average 20

21 Bond price test illustration 10-year bond price 5% flat yield curve 10 simulations Error measure: Absolute or proportional? Situation at simulation year 10 Sim Cash Accum Discount factor Bond price test Target Sim average Discrepancy in bond price absolute 1.4% proportional 2.4% Rough 95% confidence interval lower upper

22 Model vs target: bond price test example Ratio of model price to market price (and model confidence limits) Expected Average Lower limit Upper limit Year Illustration only, not a model of USD

23 Average interest rate vs initial forward curve Unexpected implications of the bond price test Year: Initial forward curve Forward rate throughout the year 5% 5% ZCB Bond Price = 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 2 Asset Measure Sim Year: 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) Average Return backed out from average DF 4.99% 4.94% 5.00% 5.00% 23

24 NIR model dynamics (volatility, mean reversion, etc?) data sources deep and liquid markets swaption volatilities caplets (if available) swaptions vs caplets swaption volatility depends on yield curve depends on interest rate volatility characteristics 24

25 USD swaption data USD swaptions (Bloomberg VOLM, ) 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% 25

26 HKD swaption data HKD swaptions (Bloomberg VOLM, ) 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% 26

27 HK Swaption vol surface (VOLM ) 70.0% 60.0% 50.0% 60.0%-70.0% 40.0% 50.0%-60.0% 30.0% 40.0%-50.0% 30.0%-40.0% 20.0% 20.0%-30.0% 10.0% 0.0% 1 YR 3 YR 5 YR Option term 7 YR 9 YR 12 YR 20 YR 30 YR 1 YR 10.0%-20.0% 6 YR 0.0%-10.0% 12 YR Swap term 27

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 YR 1 YR 7.1% 2.8% 3.0% 4.5% 3.2% 4.9% n/a n/a n/a n/a n/a 2 YR 1.1% 3.3% 3.6% 4.7% 3.4% 4.4% n/a n/a n/a n/a n/a 3 YR 1.9% 3.3% 4.1% 4.5% 5.4% 4.9% n/a n/a n/a n/a n/a 4 YR 4.3% 4.4% 3.4% 4.1% 4.4% 4.8% n/a n/a n/a n/a n/a 5 YR 3.8% 4.1% 5.8% 2.9% 4.1% 3.1% n/a n/a n/a n/a n/a 6 YR n/a n/a n/a n/a n/a 7 YR 2.6% 3.6% 2.2% 4.5% 2.9% 1.4% n/a n/a n/a n/a n/a 8 YR n/a n/a n/a n/a n/a 9 YR n/a n/a n/a n/a n/a 10 YR -3.8% 1.9% 1.9% 3.0% 1.2% -0.5% n/a n/a n/a n/a n/a 12 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 15 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 20 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 25 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/a28 30 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 missing Many quotes appear to be inactive Option Swap Ticker KWSV011 CMPL Index KWSV021 CMPL Index KWSV031 CMPL Index KWSV041 CMPL Index KWSV051 CMPL Index KWSV061 CMPL Index #N/A N/A 7 1 KWSV071 CMPL Index KWSV081 CMPL Index #N/A N/A 9 1 KWSV091 CMPL Index #N/A N/A 10 1 KWSV101 CMPL Index KWSV121 CMPL Index #N/A Invalid Security 1 2 KWSV012 CMPL Index KWSV022 CMPL Index KWSV032 CMPL Index KWSV042 CMPL Index KWSV052 CMPL Index KWSV062 CMPL Index #N/A N/A 7 2 KWSV072 CMPL Index KWSV082 CMPL Index #N/A N/A 9 2 KWSV092 CMPL Index #N/A N/A 10 2 KWSV102 CMPL Index KWSV122 CMPL Index #N/A Invalid Security 1 3 KWSV013 CMPL Index KWSV023 CMPL Index KWSV033 CMPL Index KWSV043 CMPL Index KWSV053 CMPL Index KWSV063 CMPL Index #N/A N/A 7 3 KWSV073 CMPL Index KWSV083 CMPL Index #N/A N/A 9 3 KWSV093 CMPL Index #N/A N/A 10 3 KWSV103 CMPL Index KWSV123 CMPL Index #N/A Invalid Security 29

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% 30

31 Model vs target: swaption vols Market vs Model Swaption Vols for Swap term 10 Illustration only, not a model of HKD Swaption volatility 18% 16% 14% 12% 10% 8% 6% 4% 2% 0% Lower Limit Av erage Upper Limit Market Swaption Volatilities Time (Yrs) 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) 32

33 Martingale test illustration 10-year bond price 5% flat yield curve 10 simulations Situation at simulation year 10 Sim Cash Accum Discount factor Bond Index Value today of $1 investment in bonds Bond price test Martingale test Target Sim average Discrepancy in bond price absolute 1.4% proportional 2.4% Rough 95% confidence interval lower upper

34 Average asset class return vs cash return Unexpected implications of the martingale test Asset Measure Sim Year: Cash returns Cash Return 1 4% 3% 2 6% 7% Average 5.00% 5.00% Cash Discount factor Average Version 1 Version 2 Bond portfolio returns Year: Bond Return 1 15% 12% 15% 12% 2-5% -2% -5.21% -4.56% Average 5% 5% 4.89% 3.72% Bond Index Average Martingale test Bond Discounted FV Average Martingale test discrepancy

35 Getting started who will do the work? platform: in-house or outsourced production: in-house or outsourced validation: in-house or outsourced selection of the models calibration validation uses of the model interpretation of the results 35

36 Outsource or build? Three decisions platform production validation Some considerations Initial development Future development staffing staying up to date Availability of expertise model validation internal education problem-solving status of the company Continuity 36

37 Model selection (focus on NIR model) Many NIR models available Reading 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 rates models with fewer parameters parameters which can be interpreted intuitively models which can be calibrated consistently for varying timesteps 37

38 Model selection RW vs RN plausible distribution plausible interest rate dynamics mathematically tractable internally consistent easy to calculate market prices can incorporate an investment view Real World yes yes maybe maybe no yes Risk- Neutral maybe maybe yes yes yes (*) no (*) needed for calibration 38

39 Interest rate dynamics What we expect : Longer rates are less volatile than short rates Extreme long rates don t change much Rates at different terms are correlated Interest rate volatility may be less when rates are low Implications of some models Cox-Ingersoll-Ross model Hull-White model Black-Karasinsky model LIBOR Market Model Empirical evidence 39

40 Empirical interest rate volatility HK (empirical measure related to vol) Country: HK View: +ve and -ve changes Interval: 2 % Min # data points: HK HK HK0.5 HK HK02 HK03 HK05 2 HK07 HK #N/A #N/A 1 #N/A #N/A 0.5 #N/A #N/A 0 #N/A #N/A Interest Rate (%) Delta Number of Points Interest Rate (%) 40

41 Empirical interest rate volatility US (empirical measure related to vol) Country: US View: +ve and -ve changes Interval: 2 % Min # data points: US US0.25 US0.5 2 US02 US03 US US10 US30 #N/A 1 #N/A #N/A #N/A 0.5 #N/A #N/A #N/A 0 #N/A #N/A Interest Rate (%) Delta Number of Points Interest Rate (%) 41

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 Delta Interest Rate (%) US0.25 UK0.25 JP0.25 CN0.25 HK0.25 ID0.25 MY0.25 NZ0.25 PH0.25 SG0.25 KR0.25 #N/A #N/A #N/A #N/A #N/A #N/A Number of Points Interest Rate (%) 42

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: Delta Interest Rate (%) US10 EU10 UK10 JP10 AU10 SH10 HK10 IN10 ID10 MY10 NZ10 PH10 SG10 KR10 TW10 TH10 #N/A Number of Points Interest Rate (%) 43

44 Calibration Market-consistent model calibrate to market instruments extrapolate Real-world parameters reflect our assumptions about the market Risk-neutral but not market consistent when is this appropriate? can choose parameters but... average market-consistent parameters are different from best-estimate parameters 44

45 Basic validation Sampling error vs bias Correcting one bias may introduce other hidden bias take care if sims have been adjusted Market consistent bond price test match market prices of other instruments martingale tests for various bond terms martingale tests for other asset classes Real world average returns uncertainty of returns and rates 45

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? 46

47 Communicating the meaning people don t understand risk summarising the distribution risk/return is simplistic limitations of the model 47

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. 48