Economic Scenario Generation: Some practicalities David Grundy July 2011
my perspective stochastic model owner and user practical rather than theoretical 8 economies, 100 sensitivity tests per economy interested in robust methodology and processes All my comments today are my own views. These may differ from the view of my employer. 2
Agenda Getting started Focus on the interest rate model Yield curve data Model selection Market data for volatility calibration Conclusions 3
Solvency II model components RSG = Risk Scenario Generator Generate (say) 100,000 1-year shocks. ESG = Economic Scenario Generator Generate (say) 1000 long-term market outcomes CPM = Cashflow Projection Model Cashflows in each economic scenario Lite Model Predict the outcome of ESG + CPM 4
Some themes Building your own ESG is easy. (But building a good ESG is a lot of work.) Calibration is more difficult than it seems. Validation of sim sets is always needed. 5
Getting started
Outsource or build? Some considerations Initial development Future development Availability of expertise Continuity 7
Outsource or build? Three main decisions Platform Production Validation 8
Model selection RW vs RN plausible distribution plausible interest rate dynamics mathematically tractable internally consistent closed-form calculation of prices can incorporate an investment view Real World yes yes maybe maybe maybe yes Risk- Neutral maybe maybe yes yes yes (*) no (*) needed for calibration 9
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. 10
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 11
Calibration and extrapolation processes Do we make good use of available data? Is the method stable? Are results sensible? Will it work when markets are stressed? Extrapolation of targets Economically plausible? Justifiable? Can the method be used for sensitivity tests? 12
Easy data sources for Market-Consistent calibration Model Market price data Easy Sources Interest rates level yield curve BBG, central banks volatility swaption volatility BBG, ibanks equity returns volatility implied volatility BBG, ibanks corporate bond spreads level swap rates BBG corp bond yields BBG volatility??? (history?)??? (BBG) corporate bond loss rates volatility??? (history?)??? (Moodys, S&P) Prices from deep and liquid markets?? 13
Calibration approach Market-consistent model calibrate to market instruments extrapolate Real-world parameters reflect our assumptions 14
Nominal Interest Rate (NIR) model: Data problems 1. Yield curves not as easy as they seem 2. Interest rate derivatives no caplets for most Asian markets swaption data is messy 15
Market-consistent interest rate model Yield curve
NIR model: Initial yield curve The yield curve determines future average returns Derivatives are priced from swap rates must calibrate using swap rate Most cashflow models need govt bond rates invested assets statutory valuation basis 17
NIR model data: Bloomberg yield curve Example: USD Treasury Curve 2009.12.31 18
Bloomberg yields summary Example: US Treasuries 2009.12.31 1-year rate = 0.445% 19
Underlying bond yield data US Treasuries 2009.12.31 Bloomberg 1-year rate = 0.445 But... reference bond is 11.5 months. 2010.12.16 We can estimate the 1-year rate: ~~ 0.500 20
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% 0 5 10 15 20 25 30 35 21
Forwards (fitted to the reference rates) Example: Forward curve is a step function reproduces all the reference spot prices exactly Additional reference terms will change the fit. An alternative is to fit a smooth curve to all the data. 7% 6% 5% 4% 3% 2% 1% 0% UST Actives Fwd UST On/Off the run Fwd UST Actives Spot (ZCB) UST On/Off the run Spot (ZCB) 0 10 20 30 But... no smooth curve fits all the data. 22
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% 0 5 10 15 20 25 30 35 23
Is the interest rate model market-consistent? 1. Bond price test example Cashflow of $100 in 10 years from now. Market price Assume interest rate = 5% 10-year discount factor = 1.05 ^ -10 = 0.614 Model price different in each sim depends on cash accumulation over 10 years take the average 24
Bond price test example 10-year bond price 5% flat yield curve 3 simulations Situation at projection year 10 Sim Cash Accumulation Discount factor 1 1.457 0.686 2 1.569 0.637 3 1.670 0.599 Average 0.641 Bond price test Market price of 10-year ZCB 0.614 Proportional error 4.4% 95% confidence interval (approx) lower 0.592 upper 0.692 25
Model bond price / market bond price 1.4 1.3 1.2 Mean 95% confidence Target 1.1 1.0 0.9 0.8 0 1 2 3 4 5 6 7 8 9 10 Example Bond term 26
Model bond price / market bond price 1.4 1.3 1.2 Mean 95% confidence Target 1.1 1.0 0.9 0.8 0 1 2 3 4 5 6 7 8 9 10 Example Bond term 27
Market-consistent interest rate model Model selection
Model selection (focus on NIR model) Many NIR models available 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 with consistent results using different timesteps 29
Nominal Interest Rate (NIR) model central path for cash returns implied by today s forward curve can be observed directly stochastic model of changes in cash rates mathematical formulation & parameterisation random event at each time step calibrate to today s prices for interest rate derivatives calculation of full yield curve at each time step based on the mathematical model yield curve at time t the expected path of the short rate 30
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 31
Stylised volatility characteristics of short rates volatility of yield CIR Hull-White Black Karasinski yield 32
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 3 2.5 2 1.5 1 0.5 0-2.00 0.00 2.00 4.00 6.00 8.00 10.00 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 200 150 100 50 0-2.00 0.00 2.00 4.00 6.00 8.00 10.00 Number of Points Interest Rate (%) 33
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 3 2.5 2 1.5 1 0.5 0 Delta 0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.00 Interest Rate (%) US10 EU10 UK10 JP10 AU10 SH10 HK10 IN10 ID10 MY10 NZ10 PH10 SG10 KR10 TW10 TH10 #N/A 250 200 150 100 50 0 0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.00 Number of Points Interest Rate (%) 34
Empirical interest rate volatility HK (empirical measure related to vol) Country: HK View: +ve and -ve changes Interval: 2 % Min # data points: 20 3.5 HK0.0833 HK0.25 3 HK0.5 HK01 2.5 HK02 HK03 HK05 2 HK07 HK10 1.5 #N/A #N/A 1 #N/A #N/A 0.5 #N/A #N/A 0 #N/A -2.00 0.00 2.00 4.00 6.00 8.00 10.00#N/A Delta Interest Rate (%) 150 100 50 0-2.00 0.00 2.00 4.00 6.00 8.00 10.00 Number of Points Interest Rate (%) 35
Empirical interest rate volatility US (empirical measure related to vol) Country: US View: +ve and -ve changes Interval: 2 % Min # data points: 20 2.5 US0.0833 US0.25 US0.5 2 US02 US03 US05 1.5 US10 US30 #N/A 1 #N/A #N/A #N/A 0.5 #N/A #N/A #N/A 0 #N/A 0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.00#N/A Delta Interest Rate (%) 250 200 150 100 50 0 0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.00 Number of Points Interest Rate (%) 36
Market-consistent interest rate model Data for volatility calibration
NIR model dynamics (volatility, mean reversion, etc?) data sources deep and liquid markets caplets (if available) swaption implied volatilities (Cost today of an option to lock in a future interest rate) Today s forward yield curve Option term (eg 20 years) Exercise date Swap term (eg 15 years) years 38
USD swaption data 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% 39
HKD swaption data Bloomberg VOLM, 2009.12.31 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% 40
HK Swaption vol surface (VOLM 2009.12.31) 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 41
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/a42 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
Validation: Model vs market Market vs Model Swaption Vols for Swap term 10 Illustration only S wap tion volatility 18% 16% 14% 12% 10% 8% 6% 4% 2% 0% Lower Limit Av erage Upper Limit Market Swaption Volatilities 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 7 5 Time ( Yrs) 43
Conclusions
Basic validation for market consistent sims Some possible tests bond price test match market prices of other instruments martingale tests for various bond terms martingale tests for other asset classes mean, std devn, etc for each asset class correlations Sampling error vs bias Correcting one bias may introduce other hidden bias take care if sims have been adjusted 45
Can validation be outsourced? Expertise Responsibility Credibility 46
Outsource or DIY? Three decisions three different suggestions Platform Production Validation 47
Final thought Don t have too much faith in your model. 48