The 3 rd Younger Members Convention

1. The 3rd Younger Members Convention 29-30 November 2004, The Chesford Grange Hotel, Kenilworth

2. Practical Issues in Stochastic Modelling Michael Payne 30 November 2004

3. Agenda • Stochastic Model Overview • Model Points • Economic Scenario Generator • Dynamic Decisions and Policyholder Actions • Communication • Controls

4. Financial Condition Report Graphs with distributions of key financial data Policy data grouped into “model points” Management of With-Profits Fund Stochastic model For each market scenario input this projects future revenues and balance sheets for the model points based on the decision rules and demographic assumptions input Revenue accounts and other data (bonus rates, etc) for each simulation Demographic assumptions - future mortality, persistency Individual Capital Assessment Bonus and investment decision rules Economic Scenario Generator Calculates a series of future market scenarios based on the input factors. These may be market consistent or realistic. A market scenario is a set of projections of equity returns, fixed interest yields, etc. Calculation of expected guarantee costs Realistic Balance Sheet Market scenarios Market calibration assumptions Inputs Stochastic Model - Overview Outputs Calculations

5. Complex Models • Long projection periods • Large numbers of model points • Lengthy run times • The requirement to warehouse large volumes of data • Better buy shares in Compaq?

6. Individual policy data Grouped policy data Group data Projects cashflows for individual data Projects cashflows for grouped data Stochastic Model Cashflows for individual data Cashflows for grouped data Compare outputs Yes, input to Model No, redo Results OK? Model Points

7. Model Points • Why construct Model Points ? - Memory constraints mean that we cannot run the 2 million ungrouped model points • What is the process? - Individual policy data are separated into the broad product groupings - A data manipulation package is then used to produce representative model points - There is a trade-off between the number of model points (and hence speed of the model) and how representative the grouped model points are. • How do we test the accuracy of our Model Points ? - The grouped model points are run through an actuarial liability model and compared to the original model points. - The important comparisons depend on the purpose e.g. guarantee costs for RBS work

8. Asset model choice/calibration What does market consistency mean? 7.4.168 R The market-consistent asset model in PRU 7.4.167R(1): (1) means a model that delivers prices for assets and liabilities that can be directly verified from the market; and (2) must be calibrated to deliver market-consistent prices for those assets that reflect the nature and term of the with-profits insurance liabilities of the with-profits fund.

9. Asset model choice/calibration • Price is not defined by a single model so any calibrated model is unlikely to fit all observable data. • There are few instruments of the right term and duration that look like an insurer’s portfolio • Extrapolation from short-term over 40 years is a “Herculean” assumption. • Is it spurious to worry about “moneyness” structures over 40 years? • Constant volatility often assumed even though we know it isn’t • Data suggests stability over the long-term.

10. Asset model choice/calibration • Cannot avoid the maths and delegate responsibility for completeness and appropriateness • Martingale tests for all asset classes • How many simulations should be used? • Central limit theorem/standard errors • How big an unexplained item do you want in your analysis of surplus? • How big are you prepared “unexpected” movements to be?

11. Policyholder Behaviour • Models should allow for policyholder behaviour • 7.4.57 R Policyholder actions refer to the foreseeable actions that would be taken by the firm’s policyholders, taking into account: (1) the experience of the firm in the past; and (2) the changes that may occur in the future if options and guarantees become more valuable to policyholders than in the past.

12. Policyholder Behaviour • Realism sought • Allow for likely option take-up rates • WP Bonds spot guarantee dates at key policy anniversaries • Tax-free cash in GAOs • Material guaranteed surrender values • Irrational policyholders • Limited data in extreme conditions • Contradictory data • WP PVIF value offsets

13. Dynamic Management Actions • Dynamic management actions are available to mitigate risk • 7.4.50 R In calculating the risk capital margin for a with-profits fund, a firm may reflect, in its projections of the value of assets and liabilities under the scenarios in PRU 7.4.42R, the firm’s prospective management actions (see PRU 7.4.51R). • But assumptions need to be reasonable 7.4.51 R Prospective management actions refer to the foreseeable actions that would be taken by the firm’s management, taking into account: (1) an appropriately realistic period of time for the management actions to take effect; and (2) the firm’s PPFM and its regulatory duty to treat its customers fairly.

14. Dynamic Management Actions • Why do we want to the model to make dynamic decisions? • Complex office behaviour needs replicated by model if it’s to be realistic • More useful if it’s realistic • Capital requirements based on the output of these models • Unnecessary prudence undesirable

15. Investment Decisions • Manage exposure to risky assets • Explicit stress test of the balance sheet in line with RCM (-20% equity and/or –100bps gilt yields) • Run times • Complexity • Closed fund projections • Implicitly through proxy based on FTSE • Simple

16. Regular Bonus Decisions • Projected affordability/sustainability • Smoothing of changes from one year to the next

17. Testing and checking • Start deterministic • Then scenarios • Then percentiles from stochastic • Worth the effort on • Accurate specifications • Detailed test plans • Extensive testing • Enlist the help of expert in their own areas • Extreme returns break code • “Div almost zero” errors • Taylor’s theorem relies on small interest rate deltas • Third parties can add value in reviewing • Simulation walkthrough

18. Model controls • It’s complex • Unit admin, quotation/projection and valuation systems all rolled into one! • Complexity means that it is infeasible to audit? • Sign off of the initial model • Ongoing audit trails and controls • Sign-off of master model for all purposes based on full stochastic run • Sign off of the model following a model update • Test grouped model points remain appropriate • Recalibrate and check again the economic scenario files

19. Output analysis • Analyses of change • BSM instructive • Crude deltas and other Greeks • Explanation of results from one period to the next • Changes in model • Changes to management actions • Changes in intrinsic component • Changes in time value component

20. Communication • Explaining the results is tricky! • Who is the audience ? • Actuarial / Technical • Executive • Regulator • What message are we trying to get across ? • What is the purpose of the results • What are the key messages from the results • What action should I take (if any) given this information

21. Communication • How should the results be presented ? • Single point estimate • Confidence Intervals • Percentile Graphs

22. Future Developments • RBS results currently required to go to FSA within 3 months (of year end) • FRED34 / FRS27 means that WP Funds need to be valued stochastically - results required within 2 weeks • Results rolled forward • Risk of actual being significantly different than expected • Risk of R&A differing from FSA submission • Models and methodology still being developed • Will auditors be happy to sign off on working day 10 “estimates” • Future investment decisions based on Peak 1 / Peak 2 solvency position • Stochastic within stochastic • Calibration of closed form in future time periods

23. Some statistics from a real model • Scenarios • 2000 scenarios • 95% Confidence Interval of +/- £20m • Hardware • 200 Worker PCs • Run Time • Less than 20 minutes for one scenario • 40 year monthly projection • 500 Simulations in an hour

24. Summary • Useful tool to understand dynamics of complex liabilities • Still in its infancy • Keeping things understandable is important • Thousands of model inputs and outputs • Complex models requires extensive testing • Strong auditable controls around master model developments • Tailor the output to the user The key challenge is to develop a well controlled process that produces explainable results in time to meet tight shareholder (or other) reporting deadlines