Session 174 PD, Nested Stochastic Modeling Research. Moderator: Anthony Dardis, FSA, CERA, FIA, MAAA. Presenters: Runhuan Feng, FSA, CERA

Transcription

1 Session 174 PD, Nested Stochastic Modeling Research Moderator: Anthony Dardis, FSA, CERA, FIA, MAAA Presenters: Anthony Dardis, FSA, CERA, FIA, MAAA Runhuan Feng, FSA, CERA SOA Antitrust Disclaimer SOA Presentation Disclaimer

2 Nested Stochastic Modeling Research Tony Dardis 2016 SOA Annual Meeting & Exhibit October 26, 2016, 12pm 1.15pm

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4 Nature of the Beast Taken from presentation by Tony Dardis (at the time with Moody s Analytics) at 2014 SOA Annual Meeting & Exhibit Session 88 PD ERM s Quantitative Components: Stress Testing and Economic Capital 3

5 Candidates to Tame the Beast (per the AAA Model Efficiency Work Group) Actuarial and Modeling Techniques Technology Solutions Scenario Design & Selection Hardware Design Mathematical and/or Model Design Software Design Model Data Building Techniques Hybrid Techniques 4

6 Thank you

7 2016 SOA study on nested stochastic modeling Jointly sponsored by SOA financial reporting section and modeling section

8 Background Nested stochastic modeling Do we really need it? More regulatory requirements move towards dependence on stochastic modeling Computational burden grows exponentially with nested modeling Run time can be too long to get results and take actions in a timely manner Stronger desire for efficient techniques

9 Purpose To create a resource to help financial reporting actuaries answer the following questions: Q1: In what situations is nested stochastic modeling commonly used? Q2: What other approaches can be used instead of nested stochastic modeling? Q3: What techniques can be used to accelerate the run time for nested stochastic modeling?

10 2016 SOA survey on nested stochastics Survey conducted in December 2015-January 2016 Sent to members of financial reporting section and modeling section Requested one response from each company Excluded consulting firms and software vendors 18 insurance companies participated in the survey and the majority of them focus on life and annuities

11 Survey content Part I: Context of survey participants Part II: Infrastructure and practice on general stochastic modeling Part III: Circumstances for nested stochastic modeling Part IV: Implementation Part V: Methodologies Part VI: Parting comments

12 Context of survey participants Total statutory assets at 12/31/2014 including separate accounts

13 Context of survey participants Approximate breakdown of assets backing each major product line (including separate accounts)

14 Context of survey participants Approximate breakdown of assets backing each major product line (including separate accounts)

15 Q1: In what circumstances is nested stochastics commonly used?

16 Q1: In what circumstances is nested stochastics commonly used? In what situations do you plan to use nested stochastic modeling in the future?

17 Q1: In what circumstances is nested stochastics commonly used? For which products do you plan to use nested stochastic modeling?

18 There are often possible competing factors that affect your decision to adopt a new stochastic modeling technique (e.g. a trade-off between efficiency and accuracy). Please identify the relevant factors on a scale of 1 to 5, where 1= least important at all, 5= most important Average of all respondents Average of those who plan to use nested stochastics Average of those with clear priorities

19 Important factor for adopting new technology in nested stochastics The three most important factors that affect an insurance company s decision to adopt a new stochastic modeling technique are: (in the order of importance by average rating) Timeliness of result delivery Accuracy Ability to interpret results

20 Nested stochastic modeling Nested stochastic modeling is theoretically required in a stochastic calculation where certain financial components are themselves stochastically determined.

21 Monte Carlo methods Crude Monte Carlo (easy to implement; can be extremely time-consuming) Optimal Budget Allocation (easy to implement; existing allocation strategies depend on specific risk measures) Sequential allocation (ideal use of resources; can be slow due to dynamic allocation)

22 Sequential budget allocation

23 Three categories of methods to improve efficiency Optimal allocation of resources between inner loops and outer loops Optimal budget allocation Sequential allocation Replace inner loops by approximations Analytical methods Partial differential equation methods Reduce inner loops by curve fitting techniques Preprocessed inner loops Least squared Monte Carlo Least squared Monte Carlo with basis selection

24 Preprocessed inner loops Pros Easy to understand and implement Accurate in low dimension Cons May be difficult to determine boundary points for interpolation Requires large grid in high dimensions Path-dependence (can be addressed by adding dimensions)

25 Least squared Monte Carlo Pros Accurate in low dimension Can be used for extrapolation Cons Little guidance for basis functions (can be addressed by basis selection techniques)

26 Least squared Monte Carlo Ordinary LSMC Response variable: risk metric (y) Predictor variable: time, risk factors (t, x) y=f(t,x) where f(t,x)=t+t^2+x+x^2+tx Can be more sophisticated with stepwise regression LSMC with basis selection More intelligent selection of bases from exponential functions

27 LSMC with basis selection

28 Partial differential equation methods Pros High efficiency by simultaneous computation of risk neutral values Cons Require expertise for stochastic analysis May require special algorithms for high dimensions

29 Test case II: AG-43 CTE calculation for guaranteed minimum withdrawal benefits Outer loop (AG-43 reserving CTE best efforts) Under each scenario of equity returns, we determine cash flows from separate accounts (withdrawal payments, step-up payments, interest on surplus, rider charges, management fees) and the cash flows from the hedging portfolio (buy and sell of index futures and bonds). The change in surplus is determined by the following recursive relation over each period. Change in surplus = Fee income + Surrender charge GLWB withdrawals Expenses +Investment income on cash flows Change in asset values +Investment income on surplus. An inner loop calculation is invoked every time a dynamic hedging portfolio is rebalanced.

30 Test case II: AG-43 CTE calculation for guaranteed minimum withdrawal benefits Inner loop (hedging program) The delta,, of the GLWB rider, which determines how many units of index futures to hold in the hedging portfolio, is calculated as follows. (1) Evaluate the risk-neutral value of the GLWB rider with the then-current account value and the then-current guarantee base. (2) Shock the then-current account value by 1% and evaluate the risk-neutral value of the GLWB rider. (3) Determine the delta by the difference quotient of riskneutral values.

31 How does a PDE method work?

32 Model validation: accuracy test Valuation basis for closed-form solution

33 Model validation: accuracy test

34 Model validation: accuracy test

35 Comparative analysis: efficiency test

36 Comparative analysis: efficiency test

37 Comparative analysis: efficiency test

38 Comparative analysis: efficiency test

39 Accuracy versus complexity Why bother with 5% improvement of accuracy at the expense of introducing more complex machinery? The above-described calculation is required for every node of outer loop scenario. All computations are done on an imac with 2.7 GHz Intel Core i5 and 8 GB 1600 MHz DDR3.

40 Advantage of PDE methods PDE algorithm marches through all time-space grid points, thereby producing risk-neutral values all at once.

41 AG-43 CTE(best efforts) Sigma=0.3 Terminal surplus before and after hedging Four dimensional models for LSMC & Preprocessed (time, AV, GB, lapse rate)

42 AG-43 CTE(best efforts) Sigma=0.1 Terminal surplus before and after hedging Four dimensional models for LSMC & Preprocessed (time, AV, GB, lapse rate)

43 AG-43 CTE(best efforts) Sigma=0.1 Terminal surplus before and after hedging Two dimensional models for LSMC & Preprocessed (time, AV/GB)

44 Thank you! Special thanks to the POG and Ronora Stryker for their suggestions. Final reports for this research study as well as the industrial survey will be published by the SOA. Draft available upon request. Suggestions and comments are greatly appreciated!