Asset Liability Management for Life Insurance: a Dynamic Approach

Transcription

1 Risk Consulting CAPITAL MANAGEMENT ADVISORS srl Asset Liability Management for Life Insurance: a Dynamic Approach Dr Gabriele Susinno & Thierry Bochud Quantitative Strategies Capital Management Advisors Madrid May, 23 rd, 2001

2 Contents Capital Management Advisors. Introduction: Life Insurance Embedded Options Actuarial Probabilities Insurance Market Evolution Integrated Dynamic ALM Control Parameters: Dynamic Hedging Further Developments: Optimal Control, Passport Options, Technological and Computational Issues Final Remarks 2

3 Capital Management Advisors: who we are CAPITAL MANAGEMENT ADVISORS (CMA) is a company providing specialised advisory services in the field of asset management CMA's target clients are institutional investors such as insurance companies, asset managers, pension funds, foundations and banks CMA is a partnership between Arthur Andersen and a Team of professionals with extensive experience in financial markets. CMA is a company of Arthur Andersen 3

4 Life Insurance Contracts with Minimum Guaranteed Return Insurance Contract: Entitles the policy holder to earn the maximum between a guaranteed yield and a participation β on the segregated fund performance. Given the Lifetime of the contract T and an initial investment I 0 (or a periodic payment π). Payout Premiums At maturity if survival: Endowment Conditional on death: Term or Surrender Single annual and constant annual and indexed Whole life insurance = Endowment + Term 4

5 Two types of guaranty Segregated Fund European like Minimum Guaranteed Return Cliquet Minimum Guaranteed Return The Company may withdraw his benefits during the life of the contract. This is done either on a quarterly or annual basis. Strike resets in the cliquet guaranty The insured will receive a final payment which is the maximum between a minimum guaratee and the value of the segregated fund return times his participation rate β. Maturity Ψ L T A T A0 ( A ) = L max ( 1+ r ) ; + β T 0 g 1 A 0 5

6 Cliquet Dynamics 10^3 Scenarios Σ 6

7 Embedded Options Strike Segregated Fund 1-β Claim given to the Company 1-β K K K/β NAV at maturity K K/β Premium 7

8 Insurance Guarantees as Financial Contingent Claims Brennan & Schwartz (1976) Pricing of Equity-Linked Life Insurance Policies with Asset Value Guarantee Boyle & Schwartz (1977) Equilibrium Prices of Guarantees under Equity-Linked Contracts Bacinello & Ortu (1993) Pricing Equity-Linked Life Insurance with Endogenous Minimum Guarantee Grosen & Iorgensen (1997) Fair Valuation of Life Insurance Guarantees Brys & de Varenne (1997) On the Risk of Life Insurance Liabilities: Debunking Some Common Pitfalls Susinno & al (2000) Insurance Optional Consiglio, Cocco & Zenios (2001) Scenario Optimization Asset and Liability Modeling for Endowments with Guarantees 8

9 Low Interest rates: Impact on the Interest Margin 12 % % Italian Government Benchmark 10Y Italian Government Benchmark 10Y Average Returns Policyholder Returns % 9.05% % 7.91% % 6.89% % 5.59% 4 Minimum Guaranteed Rate

10 Needs to enhance financial risk exposure Interest Margin Competition Push Push towards a major major exposition to to financial risk risk (Stocks, Corporate, ) ) % 60% 16% Treasury Corporate Azioni Altro 21% 14% Fondi Comuni 3% 4% 5% 5% 10

11 Old Eldorado New Mess 11

12 Adding Actuarial Probabilities & annual premiums Π t = N i= 1 ζ C + i i () t Whole Life Insurance: The Policyholder owns the right to exercise the guaranty at all possible exit times (American like exercise) conditional on a contractually defined event. Due to independence between mortality and financial Assets The exit may not triggered by a market event! The portfolio must be continuously re-balanced Portfolio Egineering & Dynamic Asset Allocation 12

13 Two sources of randomness Financial Financial Risk Actuarial Risk The option payoff depends on 2 orthogonal sources of randomness: Financial risk due to the development of the assets. Actuarial Risk. The payoff is not triggered by a market event but it is possible to estimate the probability of a claim C at a time t. ALM: Construct a Strategy to minimize financial risk 13

14 Mutual Aspects For one insured only a fraction of the guaranteed amount is protected at each possible exit time while 100% of the payof has to be given to the insured (Dirac*100%) T = Maturity With a large number of insured the uncertainty on the amount of capital to cover for each possible exit time is reduced and we are left with the volatility of actuarial estimations. 14

15 Target Practical Management Actions: Immunise the downside risk of the shorted put. Portfolio Insurance Define investment classes and optimal strategies. The control parameter is the mix between cash and risky assets!!! 15

16 Dynamic Asset Allocation Sensitivity: Contract s Structure Actual value of the guaranteed level Actuarial probabilities Segregated Fund Stat. Prop. Transaction Costs and Regulatory Constraints Dynamic Asset Allocation Strategy!!! CASH Simple Experiment 16

17 Death Probabilities Let with : F ( > t) = 1 F ( t) () t = f ( s) where () t ds; is the probability that the death of a subject belonging to the class a will die in the time interval T a a P T f a t a a, be the survival probability [ t; t + dt]. is the time - to - death of a the class a Few tools and definitions a. Define as well the hazard rate given the survival up to time t m a () t f a = 1 F () t () t. a : m a () t as the conditional probability in the interval [ t; t + dt] 17

18 Merging the Two Worlds Payment activated Options Term Death in t d [ν,ν+dν] ν [0,T a ]. B-S Strategy: Hold a weighted portfolio of european options for each possible time of death ν. 1 t T ( ) ()[ ( )] T > t ν ma t 1 Fa + t ν t { 1ifTa > t ( T > t) a = 1 dν = a t 0otherwise Paid if t d > T. ~ 1 t Endowment [ ( )] ( T > t) t 1 Fa + t T t { 1 if Ta > t ( T > t) 0 a = 1 = a otherwise Much simpler correction 18

19 Application Definition: t is the sensitivity at time t of a contingent claim w.r.t. a variation of the underlying value From Actuarial estimations it is possible to deduce the fraction ξ i of contracts maturing at time T i, T i < T. The event maturity can be triggered either by the end of a given contract or by a death event. 19

20 A First Approach : Delta-Hedging Shares Fixed Income } Desinvestment or Structured Products Cash Shares Fixed Income 20

21 A First Approach : Delta Hedging (Simulations) Apply Black&Scholes delta hedging to replicate the put option Consider the benchmark as the option s underlying 21

22 A Less Naive Approach : Modified Black&Scholes Option Price Option Price Risky Assets Risky Assets Cash Risky Assets Fund F 0 with volatility σ Fund (F 0 -P 0 ) with volatility σ Fund (F 0 -P 0 ) with volatility σ. (1- ) 22

23 A Less Naive Approach : Modified Black&Scholes (Simul.) Remember that no premium is paid for the put option Consider the fund (=benchmark+put) as the underlying 23

24 Proportion of Cash : Comparative Study Guaranteed minimum K Floor 24

25 Tradeoffs Expected Shortfall Expected Returns Transaction Costs Discrete Hedging Errors Precision, Variables Computation Time 25

26 Relative Performance Dynamic/Static Strategy. 26

27 Transaction Costs (Arbitrary Units) 27

28 A general scheme SHAREHOLDERS COMPANY ROE ROE ADJUSTMENTS SOLVENCY SOLVENCY MARGIN MARGIN insured COSTS INTEREST MARGIN MANAGEMENT FEES Reimbursments SEGREGATED FUND NET PREMIUMS MARKET ROA ROA * ROA= RETURN ON ASSETS 28

29 Let s Play with Real World Static Approach 29

30 Let s Play with Real World Dynamic Approach 30

31 Let s Play with Real World P&L for the Company 31

32 Further Analysis Stochastic Optimal Control Maximize a utility function given management constraints for a set of market scenarios Passport Options Option on a trading account 32

33 Technical Issues From Theory to Practice: Parameter Estimators Accuracy Number of Scenarios Optimization Number of Parameter Estimations Number of Key Variables Nvar (Liabilities, Assets, RF, ) NEED: Nscenarios X Ntimesteps X Npolicies X Nvar (e.g X 400 X 26 X Nvar) Dynamic redistribution of the workload among nodes of a computer cluster to prevent memory depletion. 33

34 Technical Issues Optimization problems may be tackled at different levels of complexity. Operational Computer Aided Asset & Liability Management may benefit from up to date computing technologies. HPC is today an attainable solution which could bring to the risk management field a new powerful instrument. 34

35 Flowchart 35

36 How to use the hidden power 36

37 CMA ALM engine DB Assets Portfolio DB Liabilities Portfolio DB Market Datas Aggregation ALM Computational Engine 37

38 Network Structure. 38

39 Portable Interface 39

40 Final Remarks Hedging of volatility risk shouldn t hide other management risks : credit, liquidity,... Portfolio s manager monitoring (tracking error) Less volatility in ROE => better public image 40

41 Final Remarks Managed Risk Compliance with regulatory constraints and rating agencies Lower capital requirements Better rating and lower cost of capital 41

42 Risk Consulting CAPITAL MANAGEMENT ADVISORS srl Asset Liability Management for Life Insurance: a Dynamic Approach Dr Gabriele Susinno & Thierry Bochud Quantitative Strategies Capital Management Advisors Madrid May, 23 rd, 2001