2007 ARIA Annual Meeting August 6, Management Strategies in Life Insurance: An Examination with Respect to Risk Pricing and Risk Measurement Québec City, August 6, 2007 Nadine Gatzert Institute of Insurance Economics University of St. Gallen 2007 ARIA Annual Meeting

August 6, Introduction (1)   Focus on participating life insurance contracts   Contain guarantees and options   Why important?   Crucial: Fair valuation, risk measurement, risk management   Related literature: - -Risk-neutral valuation: Grosen/Jorgensen (2000, 2002), Ballotta/Haberman/Wang (2006), Kling/Richter/Russ (2007) - -Risk measurement: Barbarin/Devolder (2005), Gatzert/Kling (2007) - -Risk management: Santomero/Babbel (1997), Berketi/Macdonald (1999), Babbel/Merrill (2005)

2007 ARIA Annual Meeting August 6, Introduction (2)   In literature, management decisions concerning asset allocation or surplus distribution often omitted in pricing and risk assessment   However, such strategies are very important in practice   Aim of this paper: - -Extend fair valuation method for better comparability: consider contracts with same (fair) market value and same preset safety level - -Integrate asset management and surplus distribution strategies in the fair valuation process - -Analyze impact of these strategies on pricing and insurer’s risk situation

2007 ARIA Annual Meeting August 6, Model Framework – Claims Structure   Based on Ballotta/Haberman/Wang (2006, JRI)   A(t) market value of the assets (geometric Brownian motion)   Policyholders pay up-front premium P 0 = k A 0 Equityholders’ initial contribution is E 0 = (1-k) A 0   P(t) book value of the policy reserves (mathematical reserves)   Terminal bonus participation:   Default put option:   Policyholder’s payoff:

2007 ARIA Annual Meeting August 6, Model Framework – Fair Valuation and Safety Level   Valuation   Fair contracts: calibrate (g, α, δ) to satisfy   Problem: contracts have same value but may not have same safety level   Solution: fix company’s safety level Measure safety level with default-value-to-liability ratio   Aim: Identify fair contracts with a given safety level d*

2007 ARIA Annual Meeting August 6, Model Framework – Procedure Procedure: 1) Pricing under Q a) a)for given g, calibrate α such that b) b)for (g, α) calibrate δ such that   for (g, α, δ): and   contract is fair and has safety level d* 2) Risk measurement under P: use lower partial moments Shortfall probability Expected shortfall

2007 ARIA Annual Meeting August 6, Numerical Results   Parameters: d*=9%, T=15, σ=15%, r=4%, μ=9%, P 0 =100, E 0 =10   As g increases, α decreases and δ increases   Insolvency risk decreases in g when adjusting α and δ

2007 ARIA Annual Meeting August 6, Integrating Management Strategies   Assumption of unchanged asset allocation or constant annual surplus participation is restrictive   Integration of asset management or surplus distribution strategies leads to different payoff structure   Recalibarate contract parameters to keep contract fair at inception   Analyze effect on pricing and insolvency risk   Compare (heuristic) strategies acting on asset and liability side of balance sheet   How do feasible sets of parameters change?   To what extent are such strategies beneficial in the sense that shortfall risk at maturity is reduced, while still providing fair conditions to policyholders?

2007 ARIA Annual Meeting August 6, Integrating Management Strategies   Solvency driven feedback mechanisms (Chadburn, 1998)   Determine solvency level with statutory equity (reserves) E(t) = A(t) – P(t)   Control asset side of balance sheet (asset allocation) Strategy (A) Strategy (B)   Control liability side of balance sheet (surplus distribution) Strategy (C)

2007 ARIA Annual Meeting August 6, Numerical Results

2007 ARIA Annual Meeting August 6, Integrate Asset Management and Surplus Distribution Strategies   Results are hardly comparable   Even when contracts are fair and have same market value, all contract component values can differ tremendously   Fix safety level to increase comparability   Apply extended valuation approach

2007 ARIA Annual Meeting August 6, Numerical Results, Strategy (A)   For given g, α increases when implementing (A) to keep contract fair   SP, ES are decreasing with increasing g   Results depend on risk measure: For g > 1% given (A): ES lower compared to case without (A)

2007 ARIA Annual Meeting August 6, Numerical Results, no Strategy

2007 ARIA Annual Meeting August 6, Numerical Results, Strategy (B)   For Strategy (B), α is lower compared to Strategy (A), but SP / ES both still substantially higher   Overall, higher risk level than in case without strategies

2007 ARIA Annual Meeting August 6, Numerical Results, Strategy (C)   Initial annual surplus participation rate α considerably higher than without (C)   Overall higher risk level than without strategies

2007 ARIA Annual Meeting August 6, Summary   Calibrate contracts to the same fair market value and the same preset safety level Leads to lower risk when g is raised, while α decreases and δ increases   Compare management strategies acting on asset and liability side Managerial decisions concerning asset allocation or surplus distribution have substantial impact on pricing and risk assessment Results depend on... type of strategy (A,B,C)... risk measure,... and on which parameter (g, α, δ) is adjusted to obtain fair contracts