Interest rate risk management and valuation of the surrender option in life insurance policies

The valuation of the prepayment option embedded in mortgages attracts the attention of practitioners and academics (see Schwartz and Torous, 1989) both because of its direct negative effect on the financial value of a bank balance sheet in case of drop in interest rates and also because of its impact on the design and pricing of mortgage-backed securities. In the same manner, life insurance policyholders may surrender their contracts and take advantage of higher yields available in the financial markets; this is a source of concern for life insurers, especially during periods of highly volatile interest rates such as have prevailed in recent years. We address the surrender option pricing problem as the valuation of a contingent claim for the insurer, where the contingency is closely related to the level of interest rates, and directly price by arbitrage the surrender option embedded in life insurance policies. A closed-form solution is derived in the case of a single-premium policy when the investment portfolio consists of a fixed-term zero-coupon bond, and the dynamics of stochastic interest rates are driven by the Heath-Jarrow-Morton (1992) model. The price of the option is computed in the case of French contracts using both the closed-form expression and Monte Carlo simulations