Valuation of Equity-Linked Life Insurance Contracts with Surrender Guarantees in a Regime-Switching Rational Expectation Model

Abstract

We develop a two-state regime-switching rational expectation model with the economic states recession and expansion for the valuation of equity-linked life insurance contracts with surrender guarantees. Our valuation model jointly captures the empirically observed macroeconomical regime-dependency of both the lapsing and the fi nancial market dynamics. More precisely, our surrender model incorporates both the emergency fund and the interest rate hypothesis in an intensity-based approach via a countercyclical exogenous and a procyclical endogenous surrender intensity. On the equity side the reference fund evolution allows for a countercyclical volatility and a procyclical risk-free rate. The contract value of a representative policyholder is characterized as solution of a system of two coupled PDEs, which we solve numerically by the Crank-Nicolson scheme combined with a penalty method. In extensive numerical experiments we study the effect of the model parameters on the contract values and particularly surrender option values and also compare our regime-switching rational expectation model with the regime-switching American style surrender model.