Valuation of guaranteed minimum maturity benefits under mean reversion and jump models with surrender risk

Abstract

We propose an efficient valuation approach for guaranteed minimum benefits embedded in variable annuity (VA) contracts, where the price of underlying asset is modeled by a mean reversion process with jumps. We consider the case in which early surrender is permitted, and an intensity-based framework is used to capture surrender behavior and other asset price volatilities. To analyze the contract within this complex stochastic setting, we rely on the Fourier cosine series expansion method to approximate the expectation of the value function, which serves as an estimation of the value of VA benefits. We conduct numerical examples to demonstrate the efficiency and accuracy of the proposed method. Sensitivity analysis of involved parameters is given.