Valuation of equity-linked life insurance contracts with surrender guarantees in a regime-switching rational expectation model

We develop a regime-switching rational expectation model, where both the market value of a reference fund and the surrender intensity of a policyholder change randomly over time according to the evolution of a continuous-time Markov chain with a finite number of states. The contract value of a representative policyholder is characterized as a solution of a system of coupled PDEs, which we solve numerically by the Crank--Nicolson scheme combined with a penalty method. The paper is complemented by extensive numerical experiments, where 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.