A recursive formula for a participating contract embedding a surrender option under regime-switching model with jump risks: Evidence from stock indices

This study proposes a recursive formula to value a surrenderable participating contract. To capture the dynamics of stock returns over expansion-recession cycles and the occurrence of catastrophic events, we assume the rate of return of the reference portfolio would follow a regime-switching model with jump risks. Our empirical results show that compared to the Black-Scholes model and the regime-switching model, the regime-switching model with jump risks can better explain the dynamics of the S&P 500 stock index. In addition, we give a recursive formula of a participating contract embedding a surrender option under a regime-switching model with jump risks. Sensitivity analysis shows that the changes of parameters of the regime-switching model with jump risks did influence participating contract premiums. The differences between valuations under the Black-Scholes model, the regime-switching model and the regime-switching model with jump risks suggest that it is critical to apply an appropriate model to value precisely a participating contract.