A Recursive Formula for a Participating Contract Embedding a Surrender Option under a Regime-switching Model with Jump Risk: Evidence From The S&P 500 Stock Index

Abstract

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.