A Recursive Formula of a Participating Contract Embedding a Surrender Option under Regime-Switching Model with Jump Risks: Evidence from Stock Indices

[[abstract]]Hamilton (1989) proposed the regime-switching model to explain the different behaviors of mean and volatility for returns at different states of business cycle. However, the stock price has abnormal vibrations when the unanticipated information released via the stock indices and therefore leads into the regime-switching model with jump risks. According to empirical analysis in this paper, we find that 29 stock indices suitable for the regime-switching model with jump risks via LR test in the sample observations with 31 stock indices of the study period from 1999 to 2008 by expectation-maximization (EM) algorithm and supplemented expectation-maximization (SEM) algorithm. Also, both of the regime-switching model and the regime-switching model with jump risks can address the leptokurtic feature of the asset return distribution, volatility smile, and the effects of the volatility clustering phenomenon. Therefore, we develop the recursive formula to price a participating contract embedding a surrender option under business cycle and business cycle with jump risks. Finally, we give some sensitivity analysis for the participating contract embedding a surrender option