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Pricing Survivor Swaps with Mortality Jumps and Default Risk

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Abstract

A survivor swap refers to an agreement for the future exchange of cash flows based upon a mortality-dependent index. Pricing survivor swaps involves the determination of a fixed proportional premium, π, which results in an initial zero value of the swaps for each party. In order to provide a precise valuation of a mortality derivative, such as a survivor swap, an appropriate model is necessary for the forecasting of the mortality rate. The model proposed for use in this study extends the model provided by Cox et al. (2006) by simultaneously considering mortality jumps and default risk. Using this extended model to price survivor swaps in this study, we mainly find from our simulated results, based upon the data collected, that the survivor swap premium has a positive correlation with both the market price of risk and the frequency of jumps. Furthermore, we find that a stronger jump frequency will enhance the effects of the market price of risk on the premium. On the other hand, the survivor swap premium is also found to have a positive correlation with the market price of risk and the frequency of jumps at any level of default risk. However, when the market price of risk and jump frequency levels are both fixed, a higher (lower) default risk will imply a lower (higher) premium.

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