Valuing equity-linked death benefits with a threshold expense structure under a regime-switching Lévy model

In this paper, we investigate the valuation problem of equity-linked death benefits with a threshold expense structure. Specifically, a regime-switching Lévy process is used to describe the underlying asset price process, which is monitored periodically. The fees are assumed to be continuously deducted at some constant rate from the policyholder's account between the current and next monitoring times, if the account value is smaller than a pre-specified level at the current observation time point. Under the modified threshold expense structure, some explicit valuation expressions for life-contingent call options are derived by the Fourier cosine series expansion method. Numerical results demonstrate the accuracy and efficiency of our method.