FIRST PASSAGE PROBLEMS OF REFRACTED JUMP DIFFUSION PROCESSES AND THEIR APPLICATIONS IN VALUING EQUITY-LINKED DEATH BENEFITS

This paper studies some first passage time problems in a refracted jump diffusion process with hyper-exponential jumps. Closed-form expressions for four functions associated with the first passage time are obtained by solving some ordinary integro-differential equations. In addition, the obtained results are used to value equity-linked death benefit products with state-dependent fees. Specifically, we obtain the closed-form Laplace transform of the fair value of barrier option, which is further recovered by the bilateral Abate-Whitt al-gorithm. Numerical results confirm that the proposed approach is efficient.