The distribution of refracted L\'evy processes with jumps having rational Laplace transforms

TL;DR

This paper derives explicit formulas for the distribution of refracted jump diffusion processes with rational Laplace transforms, introducing a novel approach and applying it to Variable Annuities pricing.

Contribution

It presents a new method for deriving the Laplace transform of such processes and applies it to financial product valuation.

Findings

Formulas for the Laplace transform of the process distribution

A novel approximating procedure approach

Application to Variable Annuities pricing

Abstract

We consider a refracted jump diffusion process having two-sided jumps with rational Laplace transforms. For such a process, by applying a straightforward but interesting approach, we derive formulas for the Laplace transform of its distribution. Our formulas are presented in an attractive form and the approach is novel. In particular, the idea in the application of an approximating procedure is remarkable. Besides, the results are used to price Variable Annuities with state-dependent fees.