Semi-Analytic Pricing of American Options in Time-Dependent Jump-Diffusion Models with Exponential Jumps.

In this article we propose a semi-analytic approach to pricing American options in time-dependent jump-diffusion models with exponential jumps. The idea of the method consists of further generalization of our method developed for pricing barrier (Itkin, Lipton, and Muravey 2021) and American (Carr and Itkin 2021; Itkin and Muravey 2024) options in various time-dependent one factor and even stochastic volatility models. The proposed approach: i) allows arbitrary dependencies of the model parameters on time; ii) reduces solution of the pricing problem for American options to a simpler problem of solving a system of an algebraic nonlinear equation for the exercise boundary and a linear Fredholm-Volterra integral equation for the option Gamma; once done, the American option price is presented in closed form; iii) the options' Greeks solve a similar Fredholm-Volterra linear equation obtained by just differentiating the pricing equation by the required parameter. Also, solving integral equations instead of PIDE usually brings better accuracy under the same speed, or better speed under the same accuracy. [ABSTRACT FROM AUTHOR]