Semi-analytic pricing of American options in time-dependent jump-diffusion models with exponential jumps
Semi-analytic pricing of American options in time-dependent jump-diffusion models with exponential jumps ArXiv ID: 2308.08760 “View on arXiv” Authors: Unknown Abstract In this paper we propose a semi-analytic approach to pricing American options for time-dependent jump-diffusions models with exponential jumps The idea of the method is to further generalize our approach developed for pricing barrier, [“Itkin et al., 2021”], and American, [“Carr and Itkin, 2021; Itkin and Muravey, 2023”], options in various time-dependent one factor and even stochastic volatility models. Our 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 equation for the the option price; iii) the options Greeks solve a similar Fredholm-Volterra linear equation obtained by just differentiating Eq. (25) by the required parameter. Once done, the American option price is presented in close form. ...