Semi-analytic pricing of American options in time-dependent jump-diffusion models with exponential jumps

Fuente: arXiv
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Main Author: Itkin, Andrey
Format: Preprint
Published: 2023
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author Itkin, Andrey
author_facet Itkin, Andrey
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2308_08760
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Semi-analytic pricing of American options in time-dependent jump-diffusion models with exponential jumps
Itkin, Andrey
Pricing of Securities
Computational Finance
Mathematical Finance
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.
title Semi-analytic pricing of American options in time-dependent jump-diffusion models with exponential jumps
topic Pricing of Securities
Computational Finance
Mathematical Finance
url https://arxiv.org/abs/2308.08760