Semi-analytic pricing of American options in time-dependent jump-diffusion models with exponential jumps
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866917586678054912 |
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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 |