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- Title
American Options in Time-Dependent One-Factor Models: Semi-Analytic Pricing, Numerical Methods, and ML Support.
- Authors
Itkin, Andrey; Muravey, Dmitry
- Abstract
Semi-analytical pricing of American options in a time-dependent Ornstein-Uhlenbeck model was presented in Carr and Itkin (2021). It was shown that to obtain these prices one needs to numerically solve a nonlinear Volterra integral equation of the second kind to find the exercise boundary, which is a function of the time only. Once this is done, the option prices follow. It was also shown that computationally this method is as efficient as the forward finite difference solver, while also providing better accuracy and stability. Later this approach, called "the generalized integral transform" method, was significantly extended to various time-dependent one factor (Itkin et al. 2021) and stochastic volatility (Carr et al. 2022, Itkin and Muravey 2022b) models as applied to pricing barrier options. For American options, though, despite being possible, this was not explicitly reported anywhere. In this article our goal is to fill this gap and also discuss which numerical method can be efficient to solve the corresponding Volterra equations, also including machine learning.
- Subjects
MATHEMATICAL models of pricing; NUMERICAL analysis; VOLTERRA equations; MACHINE learning; ORNSTEIN-Uhlenbeck process
- Publication
Journal of Derivatives, 2024, Vol 31, Issue 3, p74
- ISSN
1074-1240
- Publication type
Article
- DOI
10.3905/jod.2023.1.197