An integral equation approach for pricing American put options under regime-switching model

Regime-switching models have been heavily studied recently, as they have some clear advantages of over other non-constant volatility model to resolve the so-called smirk effect displayed when constant volatility models are used to price financial derivatives such as options. However, due to the incr...

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Bibliographic Details
Published inInternational journal of computer mathematics Vol. 100; no. 7; pp. 1454 - 1479
Main Authors Zhu, Song-Ping, Zheng, Yawen
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis 03.07.2023
Taylor & Francis Ltd
Subjects
39-08
American put option
free boundary problem
integral equation
Integral equations
Mathematical models
Partial differential equations
regime-switching model
Switching
Volatility
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Summary:Regime-switching models have been heavily studied recently, as they have some clear advantages of over other non-constant volatility model to resolve the so-called smirk effect displayed when constant volatility models are used to price financial derivatives such as options. However, due to the increased model complexity, the associated computational effort usually increases as well, particularly when they are used to price American-style options. In this paper, a novel computational approach based on integral equations is presented. A distinctive feature of our approach, in comparison with other numerical approaches, is that the coupled partial differential equations (PDEs) in a PDE system have been decoupled in the Fourier space, resulting in a completely decoupled integral equation for each economical states, and thus has greatly reduced computational effort. Some examples with preliminary results for a two-state regime-switching model are used to demonstrate our approach.
ISSN:0020-7160
1029-0265
DOI:10.1080/00207160.2023.2190828