Abstract
This paper investigates a numerical method for solving fractional partial integro-differential equations (FPIDEs) arising in American Contingent Claims, which follow finite moment log-stable process (FMLS) with jump diffusion and regime switching. Mathematically, the prices of American Contingent Claims satisfy a system of d problems with free-boundary values, where d is the number of regimes of the market. In addition, an optimal exercise boundary is needed to setup with each regime. Therefore, a fully implicit scheme based on the penalty term is arranged. In the end, numerical examples are carried out to verify the obtained theoretical results, and the impacts of state variables in our model on the optimal exercise boundary of American Contingent Claims are analyzed.
Highlights
More and more researchers pay much attention to the pricing problem of American Contingent Claims since the pricing model is free-boundary problem and it is of great academic value to solve this kind of model
Fan et al [19] set a fully implicit scheme with first-order accuracy based on the penalty function for the stock loan pricing model, and their method can be used to other pricing model of American Contingent Claims
We introduce our numerical method by extending the penalty method and prove the effectiveness of this method in Section 3. e numerical examples and analysis of parameter impact are displayed in Section 4, and we give the conclusions in the final section
Summary
More and more researchers pay much attention to the pricing problem of American Contingent Claims since the pricing model is free-boundary problem and it is of great academic value to solve this kind of model. Cai et al investigated the value and optimal redemption price of stock loan with infinite and finite maturity under the framework of the hyperexponential jump diffusion model, respectively [3]. Hariharan [16] gave a numerical scheme based on the wavelet technique to solve the timefractional BS model arising from European option pricing problem. Fan et al [19] set a fully implicit scheme with first-order accuracy based on the penalty function for the stock loan pricing model, and their method can be used to other pricing model of American Contingent Claims. From the existing literature, it appears that research on the numerical simulation of the coupled fractional differential equations for American Contingent Claims is relatively limited. We introduce our numerical method by extending the penalty method and prove the effectiveness of this method in Section 3. e numerical examples and analysis of parameter impact are displayed in Section 4, and we give the conclusions in the final section
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