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On a Free Boundary Problem for American Options Under the Generalized Black–Scholes Model

College of Liberal Arts, Anyang University, Gyeonggi-Do 14028, Korea
Mathematics 2020, 8(9), 1563; https://doi.org/10.3390/math8091563
Received: 4 August 2020 / Revised: 3 September 2020 / Accepted: 9 September 2020 / Published: 11 September 2020
(This article belongs to the Special Issue Advanced Methods in Mathematical Finance)
We consider the problem of pricing American options using the generalized Black–Scholes model. The generalized Black–Scholes model is a modified form of the standard Black–Scholes model with the effect of interest and consumption rates. In general, because the American option problem does not have an exact closed-form solution, some type of approximation is required. A simple numerical method for pricing American put options under the generalized Black–Scholes model is presented. The proposed method corresponds to a free boundary (also called an optimal exercise boundary) problem for a partial differential equation. We use a transformed function that has Lipschitz character near the optimal exercise boundary to determine the optimal exercise boundary. Numerical results indicating the performance of the proposed method are examined. Several numerical results are also presented that illustrate a comparison between our proposed method and others. View Full-Text
Keywords: American option pricing; generalized Black–Scholes partial differential equation; optimal exercise boundary; transformed function American option pricing; generalized Black–Scholes partial differential equation; optimal exercise boundary; transformed function
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MDPI and ACS Style

Lee, J.-K. On a Free Boundary Problem for American Options Under the Generalized Black–Scholes Model. Mathematics 2020, 8, 1563. https://doi.org/10.3390/math8091563

AMA Style

Lee J-K. On a Free Boundary Problem for American Options Under the Generalized Black–Scholes Model. Mathematics. 2020; 8(9):1563. https://doi.org/10.3390/math8091563

Chicago/Turabian Style

Lee, Jung-Kyung. 2020. "On a Free Boundary Problem for American Options Under the Generalized Black–Scholes Model" Mathematics 8, no. 9: 1563. https://doi.org/10.3390/math8091563

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