A simple numerical method for pricing American power put options

• Published in: Chaos, solitons and fractals solitons and fractals, 2020-10, Vol.139, p.110254, Article 110254
• Main Author: Lee, Jung-Kyung
• Format: Article
• Language: English
• Subjects: American power put option; Cubic spline interpolation; Optimal exercise boundary; Transformed function
• ISSN: 0960-0779; 1873-2887
• DOI: 10.1016/j.chaos.2020.110254

•The American power option payoffs offer considerable flexibility to investors.•The power options offer a much higher payoff than a vanilla option.•Valuing American options involves determining the optimal exercise boundary.•The optimal exercise boundary can be determined using the transformed function.•A numerical method is developed for appropriately pricing the American power options. In this paper, we present numerical methods to determine the optimal exercise boundary in case of an American power put option with non-dividend yields. The payoff of a power option is typified by its underlying share price raised to a constant power. The nonlinear payoffs of power options offer considerable flexibility to investors and can be applied in various applications. Herein, we exploit a transformed function to obtain the optimal exercise boundary of the American power put option. Employing it, we can easily determine the optimal exercise boundary. After determining the optimal exercise boundary, we calculate the American power put option values using the finite difference method. Generally, the optimal exercise boundary may not be observed at the grid points. Therefore, the interpolation method is used to determine the value of the American power put option. Furthermore, we present several numerical results obtained by comparing the proposed method and the existing methods.