Pricing American Options under Azzalini Ito-McKean Skew Brownian Motions

Sultan Hussain, Hifsa Arif, Muhammad Noorullah and Athanasios A. Pantelous

Applied Mathematics and Computation, 2023, vol. 451, issue C

Abstract: In this paper, the pricing of American options whose asset price dynamics follow Azzalini Itô-McKean skew Brownian motions is considered. The corresponding optimal stopping time problem is then formulated, and the main properties of its value function are provided. We show that if the payoff function is positive and decreasing, then the value function and its partial derivatives are continuous and locally bounded, and therefore several variational inequalities are derived. Furthermore, the Feyman-Kac formula is calculated. Finally, under this more general as well as very versatile setting, the Black-Scholes option pricing model is nested as a special case.

Keywords: American option pricing; Skew Brownian motion; Non-normal distribution; Optimal stopping problem; Quadratic variation (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:451:y:2023:i:c:s0096300323002096

DOI: 10.1016/j.amc.2023.128040

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