Pricing American Options under Azzalini Ito-McKean Skew Brownian Motions.

In this paper, the pricing of American options whose asset price dynamics follow Azza-lini Ito-McKean skew Brownian motions is considered. The corresponding optimal stop-ping 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 sev-eral variational inequalities are derived. Furthermore, the Feyman-Kac formula is calcu-lated. Finally, under this more general as well as very versatile setting, the Black-Scholes option pricing model is nested as a special case. (c) 2023 Elsevier Inc. All rights reserved.