Pricing discounted American capped options. (March 2022) - Zaevski, Tsvetelin S.
Highlights: Discounted American capped options are examined. The optimal regions are obtained. (Semi-) closed formulas are derived. The Crank-Nicolson finite difference approach is applied. Many numerical examples are presented. Abstract: The purpose of this paper is to present an efficient method for pricing discounted American capped options. They differ from the corresponding uncapped ones by the existing trigger level for the underlying asset. In such a way the option's seller is preserved from the possible large movements of the underlying asset. We first obtain the optimal exercise region and by the use of some hitting properties we derive the fair option price. We use the Crank-Nicolson finite difference approach together with a Monte Carlo method to implement the obtained formulas. This method applied for the pricing problem of the ordinary American options has its own significance. Finally, we present some numerical results.