A study of maximizing skew Brownian motion with applications to option pricing

The objective of this study is twofold. Firstly, to study the probabilistic distribution functions of maximum of skew-Brownian motion (SKBM) and stock price process driven by maximum of skew-Brownian motion. Secondly, to derive the pricing formulas of European style call options (with general payoff D(St)), contingent upon the maximum of skew-Brownian motion and stock price process driven by maximum of skew-Brownian motion. As an application of developed formulas, we have priced the binary (Cash or Nothing) options.

Automated summary

This study aims to analyze the probability distribution functions of the maximum value of skew-Brownian motion and the stock price process driven by the maximum value of skew-Brownian motion. It also aims to derive pricing formulas for European style call options, based on the maximum value of skew-Brownian motion and the stock price process driven by it. The developed formulas are applied to price binary (Cash or Nothing) options.