Study of European style options under Itô-McKean Brownian motion with Azzalini skew-normal distribution

In this article, we deal European style option, with arbitrary payoff which includes both put and call options, on an asset whose price evolves as It?-McKean skew Brownian motion Azzalini skew-normal distribution. Initially, investigate a condition leads the to be martingale. Next, option show that if function is convex then so function. After this, finite satisfies partial differential equation respect time. Further, provide necessary sufficient for satisfy Feymann-Kac type equation. study Black-Scholes give expressions delta hedge. Finally, particular case of in order compare some our results existing literature. Our can used optimal exercise boundary, discrete time hedging strategies etc. option.