Implementation of power barrier option valuation

Options are financial instruments that can be utilized to reduce risk in stock investment. Barrier options are one of the major types of options actively used in financial markets where its life period depends on the path of the underlying stock prices. The features of the barrier option can be used to modify other types of options. In this research, the barrier option will be implemented into power option, so it is called power barrier option. This option is an extension of the vanilla barrier options where the Call payoff being considered is defined as PC=max(STβ−Kβ,0), and the Put payoff being considered is defined as PP=max(Kβ−STβ,0). Here β > 0 and β ≠ 1, K is the strike price of the option, and ST is the price of the underlying stock at time maturity T. In this paper, we generate the prices of stock using binomial method which is adjusted to the power option. In the conclusion, the price of American power barrier option is more expensive than the price of European power barrier option.