Valuation of power option for uncertain financial market

Power option is such an option whose payoff is based on the price of the underlying asset raised to some power. Unlike Black–Scholes setting, we investigate the valuation of power options under the assumption that the underlying stock price is assumed to follow an uncertain differential equation, and derive the pricing formulas of power options for Liu’s uncertain stock model with the method of uncertain calculus based on uncertainty theory. Some numerical examples are given to illustrate the pricing formulas.