Risk-neutral valuation of power barrier options

Barrier options are standard exotic options traded in the financial market. These instruments are different from the vanilla options as the payoff of the option depends on whether the underlying asset price reaches a predetermined barrier level, during the life of the option. In this work, we extend the vanilla call barrier options to power call barrier options where the underlying asset price is raised to a constant power, within the standard Black–Scholes framework. It is demonstrated that the pricing of the power barrier options can be obtained from standard barrier options by a transformation which involves the power contract and a adjusted barrier. Numerical results are considered.