Hi. I do not how to solve financial question about derivatives.

An asset follows the following Geometric Brownian Motion: dS = gSdt + OSdz Consider a derivative on the asset that pays off S} at maturity. This derivative works like a power option with a very low exercise price, and is suitable for speculators who want to place a highly leveraged bet on the price of the underlying. (a) Derive the formula to price this derivative using the risk-neutral valuation method. (b) Show that your formula in (a) satisfies the Black-Scholes-Merton Partial Differential Equation: 02s2 = rf 2 DS2