(10 points) A power option written on a stock is a financial derivative contract that pays off the US dollar amount STn for some nN to the holder of the option at time T>0, where ST is the price of the underlying stock at that time. Let r>0 denote the risk-free interest rate (p.a. and continuously compounded). Compute today's (t=0) arbitrage-free price of this power option in the Black-Scholes-Merton model by using the risk-neutral valuation approach. Hint: You can use (without proof) the fact that E[eZ]=e212 for a normally distributed random variable ZN(0,2) with mean zero and variance 2. (10 points) A power option written on a stock is a financial derivative contract that pays off the US dollar amount STn for some nN to the holder of the option at time T>0, where ST is the price of the underlying stock at that time. Let r>0 denote the risk-free interest rate (p.a. and continuously compounded). Compute today's (t=0) arbitrage-free price of this power option in the Black-Scholes-Merton model by using the risk-neutral valuation approach. Hint: You can use (without proof) the fact that E[eZ]=e212 for a normally distributed random variable ZN(0,2) with mean zero and variance 2