申論題

8. (30%) Consider a power call or put option with the payoff at the maturity T as

respectively, where St is the stock price at time t, i is a positive-integer exponent, and Xⁱ denotes the strike price. Under the Black-Scholes framework, their respective value functions today (t = 0) are
 where, r is the risk-free interest rate, o is the stock price volatility, and N(•) is the cumulative OVF distribution function of the standard normal distribution defined as

where n(•) is the probability density function of the standard normal distribution.

(d)(4%) In what condition does