Suppose a stock price st ls lognormal. Consider a derivative with payoff at maturity. (To be sure there's no confusion: the payoff is sTr raised to the power n.) Show that its value at time t is where r is the risk-free rate and is the volatility. (Hint: the option's value is eERN[payoff.) Suppose a stock price st ls lognormal. Consider a derivative with payoff at maturity. (To be sure there's no confusion: the payoff is sTr raised to the power n.) Show that its value at time t is where r is the risk-free rate and is the volatility. (Hint: the option's value is eERN[payoff.)