3 Suppose a stock price is lognormal with volatility o. Consider a derivative with maturity T and payoff f(s(T)) = s3 (T). (a) What is its value at time 0? (b) What is the Delta of the option considered in this Problem? (Hint: your task is to evaluate eT ERN(s). Recall that under the risk-neutral probability distribution, st is lognormal, and therefore s is also lognormal. Use the fact that if Z is Gaussian with mean m and standard deviation s then Ele2] = em+s?. 3 Suppose a stock price is lognormal with volatility o. Consider a derivative with maturity T and payoff f(s(T)) = s3 (T). (a) What is its value at time 0? (b) What is the Delta of the option considered in this Problem? (Hint: your task is to evaluate eT ERN(s). Recall that under the risk-neutral probability distribution, st is lognormal, and therefore s is also lognormal. Use the fact that if Z is Gaussian with mean m and standard deviation s then Ele2] = em+s