2. Suppose a stock price is lognormal with volatility . Consider a derivative with maturity T and payoff f(87) = sr, what is its value at time 0? (Hint: your task is to evaluate e-rERNs: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 Eez] = em 82 .) 2. Suppose a stock price is lognormal with volatility . Consider a derivative with maturity T and payoff f(87) = sr, what is its value at time 0? (Hint: your task is to evaluate e-rERNs: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 Eez] = em 82 .)