Consider a non-dividend-paying stock S. Given S has price St at date t,the return on S has a log-normal distribution at T under Q with mean −(σ^2)*(T −t)/2 and variance (σ^2)*(T−t). That is, log(ST/St)∼N[(-1/2)*(σ^2)*(T-t),(σ^2)*(T−t)]
1a(i) Show,computationally,that
Expected value of [ST] under Q=St
1a(ii) Explain why it must be that (expected value of [ST] under Q=St) for the absence of arbitrage.