Assume the Black-Scholes setting for an arbitrage-free financial market, i.e. dS(t) = rS(t)dt + oS(t)d(t) and S(0) = So. (a) Show that the probability that a European call option, with maturity T and strike price K, will be exercised in a risk-neutral world is, N(d2), where d, is defined as log(So/K) + (1 - 102)T dz OVT (b) What is an expression for the value of a derivative that pays off $1 if the price of a stock at time T is greater than K? (C) Suppose r = 0.06, So 100, 0 = 0.2, T = 1. Compute the price of a derivative that pays off $1 if the price of a stock at time T = 1 is greater than 80 but less than 100? Assume the Black-Scholes setting for an arbitrage-free financial market, i.e. dS(t) = rS(t)dt + oS(t)d(t) and S(0) = So. (a) Show that the probability that a European call option, with maturity T and strike price K, will be exercised in a risk-neutral world is, N(d2), where d, is defined as log(So/K) + (1 - 102)T dz OVT (b) What is an expression for the value of a derivative that pays off $1 if the price of a stock at time T is greater than K? (C) Suppose r = 0.06, So 100, 0 = 0.2, T = 1. Compute the price of a derivative that pays off $1 if the price of a stock at time T = 1 is greater than 80 but less than 100