(All interest rates are continuously compounded) Consider a derivative security whose payoff is at maturity is max {25, ST/4}, where ST is the price of the underlying stock at maturity (say, 1 year). Suppose the current stock price is 95, its expected return is 10% p.a., the stock volatility is 30% p.a., and the risk-free rate is 6% p.a.

(a) What should be the price of this derivative under the Black-Scholes framework?

(b) Assuming that the price of the underlying stock follows a geometric Brownian motion process, what is the risk-neutral probability that the payoff of this security will exceed $28? What about the real-world probability?