8. (10 pts: 5+2+3) Assume that the price S(t) of a certain stock follows the geometric Brownian motion with the drift parameter p = 0.06 and the volatility parameter o = 0.5. (a) Given that the current price of the stock is 30 and the nominal annual interest rate is 5% compounded continuously, find the no-arbitrage cost of the derivative that pays 5 after 6 months if |S(1/2) - S(0) > 5, and O otherwise. (b) What kind of investor might be interested in buying such a derivative? Which of the trading strategies we learned can be used for the same purpose? Compare the strategies with the derivative in part (a) in terms of the payoff, cost (no calculation at this point, just a general idea), and risk. (c) Compute the cost of the strategies you found in part (b) and discuss the relationship with the cost of the derivative in part (a)