Assume that the annualized, continuously-compounded return on ABC stock is normally distributed with mean 0.18 and standard deviation of 0.35. Also, the annualized, continuously-compounded riskfree rate is 4%. The current price of ABC stock is $100. Assume that no dividends will be paid on ABC common stock over the next six-months. (a) Find the values of u, d, r, and p for a two-period binomial which you might use to price a six-month option under the assumption that ud = 1.

(b) What should be todays prices of an at-the-money European call and an at-the-money European put option on an ABC stock that matures in 6 months?

(c) State the put-call parity and show that this parity holds in the above case.

(d) What should be todays price of an at-the-money American put option on an ABC stock that matures in 6 months?

(e) ABC has decided to issue a new type of security, the PowerDerivative. Each share of the PowerDerivative pays off max(100 ST , 0)2, where ST is the stock price in three months. What is todays price of the PowerDerivative?

(f) Construct a portfolio, made only of the above American put option and lending/borrowing, which replicates the payoff of the above PowerDerivative.