38. Suppose a stock is currently trading at $50. The risk-free rate is 2%. Consider the following two ending states for a one-period binomial option pricing model State Up Stock price 60 Down 40 What is the value of a call option with a strike price of 45? *a. $8.08 b. $5.17 c. $14.71 d. $7.35 e. $9.36 Factor Increase/Decrease .2 .2

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The following information is given about an Option on a stock: S(0)=$31, X=$34, rf=9%, variance (sigma squared)=20%, T=182.5 days, Dividend $1.75 in 45 days (1) Calculate the price of a European put option using the Black-Scholes pricing model (show all workings including d1, d2, N(d1), N(d2)) (2) Calculate the price of the corresponding European call option (hint: put call parity) (3) Suppose you feel that the put option is overpriced. What strategy should you use to exploit the apparent mispricing? (4) The market has entered a state of significant volatility, and you believe the implied volatility is incorrect. You believe it should be 10% higher. What trade would you undertake to exploit this arbitrage

3. Consider a one-period binomial model with h = 1, S = 100, r = 0.08, u = 1.5, d = 0.8 and 8 = 0. Calculate the price of an American put option on this stock with strike price K = 100. Does early exercise occur?