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

Suppose the current stock price of JuJube Inc is ¥100, the risk-free interest rate is 5%, the standard deviation is 25%, the time to maturity is 4 months, the strike price is ¥85, and the price of a call option is ¥25.20. Using the put-call parity relationship, the put option price is closest to   A. ¥25.20   B. ¥16.40   C. ¥5.20   D. ¥8.80   E. None of the above

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

4. Consider a stock with a current price of S0 = $60. The value of the stock at time t = 1 can take one of two values: S1,u = $100, S1,d = $40. The price of a risk-free bond that pays out $1 in period t = 1 is $0.90. (a) Using a one-step binomial tree, write down the possible payoffs of a put option on stock S with strike K = $60 and maturity t = 1. (b) What is the price of this put option?  (c) What is the price of a call option with strike K = $60 and maturity t = 1? Please use put-call parity to find the call price.