Problem Assignment Five
Please solve the numerical portions of the problems listed below as an Excel attachment. You may solve the remainder of the other problems in the spaces provided, but please be sure to leave the question as well. You may adjust the spaces if necessary.
18-3: Suppose that you buy one Whirlpool call option with X = $30 and one with X = $40. You also sell two Whirlpool calls with X = $35. Using the prices from the table below, determine the net cost of the option portfolio and then draw a new payoff diagram showing the net payoffs at expiration. Over what range of prices would you make money, and over what range would you lose money? What is your maximum possible loss and gain?
Company Expiration Strike Call Put
Whirlpool February 30.00 7.45 1.20
36.33 March 30.00 8.05 2.05
36.33 June 30.00 9.65 4.00
36.33 February 35.00 4.10 2.75
36.33 March 35.00 4.90 3.90
36.33 June 35.00 6.85 6.20
36.33 February 40.00 1.80 5.50
36.33 March 40.00 2.60 6.70
36.33 June 40.00 4.65 9.05
36.33 February 45.00 0.60 9.35
36.33 March 45.00 1.25 10.35
36.33 June 45.00 3.10 12.45
18-4: Draw a payoff diagram for each of the following portfolios (X = strike price):
a. Buy a bond with a face value of $80, buy a call with X = $80, and sell a put with X = $80.
b. Buy a share of stock, buy a put with X = $80, and sell a call with X = $80.
c. Buy a share of stock, buy a put with X = $80, and sell a bond with a face value of $80.
18-7: Imagine that a stock sells for $33. A call option with a strike price of $35 and an expiration date in six months sells for $4.50. The annual risk-free rate is 5%. Calculate the price of a put option that expires in six months and has a strike price of $35.
18-13: A call option expires in three months and has a strike price X = $40. The underlying stock is worth $42 today. In three months, the stock may increase by $7 or decrease by $6. The risk-free rate is 2% per year. Use the binomial option pricing model to value the call option. Then, a certain stock sells for $42 today, but in three months it may be worth $49 or $36. Value a 3-month put option with a strike price of X = $40. The risk-free rate is 2% per year. Given the call and put prices calculated above, check and see if put-call parity holds.
19-1: Price a 6-month call option with a strike price of $40.00, assuming an annual standard deviation of 30% on returns, a risk-free rate of 5%, and a current stock price of $41.25. Price the associated put using put-call parity. Re-price both options after changing the risk-free rate to 6%.
19-4: Use the Black and Scholes model to value a call option with the following characteristics: the strike price is $55, the underlying stock's price is $65, the risk-free rate is 4%, the time to expiration is six months, and the standard deviation of the underlying asset is 35%. What is the value of N(d1)?