Stock ABC sells for $64 and is not to pay any dividend in next year. Several 6-month European options on MFN are listed below with their market prices:
Option name Type Strike price Market price N(d1) N(d2)
A Call $60 8.4 0.70 0.62
B Call $65 5.8
C Call $70 3.7
D Put $60 3.0
E Put $65 5.1
F Put $70
Assume the continuously compounded interest rate is 6% per annum for all terms and the volatility of Stock ABC is 0.3.
a. What are the prices of option A and D according to the Black-Scholes-Merton model?
b. If the stock price changes to $64.5, while other variables stay the same, what would be your estimates of the market price of Option A?
c. If the stock price changes to $63.2, while other variables stay the same, what would be your estimates of the market price of Option D?
d. Assume that Option B has a delta of 0.56. The probability that the option will be exercised on maturity date is 0.48. Use the B-S-M model to determine if Option B is overpriced, fairly priced, or underpriced?
e. Suppose you short 100 Option B, how many shares do you need to hedge your position?
f. Suppose an investor expects the stock price to remain at about $64 and decides to execute a butterfly spread using options A, B, and C. What will be the profit if the stock price at expiration is $66.50?
g. Consider a long straddle constructed using the options with X=65. What are the two breakeven stock prices at expiration? What is the profit if the stock price at expiration is at $60?
h. Now suppose that ABC stock is expected to pay a continuous dividend yield of 2% per annum and option C has a fair price of 3.5. What should the price of Option F be?