(Solved by Humans)-(40 marks) Stock ABC sells for $64 and is not to pay any dividend

Question

(40 marks) 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.

• What are the prices of option A and D according to the Black-Scholes-Merton model? (5 marks)

• 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? (5 marks)

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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? (5 marks)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? (5 marks)Suppose you short 100 Option B, how many shares do you need to hedge your position? (5 marks)

• 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? (5 marks)

• Consider a long straddle constructed using the options with . What are the two breakeven stock prices at expiration?? What is the profit if the stock price at expiration is at $60? (5 marks)

• 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? (5 marks)

Option - A

Black-Scholes Option Value
Input Data
Stock Price now (P)
Exercise Price of Option (EX)
Number of periods to Exercise in years (t)
Compounded Risk-Free Interest Rate (rf)
Standard...