Finance Assignment 1

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Assignment 1 Details

Complete and submit Assignment 1, which is worth 15% of your final grade, after

you have finished Unit 3. If you have any questions about this assignment and how

to complete it, contact the Student Support Centre.

This assignment contains six problems and is worth a total of 100 marks.

Read the requirements for each problem and plan your responses carefully. Ensure

that you answer each of the required questions as concisely and as completely as

possible and include supporting calculations where required.

1. (10 marks) A stock sells for $52 per share, and the 6-month European call on

the stock with a strike price of $50 sells for $2.50. The stock is not expected to

pay any dividends in next six months. The risk free interest rate is 4% per

annum, continuously compounded. How can you get a free lunch from the

market? Describe your transactions clearly.

2. (10 marks) An at-the-money three-month European call option on a non-

dividend-paying stock has a market price of $1.27. The stock price is $20 and the

risk-free interest rate is 5% per annum, with continuous compounding. Verify

that the implied volatility is about 27%.

3. (10 marks) A European call option and put option on a stock both have a strike

price of $20 and an expiration date in three months. Both sell for $3. The risk-

free interest rate is 10% per annum, the current stock price is $19, and no

dividend is expected in three months. How can you make a free lunch in these

markets?

4. (10 marks) A non-dividend-paying stock sells for $42 per share. The

continuously compounded risk-free interest rate is 6% per annum, and the

volatility of the stock price is 30% per annum. Use the Black-Scholes-Merton

model to determine the price of a 3-month European call on the stock with a

strike price of $40.

5. (20 marks) A stock price is currently $60, with an annual volatility of 0.30. The

risk-free rate is 4% per annum. Use the two-period binomial model to

a. calculate the price of a one-year European put option on the stock with a

strike price of $60. (12 marks)

b. calculate the price of a one-year American put option on the stock with a

strike price of $60. (8 marks)

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6. (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.

a. What are the prices of option A and D according to the Black-Scholes-

Merton model? (5 marks)

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? (5 marks)

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? (5 marks)

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? (5

marks)

e. Suppose you short 100 Option B, how many shares do you need to hedge

your position? (5 marks)

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? (5 marks)

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? (5 marks)

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? (5 marks)