# Assignment Details Complete and submit Assignment 1, which is worth 15% of your final grade, after you have finished Unit 3….

Assignment 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 eight 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. Distinguish between hedgers, speculators, and arbitrageurs.
(5 marks)
2. ATX is a European call option on stock A and BED is a European call option on stock B with parameters as given in the following chart. Assume that both stock A and B pay no dividends.
Call T X S r Option price
A 0.25 105 100 0.05 \$15
B 0.25 105 100 0.05 \$12

Which stock, A or B, has the higher volatility? Explain.
(5 marks)
3. The market price of a one-year European call option on a non-dividend-stock is \$4. The strike price of the option is \$42, the stock price is \$40, and the risk-free rate is 8%.

a. What is the price of an otherwise identical put option?
(6 marks)
b. What is the price of an otherwise identical American call option?
(4 marks)
4. A three-month European call on a non-dividend-paying stock is currently selling for \$1. The strike price of the option is \$80. The underlying stock trades for \$80. The risk-free interest rate is 6%. Does there exist any arbitrage opportunity? If yes, what type of transaction should you execute to make an arbitrage profit?
(15 marks)
5. A stock price is currently \$60. Over each of the next two six-month periods, it is expected to rise by 10% or drop by 10%. The risk-free rate is 4% for each period. Using the two-period binomial model, calculate the option price in the four situations that follow.

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a. Calculate the price of a one-year European call option on the stock with a strike price of \$62.
(6 marks)
b. Calculate the price of a one-year European put option with a strike price of \$62. Is your result consistent with the put-call parity?
(6 marks)
c. Calculate the value of a one-year American call option with a strike price of \$62. What is the early exercise premium?
(4 marks)
d. Calculate the value of a one-year American put option with a strike price of \$62. What is the early exercise premium?
(4 marks)
6. A non-dividend-paying stock sells for \$20 per share. The continuously compounded risk-free interest rate is 8% per annum, and the volatility of the stock price is 20% per annum. Using the Black-Scholes-Merton model, determine the price of a six-month European call on the stock with a strike price of \$20.
(14 marks)
7. Consider three six-month European put options on a stock with the strike prices of \$100, \$110, and \$120. The market price of the stock is \$105, and the market prices of the puts are \$3.30, \$6.50, and \$11.50, respectively.

a. Construct a butterfly spread using those three put options.
(4 marks)
b. Use formula, table, and diagram to show the payoff and profit pattern of the butterfly.
(6 marks)
c. For what range of stock prices would the butterfly spread lead to a profit?
(3 marks)
d. What are the maximum potential profit and loss?
(2 marks)

8. The following is information regarding three one-year options on stock SBY. Assume the market price of stock SBY is \$30.
Option Call 1 Put 1 Call 2
Strike price 30 30 35
Option price 3.0 1.8 1.1

a. Construct a straddle using Call 1 and Put 1. Draw a diagram showing the profit from the strategy. Indicate the breakeven points and the maximum loss.
(8 marks)
b. A strangle is similar to a straddle except that the call and put have different strike prices. Construct a strangle using Call 2 and Put 1. Draw a diagram showing the profit from the strategy. Indicate the breakeven points and the maximum loss. (8 marks)