Question 1

1. What would happen in the options market if the price of an American call were less than the value Max (0, S0 X)? Would your answer differ if the option were European? Explain. (5 Marks)

2. Critique the following statement made by an options investor in American call option: My call option is very deep in-the-money. I dont see how it can go any higher. I think I should exercise it. (5 Marks)

3. Why do higher interest rates lead to higher call option prices but lower put option

prices? (5 Marks)

4. Suppose a European put price exceeds the value predicted by putcall parity. How could an investor profit? Demonstrate that your strategy is correct by constructing a payoff table showing the outcomes at expiration. (5 Marks)

5. Consider a two-period, two-state world. Let the current stock price be 45 and the risk-free rate be 5 percent. Each period the stock price can go either up by 10 percent or down by 10 percent. A call option expiring at the end of the second period has an exercise price of 40.
   1. Find the stock price sequence.
   2. Determine the possible prices of the call at expiration.
   3. Find the possible prices of the call at the end of the first period.
   4. What is the current price of the call?

(5 Marks)

Question 2

1. A portfolio manager desires to generate $10 million 100 days from now from a portfolio that is quite similar in composition to the S&P 100 index. She requests a quote on a short position in a 100-day forward contract based on the index with a notional amount of $I0 million and gets a quote of $25.2. If the index level at the settlement date is $35.7, calculate the amount the manager will pay or receive to settle the contract. (5 Marks)

2. A forward contract covering a $10 million face value of T-bills that will have 100 days to maturity at contract settlement is priced at 1.96 on a discount yield basis. Compute the dollar amount the long must pay at settlement for the T-bills.

(5 Marks)

3. Consider an FRA that:
   • Expires/settles in 30 days.
   • Is based on a notional principal amount of $1 million.
   • Is based on 9O-day LIBOR.
   • Specifies a forward rate of 5%.

Assume that the annual 9O-day LIBOR 30-days from now (at expiration) is 6%. Compute the cash settlement payment at expiration and identify which party makes the payment. (5 Marks)

4. Consider a long position of five July wheat contract futures contract each of which covers 5,000 bushels. Assume that the contract price is $2.00 per bushel and that each contract requires an initial margin deposit of $150 and a maintenance margin of $100. Compute the margin balance for this position after a 2-cent decrease in price on Day 1, a l-cent increase in price on Day 2, and a l-cent decrease in price on Day 3. (5 Marks)

5. BB can borrow in the United States for 9%, while AA has to pay 10% to borrow in the United States. AA can borrow in Australia for 7%, while BB has to pay 8% to borrow in Australia. BB will be doing business in Australia and needs AUD, while AA will be doing business in the United States and needs USD. The exchange rate is 2AUD/USD. AA needs USD1.0 million, and BB needs AUD2.0 million. They decide to borrow the funds locally and swap the borrowed funds. The swap period is for five years. Calculate the cash flows for this swap. (5 Marks)

Question 3

1. Explain why an options time value is greatest when the stock price is near the exercise price and why it nearly disappears when the option is deep-in- or out-of- the-money. (5 Marks)

2. Call prices are directly related to the stocks volatility, yet higher volatility means that

the stock price can go lower. How would you resolve this apparent paradox?

(5 Marks)

3. The value Max [0, X (1+r) ^T S0] was shown to be the lowest possible value of a European put. Why is this value irrelevant for an American put? (5 Marks)

4. Buying an at-the-money put has a greater return potential than buying an out-of- the-money put because it is more likely to be in-the-money. Appraise this statement. (5 Marks)

5. Explain the advantages and disadvantages to a covered call writer of closing out the position prior to expiration. (5 Marks)

Question 4

Suppose that each of two investments has a 4% chance of a loss of $10 million, a 2% chance of a loss of $1 million, and a 94% chance of a profit of $1 million. They are independent of each other.

1. What is the VaR for one of the investments when the confidence level is

95%? (5 Marks)

2. What is the expected shortfall when the confidence level is 95%?

3. What is the VaR for a portfolio consisting of the two investments when the

confidence level is 95%? (5 Marks)

4. What is the expected shortfall for a portfolio consisting of the two

investments when the confidence level is 95%? (5 Marks)

5. Show that, in this example, VaR does not satisfy the subadditivity condition, whereas expected shortfall does. (5 Marks)