Homework Solutions (Options and Futures)

1.Consider a trader who opens a short futures position. The contract size is £62,500, the maturity is six months, and the initial price is $1.50 = £1. The next day, the settlement price is $1.60 = £1. What is the amount of the trader’s gain or loss?

A) Gain of $6,250.

B) Loss of $6,250. (1.6 USD – 1.5 USD = 0.1 USD per 1 EUR loss; 0.1 * 62,500)

C) Gain of $2,604.

D) No gain or loss, since maturity has not arrived.

2. Suppose you wish to speculate on a rise in the value of the euro. If you are correct and the value of the euro does indeed rise in the future, you would profit with

A) a short position in a futures contract on the euro.

B) a long position in a futures contract on the euro.

C) a short position in a forward contract on the euro.

D) None of the above.

3. Explain the basic differences between the operation of a currency forward market and a futures market.

4. A call option:

A) is a contract to buy a certain quantity of a specific underlying asset at a specific price at a specified date in the future.

B) gives the holder the right, but not the obligation, to sell the underlying asset for a stated price over a stated time period.

C) is an exchange-traded contract to buy a certain quantity of a specific underlying asset at a specific price at a specified date in the future.

D) gives the holder the right, but not the obligation, to buy the underlying asset for a stated price over a stated time period.

5. Consider a put option written on €100,000. The strike price is $1.50 = €1.00 and the option premium is $0.02 per euro. What is the theoretical maximum gain on this position?

A) There is unlimited upside potential.

B) $80,000

C) $148,000 (1.50 USD – 0.02 USD = 1.48 USD; 1.48 USD per 1 EUR * 100,000 EUR)

D) $2,000

6. Consider a trader who buys a European call option on euro. The contract size is €62,500, the maturity is six months, and the strike price is $1.50 = €1. At maturity, the settlement price is $1.60 = €1. What is the amount of the trader’s gain or loss?

A) Gain of $6,250. (1.6 USD – 1.5 USD = 0.1 USD per 1 EUR gain; 0.1 * 62,500)

B) Loss of $6,250.

C) Gain of $2,604.

D) No gain or loss, since expiry has not arrived.

7. Consider a put option written on €100,000. The strike price is $1.50 = €1.00 and the option premium is $0.02. At what exchange rate will the buyer of this put option break even?

A) $1.00 = €.667

B) $1.52 = €1.00

C) $1.48 = €1.00 (1.50 USD – 0.02 USD = 1.48 USD per 1 EUR)

D) $1.50 = €1.00

8. What is meant by the terminology that an option is in-, at-, or out-of-the-money?

9. Assume that the Japanese yen is trading at a spot price of 92.04 cents per 100 yen.   Further assume that the premium of an American call (put) option with a striking price of 93 is 2.10 (2.20) cents. Calculate the intrinsic value and the time value of the call and put options.