Exam 7: Futures and Options on Foreign Exchange

Find the hedge ratio for a call option on £10,000 with a strike price of €12,500. The current exchange rate is €1.50/£1.00 and in the next period the exchange rate can increase to €2.40/£ or decrease to €0.9375/€1.00 . The current interest rates are i_€ = 3% and are i_£ = 4%. Choose the answer closest to yours.

Empirical tests of the Black-Scholes option pricing formula

A CME contract on €125,000 with September delivery

The same call from the last question (a 1-period call option on €10,000 with a strike price of $12,500. could also be thought of as a 1-period at-the-money put option on $12,500 with a strike price of €10,000. As before, the spot exchange rate is €1.00 = $1.25. In the next period, the euro can increase in dollar value to $2.00 or fall to $1.00. The interest rate in dollars is i_$ = 27.50%; the interest rate in euro is i_€ = 2%. Draw the binomial tree for this putoption.

Empirical tests of the Black-Scholes option pricing formula

Suppose that you have written a call option on €10,000 with a strike price in dollars. Suppose further that the hedge ratio is ½. Which of the following would be an appropriate hedge for a short position in this call option?

Use your results from the last three questions to verify your earlier result for the value of the call.

An investor believes that the price of a stock, say IBM's shares, will increase in the next 60 days. If the investor is correct, which combination of the following investment strategies will show a profit in all the choices? (i) - buy the stock and hold it for 60 days (ii) - buy a put option (iii) - sell (write) a call option (iv) - buy a call option (v) - sell (write) a put option

Draw the binomial tree for this option.

If the call finishes in-the-money what is your replicating portfolio cash flow?

Three days ago, you entered into a futures contract to sell €62,500 at $1.50 per €. Over the past three days the contract has settled at $1.50, $1.52, and $1.54. How much have you made or lost?

Value a 1-year call option written on £10,000 with an exercise price of $2.00 = £1.00. The spot exchange rate is $2.00 = £1.00; The U.S. risk-free rate is 5% and the U.K. risk-free rate is also 5%. In the next year, the pound will either double in dollar terms or fall by half (i.e. u = 2 and d = ½). Hint: H = ⅔.

Consider a 1-year call option written on £10,000 with an exercise price of $2.00 = £1.00. The current exchange rate is $2.00 = £1.00; The U.S. risk-free rate is 5% over the period and the U.K. risk-free rate is also 5%. In the next year, the pound will either double in dollar terms or fall by half (i.e. u = 2 and d = ½). If you write 1 call option, what is the value today (in dollars) of the hedge portfolio?

Verify that the dollar value of your put option equals the dollar value of your call. Your answer is worth zero points if it does not include currency symbols ($,€)!

Find the risk neutral probability of an "up" move.

If a currency futures contract (direct quote) is priced below the price implied by Interest Rate Parity (IRP), arbitrageurs could take advantage of the mispricing by simultaneously

For European options, what of the effect of an increase in the strike price E?

Find the hedge ratio for a put option on $15,000 with a strike price of €10,000. In one period the exchange rate (currently S($/€) = $1.50/€) can increase by 60% or decrease by 37.5% .

Find the hedge ratio for a put option on €10,000 with a strike price of $15,000. In one period the exchange rate (currently S($/€) = $1.50/€) can increase by 60% or decrease by 37.5% .

The "open interest" shown in currency futures quotations is