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.

Find the Black-Scholes price of a six-month call option written on €100,000 with a strike price of $1.00 = €1.00.The current exchange rate is $1.25 = €1.00; The U.S.risk-free rate is 5% over the period and the euro-zone risk-free rate is 4%.The volatility of the underlying asset is 10.7 percent.

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% .

Draw the binomial tree for this option.

Exercise of a currency futures option results in

Suppose the futures price is below the price predicted by IRP.What steps would assure an arbitrage profit?

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

The current spot exchange rate is $1.55 = €1.00 and the three-month forward rate is $1.60 = €1.00.Consider a three-month American call option on €62,500.For this option to be considered at-the-money,the strike price must be

Find the dollar value today of a 1-period at-the-money call option on ¥300,000.The spot exchange rate is ¥100 = $1.00.In the next period,the yen can increase in dollar value by 15 percent or decrease by 15 percent.The risk free rate in dollars is i_$ = 5%; The risk free rate in yen is i_¥ = 1%.

Suppose you observe the following 1-year interest rates,spot exchange rates and futures prices.Futures contracts are available on €10,000.How much risk-free arbitrage profit could you make on 1 contract at maturity from this mispricing?

You have written a call option on £10,000 with a strike price of $20,000.The current exchange rate is $2.00/£1.00 and in the next period the exchange rate can increase to $4.00/£1.00 or decrease to $1.00/€1.00 .The current interest rates are i_$ = 3% and are i_£ = 2%.Find the hedge ratio and use it to create a position in the underlying asset that will hedge your option position.

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 put option.

Draw the tree for a put option on $20,000 with a strike price of £10,000.The current exchange rate is £1.00 = $2.00 and in one period the dollar value of the pound will either double or be cut in half.The current interest rates are i_$ = 3% and are i_£ = 2%.

Consider an option to buy €12,500 for £10,000. In the next period, the euro can strengthen against the pound by 25% (i.e. each euro will buy 25% more pounds) or weaken by 20%. Big hint: don't round, keep exchange rates out to at least 4 decimal places. -Find the risk neutral probability of an "up" move.

Assume that the dollar-euro spot rate is $1.28 and the six-month forward rate is .The six-month U.S.dollar rate is 5% and the Eurodollar rate is 4%.The minimum price that a six-month American call option with a striking price of $1.25 should sell for in a rational market is

A CME contract on €125,000 with September delivery

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 ($,€)!

In which market does a clearinghouse serve as a third party to all transactions?

Draw the tree for a call option on $20,000 with a strike price of £10,000.The current exchange rate is £1.00 = $2.00 and in one period the dollar value of the pound will either double or be cut in half.The current interest rates are i_$ = 3% and are i_£ = 2%.

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