Exam 7: Futures and Options on Foreign Exchange

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 with a strike price of $1.50 = €1.00.Immediate exercise of this option will generate a profit of

Comparing "forward" and "futures" exchange contracts,we can say that

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%.

For European currency options written on euro with a strike price in dollars,what of the effect of an increase in the exchange rate S(€/$)?

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?

Exercise of a currency futures option results in

Which of the following is correct?

Which of the lines is a graph of the profit at maturity of writing a call option on €62,500 with a strike price of $1.20 = €1.00 and an option premium of $3,125?

For European currency options written on euro with a strike price in dollars,what of the effect of an increase r_€?

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.

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

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?

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. -Calculate the hedge ratio.

In reference to the futures market,a "speculator"

Consider an option to buy £10,000 for €12,500. In the next period, if the pound appreciates against the dollar by 37.5 percent then the euro will appreciate against the dollar by ten percent. On the other hand, the euro could depreciate against the pound by 20 percent. Big hint: don't round, keep exchange rates out to at least 4 decimal places. -Calculate the hedge ratio.

Find the value of a call option written on €100 with a strike price of $1.00 = €1.00.In one period there are two possibilities: the exchange rate will move up by 15% or down by 15% .The U.S.risk-free rate is 5% over the period.The risk-neutral probability of dollar depreciation is ²/₃ and the risk-neutral probability of the dollar strengthening is ¹/₃.

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

Consider an option to buy £10,000 for €12,500. In the next period, if the pound appreciates against the dollar by 37.5 percent then the euro will appreciate against the dollar by ten percent. On the other hand, the euro could depreciate against the pound by 20 percent. Big hint: don't round, keep exchange rates out to at least 4 decimal places. -Find the risk neutral probability of an "up" move.

For European options,what of the effect of an increase in S_t?

Comparing "forward" and "futures" exchange contracts,we can say that