Exam 7: Futures and Options on Foreign Exchange

Assume that the dollar-euro spot rate is $1.28 and the six-month forward rate is $F _ { T } = S _ { t } e ^ { \left( r _ { \$ } - r _ { € } \right) T } = \$ 1.28 e ^ { .01 \times .5 } = \$ 1.2864$ .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

Yesterday,you entered into a futures contract to sell €62,500 at $1.50 per €.Your initial performance bond is $1,500 and your maintenance level is $500.At what settle price will you get a demand for additional funds to be posted?

Which equation is used to define the futures price?

A currency futures option amounts to a derivative on a derivative.Why would something like that exist?

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

Empirical tests of the Black-Scholes option pricing formula

Find the dollar value today of a 1-period at-the-money call option on €10,000.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%.

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.

In the event of a default on one side of a futures trade,

American call and put premiums

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

Which of the following is correct?

Yesterday,you entered into a futures contract to buy €62,500 at $1.50 per €.Suppose the futures price closes today at $1.46.How much have you made/lost?

The volume of OTC currency options trading is

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 risk-neutral probability of an "up" move FOR YOUR TREE.Hint: you can't recycle your risk neutral probability from the call option.

Find the cost today of your hedge portfolio in pounds.

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.

A European option is different from an American option in that

Using your results from parts a)and b)find the value of this put option (in €). Your answer is worth zero points if it does not include currency symbols (€)!