Exam 7: Futures and Options on Foreign Exchange

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.

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

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

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

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 European option is different from an American option in that

State the composition of the replicating portfolio; your answer should contain "trading orders" of what to buy and what to sell at time zero.

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?

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 (€)!

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

Find the cost today of your hedge portfolio in pounds.

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

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%.

Calculate the current €/£ spot exchange rate.

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.

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

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?

Most exchange traded currency options

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?

Today's settlement price on a Chicago Mercantile Exchange (CME) Yen futures contract is $0.8011/¥100. Your margin account currently has a balance of $2,000. The next three days' settlement prices are $0.8057/¥100, $0.7996/¥100, and $0.7985/¥100. (The contractual size of one CME Yen contract is ¥12,500,000). If you have a long position in one futures contract, the changes in the margin account from daily marking-to-market, will result in the balance of the margin account after the third day to be