Assignment
1. Find the dollar value today of a 1-period at-the-money cal) 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%.
2. 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 percent over the period and the euro-zone risk-free rate is 4 percent. The volatility of the underlying asset is 10.7 percent.
3. Show that in the Black Scholes formula d2 = d1 - σ(T1/2)
4. 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%.
5. 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. If you pay an option premium of $5,000 to buy this call, at what exchange rate will you break-even?
6. From the perspective of the writer of a put option written on €62,500. If the strike price is $1.55/€, and the option premium is $1,875, at what exchange rate do you start to lose money?
7. Suppose you observe the following one-year interest rates, spot exchange rates and futures prices. Futures contracts are available on €10,000. How much risk-free arbitrage profit could you make on one contract at maturity from this mispricing?
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Exchange Rate
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Interest Rate
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APR
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S0($/€)
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$1.45 = €1.00
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i$
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4%
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F360($/€)
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$1.48 = €1.00
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i€
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3%
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8. 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:
9. 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?
Format your assignment according to the following formatting requirements:
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