OPTION STRATEGIES AND CURRENCY FORWARDS

Question 01: Currency Forward

Where to lend and borrow?

Suppose we invest $1 in U.S. denominated T-bonds. In 1-year, we will gain interest rate which is 4% ´ $1 = $0.04. If we convert $1 into pound and invest in pound-denominated bonds, we will gain 7% ´ £0.625 = £0.044. If the exchange rate was not changed, then we will get £0.044 ´ $1.6 = $0.07. Since we have greater gains from converting U.S. dollars to pounds and investing in pound-denominated bonds than gains from investing in U.S dollar-denominated bonds ($0.07 vs. $0.04), we would like to borrow U.S. dollars in the U.S. and lend pounds in UK. This is because we can gain more profits from lending pounds in UK due to r_uk is greater than r_us. However, we may face the risk of the exchange rate. To hedge against the volatility of exchange rate, we should enter a forward foreign exchange rate contract.

Arbitrage

1. Borrow U.S dollars in the U.S, convert this amount to pounds and lend pounds in UK (e.g buy pound-denominated bonds).

2. Sell a forward contract in the amount of the proceeds of the investment amount in pounds back to US dollar.

Assume lending pounds at risk-free and interest paid one time at the end of the investment horizon. Below is an example of arbitrage:

Cash flow

Year 0 Year 1

$ £ $ £

1. Borrow dollars r_us = 4% +1.6 -1.664

2. Convert to pound at $1.6/£ -1.6 +1

3. Invest in pound-denominated bonds -1 +1.07

at interest rate r_uk = 7%

4. Sell a forward contract at £1.07 +1.6906 -1.07

value at today forward rate $1.58/£

Total 0 0 +0.0264 0

If we ignore the transaction cost, the arbitrage profit is $0.0264. The above transactions show that we can arbitrage with zero initial investment by borrowing US. dollars, converting into pounds and invest in pound-denominated bills. At the same time, we hedge against currency exchange rate risk by selling a forward contract. This arbitrage is call covered interest arbitrage.

Conclusion

If we want to invest dollars, there are 2 ways:

1. Buy dollar-dominated bonds in the U.S.

2. Exchange dollars into pounds, buy pound-denominated bonds and enter a currency forward contract to guarantee the exchange rate in which we will convert back pounds into dollars.

In general, the second way is preferable because we can gain arbitrage profits while hedging the position.

Question 02: Arbitrage Profit through Yen/U.S. dollar Currency Forwards

Yen/ U.S.$ currency forwards contract price

From the perspective of a Japanese investor, the price of a 6-month Yen/U.S.$ currency forward contract is F_o,T = x_o e^(ry-rus).T (x_o: exchange rate; r_y : 6-month Japanese interest rate; r_us : 6-month interest rate). In other words, F_o,T = 124.30 e^{(0.001-0.038)x0.5} = \122.0216.

Yen arbitrage profit

We ignore the transaction cost and assume lending at risk-free and continuous compounded interest during 3-month investment period.

Cash flow (million)

Month 0 Month 3

$ \ $ \

1. Borrow dollars r_us =3.5% +1 -1.0088

2. Convert to Yen at \124.30/$ -1 +124.30

3. Invest in Yen-denominated bonds -124.30 +124.4555

at interest rate r_y = 0.50%

4. Buy a forward contract at $1.0088 +1.0088 -124.3452

value at today forward rate \123.2605/$

Total 0 0 0 +0.1103

The Yen arbitrage profit is \0.1103 million.

Question 03: Long Strangle Strategy

· Donie should choose a long strangle strategy by buying out-of-the money calls and a puts with the same time to expiration to achieve the client’s objective. The reasons for choosing this strategy are:

- The premium of acquiring the position is minimum.

- The client expects an extremely high increase in volatility in the stock price of TRT Co. in either direction in response to the court’ decision.

· The long strangle strategy will provide the client with following benefits:

- Reward: Unlimited

- Profit: The potential maximum gain per share is unlimited when the substantial up and down movements of the stock are significant.

- Loss: The loss is limited to the cost of acquiring the position, which is the total premium paid for buying a call and a put option: $4 + $5 = $9.

- Breakeven stock prices: The breakeven happens when:

- The stock price (S) rises above the strike price of the call option ($60) by an amount equal to the cost of acquiring the position ($9). Or S> $69.

- The stock price (S) falls below the strike price of the put option ($55) by an amount equal to the premium paid to acquire the position ($9). Or S< $46.

Question 04: Transactions to obtain arbitrage profits without initial investment

Yen arbitrage profit with 0.0084 forward exchange rate

From the perspective of American investors. We ignore the transaction cost and assume lending at risk-free and continuous compounded interest during 1-year investment period.

Cash flow

Year 0 Year 1

$ \ $ \

1. Borrow dollars r_us =5% +0.008 -0.0084

2. Convert to Yen at $0.008/\ -0.008 +1

3. Invest in Yen-denominated bonds -1 +1.0101

at interest rate r_y = 1%

4. Sell a forward contract at $1.0101 +0.0085 -1.0101

value at today forward rate $0.0084/\

Total 0 0 +0.0001 0

The arbitrage profit is $0.0001 per Yen.

Yen arbitrage profit with 0.0083 forward exchange rate

Cash flow

Year 0 Year 1

$ \ $ \

1. Borrow dollars r_us =5% +0.008 -0.0084

2. Convert to Yen at $0.008/\ -0.008 +1

3. Invest in Yen-denominated bonds -1 +1.0101

at interest rate r_y = 1%

4. Sell a forward contract at $1.0101 +0.0084 -1.0101

value at today forward rate $0.0083/\

Total 0 0 0 0

The arbitrage profit is zero. This might be because forward exchange rate equals the exchange rate in 1 year.