Question 1 Carrick Hargreaves Junior works in the currency-trading unit of Barclays Bank in Manchester, England. His latest speculative move is to profit from his expectation that the Hong Kong dollar will rise significantly against the Taiwanese dollar in the next 90 days. The current spot rate is TWD3.7788/HKD. Based on his expectation, he would like to long a call option contract on Hong Kong dollar and short a put option contract on Hong Kong dollar.
Transcript
Tutorial 7- Foreign currency derivatives
Question 1
Carrick Hargreaves Junior works in the currency-trading unit
of Barclays Bank in Manchester, England. His latest
speculative move is to profit from his expectation that the
Hong Kong dollar will rise significantly against the Taiwanese
dollar in the next 90 days. The current spot rate is
TWD3.7788/HKD. Based on his expectation, he would like to
long a call option contract on Hong Kong dollar and short a
put option contract on Hong Kong dollar.
Details on the 90 day options are as follow:
Calculate the net pay off(in Taiwanese dollar) on the long call, the short put and the combined position if the spot exchange rates at the end of 90 days turn out to be (i)TWD3.9300/HKD, (ii) TWD3.8300/HKD, and
(iii) TWD3.7300/HKD respectively.
Options Contract size
Premium Strike price
Call on HKD
HKD 500,000
TWD 0.0500/HKD TWD 3.8200/HKD
Put on HKD
HKD 500,000
TWD 0.0750/HKD TWD 3.8200/HKD
Long a HKD Call OptionsContract Size = HKD 500,000 ; Strike Price = TWD3.8200/HKD
Premium = TWD0.0500/HKD
Spot rate at maturity
Will call buyer
exercise?
Net profit/loss for call buyer =[(spot-strike) – Premium] * Size OR = -Premium*Size
Hans believes the Swiss Franc will appreciate versus the U.S. dollar in the coming three-month period. He has $100,000 to invest. The current spot rate is$0.5820/SF, the three-month forward rate is $0.5640/SF, and he expects the spot rate to reach $0.6250/SF in the three months.
a) Calculate Han’s expected profit assuming a pure spot market speculation strategy.
Therefore, Hans exchange $100,000 at current spot rate.
$100,000 ÷ $0.5820 /SF = SF171,821.31
Then he waited 3 months, and sold at spot rate. (3rd month)
SF171,821.31 x $0.6250 /SF = $107,388.32
Expected profit earned
= $107,388.32 - $100,000 = $7,388.32
b) Calculate Han’s expected profit assuming he buys or sells SF three months forward.
Forward rate of SF is lower than expected future spot rate, Hans buy SF at today’s forward rate and sell it at higher future spot rate later.
Step 1: use $100000 purchase SF177304.96 forward 3 month at forward rate of $0.5640/SF and fulfill the contract receiving SF 177304.96 at maturity date.
Step 2: simultaneously sell the SF177304.96 in the spot market at Hans’ expected spot rate of $0.6250/SF, receiving SF177304.96*$0.6250/SF=$ 110815.60
Profit= $110815.60-$100000=$10815.60.
Hagi Stoichkow works in the currency-trading unit of La Caxia Bank in Barcelona, Spain. Contrary to most forcecasters, he believes that the Australian dollar(A$) will depreciate versus the US dollar over the coming 30 days although the Federal Reserves is likely to reduce interest rates in US. The current spot exchange rate is $0.7000/A$. Hagi may choose between the following option on the Australian dollar (A$):
Option strike price Premium
Call on A$ $0.7250/A$ $0.0075/A$
Put on A$ $0.7250/A$ $0.0025/A$
a) Should Hagi purchase call option on the Australian dollar or put option on the Australian dollar ? Explain.
Hagi should purchase put option on the Australian dollar as he believes that the Australian dollar(A$) will depreciate over the coming 30 days. If his expectation is right, he have the right to exercise the put option and earn a profit.
b) What is Hagi’s net profit per unit of Australian dollar if the spot exchange rate at the end of the 30 days is $0.6900/A$ ?
Net profit[Put]
=(Strike-Spot)-Premium
=(0.7250-0.6900)- 0.0025
= $0.0325/A$
Question 5
Katya Berezovsky works in the currency-trading unit of Sumara Workers Bank in Togliatti, Russia. Her latest speculative position is to profit from her expectation that the U.S. dollar will rise significantly against the Japanese Yen. The current spot rate is ¥120.00/$. She must choose between the following 90-day options on Japanese Yen:
Option Strike price Premium
Put on Yen ¥125/$ $0.00003/¥
Call on Yen ¥125/$ $0.00046/¥
a) Should Katya buy a put on Yen or a call on Yen?
Katya should buy a put on Yen as he believes that the Yen will depreciate over the coming 90 days. If his expectation turn out to be right, he have the right to exercise the put option(ITM) and earn a profit.
b) Using your answer to part (a), what is Katya’s break-even price?
Katya buys a put on Yen and pays the premium today. In 90 days, exercises the put on Yen and receiving $.
Convert Yen to be denominator since put on Yen. Strike Price: 1÷¥125/$ = $0.008/¥ Premium = $0.00003/¥ Put option buyer: Break-even price = (Strike – Premium) = ( 0.008– 0.00003) = $0.00797/ ¥
c) Using your answer to part (a), what is Katya’s gross profit and net profit (including the premium) if the spot rate at the end of the 90 days is ¥140/$?
Convert the expected spot rate of ¥140/$ to:
1÷ ¥140/$ = $0.00714 /¥
Gross profit = (Strike – Spot)
= (0.008 - 0.00714)
= $0.00086/ ¥
Net Profit = Gross profit – Premium
= $0.00086 /¥ - $0.00003/¥
= $ 0.00083 /¥
Question 6
Explain the difference between foreign currency options and futures and when either might be most appropriately used?
The difference is that an option gives the buyer to choose from exercising or not exercising. The future requires a mandatory delivery. The future is a standardized exchange-traded contract as an alternative to a forward contract.
Reasons why be most appropriately used: Should use option when there is contingency liability where the risk is uncertain in
the future. For example, ABC company sued by foreign customer. ABC company still haven’t know whether can win the lawsuit or not. Therefore, should use option as it has the right to exercise or not to exercise, but not a future contract. Because future is an obligation. At the end of the day, when company win, it can choose to not to exercise the option as it no need to pay compensation in foreign currency.
Should use option when Speculator that have limited capital or borrowing capacity. For example, Speculator uses option to speculate because there is a limit to their losses as he can choose not to speculate, the only loss is the premium.
Question 7Why would anyone write an option, knowing that the gain from receiving the option premium is fixed but the loss if the underlying price goes in wrong direction could be extremely large?
From the option writer’s point of view, only two events can take place:
(1) The option is not exercised. The writer gains the option premium.
(2)The option is exercised. Writer have obligation to fulfill the option buyer. If option exercised, the option writer (i) gains the premium and (ii) experiences only an opportunity cost loss. In other words, the loss is not a cash loss, but rather the opportunity cost loss of having foregone the potential of making even more profit had the underlying currency been sold at a more advantageous price. This is somewhat equivalent of having sold (call option writer) or bought (put option writer) at a price better than current market, only to have the market price move even further in a beneficial direction.
Question 8
A trader holds a call and a put on the British pound. The following information is available:Size of option contract = GBP200,000Price of call AUD0.01/GBPPrice of put AUD0.008/GBPExercise exchange rate of call AUD2.50/GBPExercise exchange rate of put AUD2.50/GBPCalculate the net pay-off on the call, the put and the combined position at the following spot exchange rates (AUD/GBP): (a) 2.505, (b) 2.540, (c) 2.495 and (d) 2.480.
