A US importer will have a net cash outflow of EURO2,500,000 in payment for goods bought in January 2015 (assumed to be 0.25 years away). The importer wishes to hedge this risk to avoid the exchange rate risk and is considering hedging using (i) at the money call options on the pound; (ii) a forward contract and (iii) a combination of calls and puts.
The prevailing market data is given below:
Market Data (1st October 2014)
Spot Exchange Rate = Spot Exchange Rate = $1.2596/Euro
Three month Euro interest rate = 0.1% p.a.
Three month US Dollar interest rate = 0.3% p.a.
Premium on a May Euro Call Option, Strike = $1.24/Euro = 2.89 cents/Euro
Premium on a May Euro Call Option, Strike = $1.26/Euro = 1.72 cents/Euro
Premium on a May Euro Call Option, Strike = $1.28/Euro = 0.91 cents/Euro
Premium on a May Euro Put Option, Strike = $1.24/Euro = 0.87 cents/Euro
Premium on a May Euro Put Option, Strike = $1.26/Euro= 1.70 cents/Euro
Premium on a May Euro Put Option, Strike = $1.28/Euro = 2.89 cents/Euro
Required:
1. What is meant by covered interest parity? Using the data above calculate a three month forward rate to buy Euro’s for dollars.
2. Explain, using the market data above, how call options on foreign currenct can be used to establish a ceiling price when purchasing foreign currency and how put options can be used to establish a floor price when selling foreign currency.
3. Consider, using the market data above, the obligations on the SELLER of each of these calls and puts if the option were to be exercised. Identify the circumstances when the options would be exercised.
Covered Interest Parity is such situation where the interest rate becomes almost equal to currency value of two nations. In such situation, any arbitrage opportunities or return cannot be possible to earn doing trading between the currencies of two countries (Aizenman, J. and Hutchison, M. 2010).
As for example, the currency value and interest rate of Country A and Country B are same. The interest rates of Country A and Country B are respectively 10% and 7%. An investor borrows a certain amount in the currency of Country B and he thinks to invest the money in the currency of Country A. So, it is required to convert the money with spot price of Country A. For the repayment of borrowing money, the investor needs to go for a forward back for bringing back the money from the currency of Country A to Country B. At that time, the inventors cannot earn any profit due to existence of covered interest parity. Covered interest parity eradicates the entire profits from the trading of currency (Chandler, M. 2009).
Forward is the currency exchange rate for future. A commercial bank gives guarantee to exchange the currency of a country to another currency of a country and obviously at a specified future date. It is calculated on the basis of spot price of currency (Chen, J. 2009).
Forward can be calculated by using following formula:
Where, ‘S’ is spot exchange rate of two countries.
‘rd’ is domestic interest rate
‘rf’ is foreign interest rate
Given, Spot Exchange rate is $1.2596/Euro
Three months Euro interest rate is 0.1% p.a.
Three month US Dollar interest rate is 0.3% p.a.
It is assumed that the total number of days in a year is 360 (Croke, L. 2009).
So, the forward rate is calculated as follows:
=1.2589
Therefore, the three months forward rate of Dollar and Euro is 1.2589.
Ceiling price is the highest price where buyer has to pay for buying the options. Ceiling price is the highest price limit where sell can charge against an option (CÌŒuhaj, G. 2009). If the ceiling is price is greater than the current spot price than buyer of the call option can exercise the options.
Ceiling Price = Strike Price + Premium
Strike price is price of a option which is the particular price at which the currency option can be purchased or sold by the possessor or the purchaser of the option contract (Davidson, A. 2009). Usually, the strike price is set which is closer to current spot price.
Premium is a price which is paid by the buyer of an option for right to buy or sell the option. The premium price is paid to seller of an option (Dobeck, M. and Elliott, E. 2007).
|
Strike Price |
Premium |
Ceiling Price |
Situation |
|
$1.24 |
0.0289 |
$1.27/Euro |
Ceiling Price > Spot Price |
|
$1.26 |
0.0172 |
$1.28/Euro |
Ceiling Price > Spot Price |
|
$1.28 |
0.0091 |
$1.29/Euro |
Ceiling Price > Spot Price |
Here, the spot price is $1.2596/Euro.
It is observed in the above table that the all the cases have the ceiling price greater than the current spot price of option. So, the buyer may not exercise the option.
Floor price is the lowest price at which seller of the option allows to sold the option. If the floor price is less than current spot price the seller of the put option would not exercise the option (Fabozzi, et al, M. 2002).
Floor Price = Strike Price – Premium
|
Strike Price |
Premium |
Floor Price |
Situation |
|
$1.24 |
0.0087 |
$1.23/Euro |
Floor Price < Spot Price |
|
$1.26 |
0.017 |
$1.24/Euro |
Floor Price < Spot Price |
|
$1.28 |
0.0289 |
$1.25/Euro |
Floor Price < Spot Price |
In the above table, it can be seen that the all the case of put options have the floor price is less than the current spot price of option. So, the seller may not exercise the option (Hömberg, D. and Tröltzsch, F. 2013).
Seller obligation on call options
The obligation of seller is to sell the underlying security if the call option is exercised by the call purchaser on or before the expiry date of option (Jacque, L. 2010).
If the spot price is less than equal to exercise price or strike price, the seller only can earn the premium amount from the call option (Landuyt, G. et al R. 2009). When the spot price of currency call option is greater than the strike price or exercise price, the seller may have to bear loss beyond the premium amount (Makin, A. 2009).
In case of Spot Price ≤ Strike Price,
Seller’s Payoff for Call Option (US$/Euro) = Premium Price
In case of Spot Price > Strike Price,
Seller’s Payoff for Call Option (US$/Euro) = Spot Price – (Strike Price + Premium)
|
Strike Price |
Premium |
Spot Price |
Payoff |
|
$1.24 |
0.0289 |
$1.2596 |
($0.0093) |
|
$1.26 |
0.0172 |
$1.2596 |
$0.0172 |
|
$1.28 |
0.0091 |
$1.2596 |
$0.0091 |
According to the above table, it can be observed that the payoff of selling a call option is negative. So, at strike price of $1.24, seller has to bear loss of $0.0093 if it is exercised by the call buyer (Neaime, S. and Colton, N. 2005).
At strike price $1.26; the seller can earn the profit equal to premium price $0.0172 if the call holder exercises the option.
At strike price $1.28; the seller also can earn only the premium price $0.0172 if it is exercised by the call buyer.
Seller obligation on put options
The obligation of seller in case of put option is to purchase the underlying security if the pet option is exercised by the put holder on or before expiry date (Rebonato, et al 2009).
If the spot price is less than equal to exercise price or strike price of a put option, the seller may earn or may have to bear the loss. The loss or earnings depends on the premium amount of the put option. When, the spot price is greater than the strike price, the seller can earn only the premium amount of put option (Ramaswamy, S. 2011).
In case of Spot Price ≤ Strike Price,
Seller’s Payoff for Put Option (US $/Euro) = (Spot Price – Strike Price) + Premium
In case of Spot Price > Strike Price,
Seller’s Payoff for Put Option (US $/Euro) = Premium Price
|
Strike Price |
Premium |
Spot Price |
Payoff |
|
$1.24 |
0.0087 |
$1.2596 |
$0.0087 |
|
$1.26 |
0.017 |
$1.2596 |
$0.0166 |
|
$1.28 |
0.0289 |
$1.2596 |
$0.0085 |
In case of strike price of $1.24, the seller can only earn the premium amount ($0.0087) of the put options if it is exercised by the put buyer.
In case of strike price of $1.26, the seller can gain more ($0.0166) from selling of put option if it is exercised by the put buyer.
In case of strike price of $1.28, the seller can also gain profit of $0.0085 from the selling of put option if it is exercised by the put buyer.
Buyer’s Payoff for a call option
|
Strike Price |
Premium |
Spot Price |
Payoff |
|
$1.24 |
0.0289 |
$1.2596 |
-$0.0093 |
|
$1.26 |
0.0172 |
$1.2596 |
-$0.0172 |
|
$1.28 |
0.0091 |
$1.2596 |
-$0.0091 |
The above table describes that, the buyer has to bear loss less at $1.24 among the others strike prices. In case of others strike prices, the buyer can suffer equal to premium price.
Buyer’s Payoff for a put option
|
Strike Price |
Premium |
Spot Price |
Payoff |
|
$1.24 |
0.0087 |
$1.2596 |
-$0.0087 |
|
$1.26 |
0.017 |
$1.2596 |
-$0.0166 |
|
$1.28 |
0.0289 |
$1.2596 |
-$0.0085 |
According to the above table, it is observed that the buyer can bear loss equal to premium price at strike price $1.24. The highest loss will be at strike price $1.26. The loss is less at strike price $1.28 among the others strike prices (Senders, S. and Truitt, A. 2007).
Table 1:
|
Price on expiry date |
Exercise price |
Premium in cents |
Pay off |
Exercise Price |
Premium in cents |
Pay off |
Net Pay Off |
|
1.20 |
1.25 |
2.89 |
(2.89) |
1.25 |
0.87 |
0.87 |
(2.02) |
|
1.21 |
1.25 |
2.89 |
(2.89) |
1.25 |
0.87 |
0.87 |
(2.02) |
|
1.22 |
1.25 |
2.89 |
(2.89) |
1.25 |
0.87 |
0.87 |
(2.02) |
|
1.23 |
1.25 |
2.89 |
(2.89) |
1.25 |
0.87 |
0.87 |
(2.02) |
|
1.24 |
1.25 |
2.89 |
(2.89) |
1.25 |
0.87 |
0.87 |
(2.02) |
|
1.25 |
1.25 |
2.89 |
(2.89) |
1.25 |
0.87 |
0.87 |
(2.02) |
|
1.26 |
1.25 |
2.89 |
0.05 |
1.25 |
0.87 |
(0.01) |
0.04 |
|
1.27 |
1.25 |
2.89 |
0.07 |
1.25 |
0.87 |
(0.02) |
0.05 |
|
1.28 |
1.25 |
2.89 |
0.09 |
1.25 |
0.87 |
(0.03) |
0.06 |
|
1.29 |
1.25 |
2.89 |
0.11 |
1.25 |
0.87 |
(0.04) |
0.07 |
|
1.30 |
1.25 |
2.89 |
0.14 |
1.25 |
0.87 |
(0.05) |
0.09 |
|
1.31 |
1.25 |
2.89 |
0.16 |
1.25 |
0.87 |
(0.06) |
0.10 |
|
1.32 |
1.25 |
2.89 |
0.18 |
1.25 |
0.87 |
(0.07) |
0.11 |
According to the table 1, the research analyst analyses that United States of American importer has hedged his money and the analyst observed that the importer has faced a loss by hedging his portfolio. The total net pay off the U.S. importer is -11.60 in cents (Singh, M. 2010).
Table 2:
|
Price on expiry date |
Exercise price |
Premium in cents |
Pay off |
Exercise Price |
Premium in cents |
Pay off |
Net Pay Off |
|
1.20 |
1.25 |
1.72 |
(1.72) |
1.25 |
1.70 |
1.70 |
(0.02) |
|
1.21 |
1.25 |
1.72 |
(1.72) |
1.25 |
1.70 |
1.70 |
(0.02) |
|
1.22 |
1.25 |
1.72 |
(1.72) |
1.25 |
1.70 |
1.70 |
(0.02) |
|
1.23 |
1.25 |
1.72 |
(1.72) |
1.25 |
1.70 |
1.70 |
(0.02) |
|
1.24 |
1.25 |
1.72 |
(1.72) |
1.25 |
1.70 |
1.70 |
(0.02) |
|
1.25 |
1.25 |
1.72 |
(1.72) |
1.25 |
1.70 |
1.70 |
(0.02) |
|
1.26 |
1.25 |
1.72 |
(0.80) |
1.25 |
1.70 |
0.53 |
(0.27) |
|
1.27 |
1.25 |
1.72 |
(0.79) |
1.25 |
1.70 |
0.52 |
(0.27) |
|
1.28 |
1.25 |
1.72 |
(0.78) |
1.25 |
1.70 |
0.51 |
(0.27) |
|
1.29 |
1.25 |
1.72 |
(0.77) |
1.25 |
1.70 |
0.50 |
(0.27) |
|
1.30 |
1.25 |
1.72 |
(0.76) |
1.25 |
1.70 |
0.49 |
(0.27) |
|
1.31 |
1.25 |
1.72 |
(0.75) |
1.25 |
1.70 |
0.48 |
(0.27) |
|
1.32 |
1.25 |
1.72 |
(0.74) |
1.25 |
1.70 |
0.47 |
(0.27) |
According to the table 2, the research analyst analyses that United States of American importer has hedged his money and the analyst observed that the importer has faced a loss by hedging his portfolio. The total net pay off the U.S. importer is -2.01 in cents (Williams, R. 2011).
Table 3:
|
Price on expiry date |
Exercise price |
Premium in cents |
Pay off |
Exercise Price |
Premium in cents |
Pay off |
Net Pay Off |
|
1.20 |
1.25 |
0.91 |
(0.91) |
1.25 |
2.89 |
2.89 |
1.98 |
|
1.21 |
1.25 |
0.91 |
(0.91) |
1.25 |
2.89 |
2.89 |
1.98 |
|
1.22 |
1.25 |
0.91 |
(0.91) |
1.25 |
2.89 |
2.89 |
1.98 |
|
1.23 |
1.25 |
0.91 |
(0.91) |
1.25 |
2.89 |
2.89 |
1.98 |
|
1.24 |
1.25 |
0.91 |
(0.91) |
1.25 |
2.89 |
2.89 |
1.98 |
|
1.25 |
1.25 |
0.91 |
(0.91) |
1.25 |
2.89 |
2.89 |
1.98 |
|
1.26 |
1.25 |
0.91 |
(0.02) |
1.25 |
2.89 |
0.04 |
0.02 |
|
1.27 |
1.25 |
0.91 |
(0.01) |
1.25 |
2.89 |
0.02 |
0.01 |
|
1.28 |
1.25 |
0.91 |
0 |
1.25 |
2.89 |
0 |
0 |
|
1.29 |
1.25 |
0.91 |
0.01 |
1.25 |
2.89 |
(0.02) |
(0.01) |
|
1.30 |
1.25 |
0.91 |
0.02 |
1.25 |
2.89 |
(0.04) |
(0.02) |
|
1.31 |
1.25 |
0.91 |
0.03 |
1.25 |
2.89 |
(0.06) |
(0.03) |
|
1.32 |
1.25 |
0.91 |
0.04 |
1.25 |
2.89 |
(0.08) |
(0.04) |
According to the table 3, the research analyst analyses that United States of American importer has hedged his money and the analyst observed that the importer has made a profit by hedging his portfolio. The total net pay off the U.S. importer is 11.85 in cents (Zeldes, S. and Geanakoplos, J. 2009).
The research analyst observed that the U.S. importer has made a loss from his portfolio by hedging in different ways. From the above three table i.e., table 1, table, and table 3, the importer has made a loss of (11.6) cents from the table 1, from table 2 the importer has made a loss of (2.01) cents and from table 3 the importer has made a profit of 11.85 cents. But the total net loss made by the importer by hedging is (1.76) cents (Makin, A. 2009).
References:
Aizenman, J. and Hutchison, M. (2010). Exchange market pressure and absorption by international reserves. Cambridge, Mass.: National Bureau of Economic Research.
Chandler, M. (2009). Making sense of the dollar. New York: Bloomberg Press.
Chen, J. (2009). Essentials of foreign exchange trading. Hoboken, N.J.: John Wiley.
Croke, L. (2009). I’m broke!. St. Catharines, Ont.: Crabtree Pub.
CÌŒuhaj, G. (2009). Standard catalog of world paper money. Iola, WI: Krause.
Davidson, A. (2009). How the global financial markets really work. London: Kogan Page.
Dobeck, M. and Elliott, E. (2007). Money. Westport, Conn.: Greenwood Press.
Fabozzi, F., Mann, S. and Choudhry, M. (2002). The global money markets. Hoboken, N.J.: J. Wiley.
Makin, A. (2009). Global imbalances, exchange rates and stabilization policy. Basingstoke, Hampshire: Palgrave Macmillan.
Hömberg, D. and Tröltzsch, F. (2013). System modeling and optimization. Berlin: Springer.
Jacque, L. (2010). Global derivative debacles. Singapore: World Scientific.
Landuyt, G., Choudhry, M., Joannas, D., Pereira, R. and Pienaar, R. (2009). Capital market instruments ;Analysis and valuation. Basingstoke: Palgrave Macmillan.
Neaime, S. and Colton, N. (2005). Money and finance in the Middle East. Amsterdam: Elsevier JAI.
Ramaswamy, S. (2011). Market structures and systemic risks of exchange-traded funds. [Basel, Switzerland]: Bank for International Settlements, Monetary and Economic Dept.
Rebonato, R., McKay, K. and White, R. (2009). The SABR/LIBOR market model. Hoboken, NJ: John Wiley & Sons.
Senders, S. and Truitt, A. (2007). Money. Oxford: Berg.
Singh, M. (2010). Collateral, Netting and Systemic Risk in the OTC Derivatives Market. Washington: International Monetary Fund.
Makin, A. (2009). Global imbalances, exchange rates and stabilization policy. Basingstoke, Hampshire: Palgrave Macmillan.
Williams, R. (2011). An introduction to trading in the financial markets. Burlington, MA: Academic Press/Elsevier.
Zeldes, S. and Geanakoplos, J. (2009). Market Valuation of Accrued Social Security Benefits.. Cambridge, Mass.: National Bureau of Economic Research.
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