Exhibit 27 illustrates the profit/loss profile of a European-style call option on British pounds.
The call option allows the holder to buy British pounds (£) at a strike price of $1.70/£. The value of this call option is actually the sum of two components:
Total Value (Premium) = Intrinsic Value + Time Value
Intrinsic value is the financial gain if the option is exercised immediately. It is shown by the solid line in Exhibit 28, which is zero until reaching the strike price, then rises linearly (1 cent for each 1 cent increase in the spot rate). Intrinsic value will be zero when the option is out-of-the-money—that is, when the strike price is above the market price—as no gain can be derived from exercising the option. When the spot price rises above the strike price, the intrinsic value becomes positive because the option is always worth at least this value if exercised. The time value of an option exists since the price of the underlying currency, the spot rate, can potentially move further in-the-money between the present time and the option’s expiration date.
EXHIBIT 26
German Mark Put Option (Profit or Loss Per Option)
(800) (600) (400) (200) 0 200 400 600 800
Profit or loss per option, $
0.470 0.475 0.480 0.485 0.490 0.495 0.500
Spot price of underlying currency, $/DM Buyer of a Put Seller of a Put CURRENCY OPTION
68
Note from Exhibit 28 that the time value of a call option varies with option contract periods.
Note from Exhibit 29 that the time value of a call option varies with option contract periods.
EXHIBIT 27
Intrinsic Value, Time Value, Total Value of a Call Option on British Pounds
Spot($/£) (1)
Strike Price (2)
Intrinsic Value of Option (1) − (2) = (3)
Time Value of Option
(4)
Total Value (3) + (4) = (5)
1.65 1.70 0.00 1.37 1.37
1.66 1.70 0.00 1.67 1.67
1.67 1.70 0.00 2.01 2.01
1.68 1.70 0.00 2.39 2.39
1.69 1.70 0.00 2.82 2.82
1.70 1.70 0.00 3.30 3.30
1.71 1.70 1.00 2.82 3.82
1.72 1.70 2.00 2.39 4.39
1.73 1.70 3.00 2.01 5.01
1.74 1.70 4.00 1.67 5.67
1.75 1.70 5.00 1.37 6.37
EXHIBIT 28
Intrinsic Value, Time Value, Total Value of a Call Option on British Pounds
1.65 1.66 1.67 1.68 1.69 1.70 1.71 1.72 1.73 1.74 1.75 Spot Rate
Intrinsic Value Total Value
0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00
Option Premiun (cents/pound)
CURRENCY OPTION
69
See also CURRENCY OPTION PRICING.
CURRENCY OPTION PRICING
Based on the work of Black and Scholes and others, the model yields the option premium.
The basic theoretical model for the pricing of a European call option is:
where
V = Premium on a European call e = 2.71828
S = spot exchange rate (in direct quote) E = exercise or strike rate
rf = foreign interest rate rd = domestic interest rate
t = number of time periods until the expiration date (For example, 90 days means t = 90/365 = 0.25)
N(d) = probability that the normally distributed random variable Z is less than or equal σ = standard deviation per period of (continuously compounded) rate of returnto d The two density functions, d1 and d2, and the formula are determined as follows:
EXHIBIT 29
The Value of a Currency Call Option before Maturity
0
Total value of option (dotted lines)
Time value Intrinsic value Six months
Three months One month
Strike price At the money
Out of the money In the money
Spot price of underlying currency 0
Total value of option (dotted lines)
Time value Intrinsic value Six months
Three months One month
Strike price At the money
Out of the money In the money
Spot price of underlying currency 0
Total value of option (dotted lines)
Time value Intrinsic value Six months
Three months One month
Strike price At the money
Out of the money In the money
Spot price of underlying currency
V ef –rt
S N d[ ( )1 ] ed –rt
E N d[ ( )2 ] –
=
V FN d( )1 E N d[ ( )2 ]ed –rt
[ –
=
d1 = ln[F/E]⁄σ t +σ t⁄2 d2 = d1–σ t
CURRENCY OPTION PRICING
70
Note: In the final derivations, the spot rate (S) and foreign interest rate (rf) have been replaced with the forward rate (F).
The premium for a European put option is similarly derived:
EXAMPLE 35
Given the following data on basic exchange rate and interest rate values:
The values of d1 and d2 are found from the normal distribution table (see Table 5 in the Appendix).
N(d1) = 0.51; N(d2) = 0.49 Substituting these values into the option premium formula yields:
See also BLACK-SCHOLES OPTION PRICING MODEL.
CURRENCY OPTION PRICING SENSITIVITY
If currency options are to be used effectively for hedging or speculative purposes, it is important to know how option prices (values or premiums) react to their various components. Four key variables that impact option pricing are: (1) changing spot rates, (2) time to maturity, (3) changing volatility, and (4) changing interest differentials.
The corresponding measures of sensitivity are:
1. Delta—The sensitivity of option premium to a small change in the spot exchange rate.
2. Theta—The sensitivity of option premium with respect to the time to expiration 3. Lambda—The sensitivity of option premium with respect to volatility.
4. Rho and Phi—The sensitivity of option premium with respect to the interest rate differentials.
Data Symbols Numerical values
Spot rate S $1.7/£
90-day forward F $1.7/£
Exercise or strike rate E $1.7/£
U.S. interest rate rd 0.08 = 8%
British pound interest rate rf 0.08 = 8%
Time t 90/365
Standard deviation σ 0.01 = 10%
V {F N d[ ( )1 –1]–E N d[ ( )2 –1]}ed –rt
=
d1 = ln[F/E]⁄σ t+σ t⁄2
d1 = ln[1.7/1.7]⁄( 90 365⁄ )+( ).1 90 365⁄ ⁄2 = 0.025 d2 = d1–σ t = 0.025–( ).1 90 365⁄ = –0.025
V FN d( )1 –E N d[ ( )2 ]ed –rt
[ [(1.7)(0.51)–(1.7)(0.49)]2.71827–0.08 90/365( )
= =
$0.033/£
=
CURRENCY OPTION PRICING SENSITIVITY
71
Exhibit 30 describes how these sensitivity measures are interpreted.
See also CURRENCY OPTION; CURRENCY OPTION PRICING.
CURRENCY PUT OPTION See CURRENCY OPTION.
CURRENCY QUOTATIONS
Currency quotes are always given in pairs because a dealing bank usually does not know whether a prospective customer is in the market to buy or to sell a foreign currency. The first rate is the bid, or buy rate; the second is the sell, ask, or offer rate.
EXAMPLE 36
Suppose the pound sterling is quoted at $1.5918–29. This quote means that banks are willing to buy pounds at $l.5918 and sell them at $1.5929. Note that the banks will always buy low and sell high. In practice, however, they quote only the last two digits of the decimal. Thus, sterling would be quoted at 18–19 in this example.
Note that when American terms are converted to European terms or direct quotations are converted to indirect quotations, bid and ask quotes are reversed; that is, the reciprocal of the American (direct) bid becomes the European (indirect) ask and the reciprocal of the American (direct) ask becomes the European (indirect) bid.
EXHIBIT 30
Interpretations of Option Pricing Sensitivity Measures
Sensitivity
Measures Interpretation Reasoning
Delta The higher the delta, the greater the chance of the option expiring in-the-money.
Deltas of .7 or up are considered high.
Theta Premiums are relatively insensitive until the last 30 or so days.
Longer maturity options are more highly valued.
This gives a trader the ability to alter an option position without incurring significant time value deterioration.
Lambda Premiums rise with increases in volatility. Low volatility may cause options to sell. A trader is hoping to buy back for a profit immediately after volatility falls, causing option premiums to drop.
Rho Increases in home interest rates cause call option premiums to increase.
A trader is willing to buy a call option on foreign currency before the home interest rate rises (interest rate for the home currency), which will allow the trader to buy the option before its price increases.
Phi Increases in foreign interest rates cause call option premiums to decrease.
A trader is willing to sell a call option on foreign currency before the foreign interest rate rises (interest rate for the foreign currency), which will allow the trader to sell the option before its price decreases.
CURRENCY QUOTATIONS
72
EXAMPLE 37
So, in Example 1, the reciprocal of the American bid of $1.5918/£ becomes the European ask of £0.6282 and the reciprocal of the American ask of $1.5929/£ equals the European bid of
£0.6278/$ resulting in a direct quote for the dollar in London of £0.6278–82. Exhibit 31 sum- marizes this result.
See also BID–ASK SPREAD; DIRECT QUOTE; INDIRECT QUOTE.
CURRENCY REVALUATION
Also called appreciation or strengthening, revaluation of a currency refers to a rise in the value of a currency that is pegged to gold or to another currency. The opposite of revaluation is weakening, deteriorating, devaluation, or depreciation. Revaluation can be achieved by raising the supply of foreign currencies via restriction of imports and promotion of exports.
See also DEVALUATION.
CURRENCY RISK
Also called foreign exchange risk, exchange rate risk, or exchange risk, currency risk is the risk that tomorrow’s exchange rate will differ from today’s rate. In financial activities involv- ing two or more currencies, it reflects the risk that a change (gain or loss) in an entity’s economic value can occur as a result of a change in exchange rates. Currency risk applies to all types of multinational businesses—international trade contracts, international portfolio investments, and foreign direct investments (FDIs). Currency risk exists when the contract is written in terms of the foreign currency or denominated in foreign currency. Also, when you invest in a foreign market, the return on the foreign investment in terms of the U.S. dollar depends not only on the return on the foreign market in terms of local currency but also on the change in the exchange rate between the local currency and U.S. dollar.
The idea of exchange risk in trade contracts is illustrated in the following example.
EXAMPLE 38
Case I. An American automobile distributor agrees to buy a car from the manufacturer in Detroit.
The distributor agrees to pay $25,000 upon delivery of the car, which is expected to be 30 days from today. The car is delivered on the thirtieth day and the distributor pays $25,000. Notice that, from the day this contract was written until the day the car was delivered, the buyer knew the exact dollar amount of his liability. There was, in other words, no uncertainty about the value of the contract.
Case II. An American automobile distributor enters into a contract with a British supplier to buy a car from the United Kingdom for 8,000 pounds. The amount is payable on the delivery of the car, 30 days from today. Suppose, the range of spot rates that we believe can occur on the date the contract is consummated is $2 to $2.10. On the thirtieth day, the American importer will pay
EXHIBIT 31
Direct Versus Indirect Currency Quotations
Direct (American) Indirect (European)
$1.5918–29 £0.6278–82
CURRENCY REVALUATION
73
some amount in the range of 8,000 × $2.00 = $16,000 to 8,000 × 2.10 = $16,800 for the car. As of today, the American firm is uncertain regarding its future dollar outflow 30 days hence. That is, the dollar value of the contract is uncertain.
These two examples help illustrate the idea of foreign exchange risk in international trade contracts. In the case of the domestic trade contract, given as Case I, the exact dollar amount of the future dollar payment is known today with certainty. In the case of the international trade contract given in Case II, where the contract is written in the foreign currency, the exact dollar amount of the contract is not known. The variability of the exchange rate induces variability in the future cash flow. This is the risk of exchange-rate changes, exchange risk, or currency risk. Currency risk exists when the contract is written in terms of the foreign currency or denominated in foreign currency. There is no exchange risk if the international trade contract is written in terms of the domestic currency. That is, in Case II, if the contract were written in dollars, the American importer would face no exchange risk. With the contract written in dollars, the British exporter would bear all the exchange risk, because the British exporter’s future pound receipts would be uncertain. That is, he would receive payment in dollars, which would have to be converted into pounds at an unknown (as of today) pound–
dollar exchange rate. In international trade contracts of the type discussed here, at least one of the two parties bears the exchange risk. Certain types of international trade contracts are denominated in a third currency, different from either the importer’s or the exporter’s domestic currency. In Case II, the contract might have been denominated in the Deutsche mark. With a DM contract, both the importer and the exporter would be subject to exchange-rate risk.
Exchange risk is not limited to the two-party trade contracts; it exists also in foreign direct or portfolio investments. The next example illustrates how a change in the dollar affects the return on a foreign investment.
EXAMPLE 39
You purchased bonds of a Japanese firm paying 12% interest. You will earn that rate, assuming interest is paid in marks. What if you are paid in dollars? As Exhibit 32 shows, you must then convert yens to dollars before the payout has any value to you. Suppose that the dollar appreciated 10% against the yen during the year after purchase. (A currency appreciates when acquiring one of its units requires more units of a foreign currency.) In this example, 1 yen required 0.01 dollars, and later, 1 yen required only 0.0091 dollars; at the new exchange rate it would take 1.099 (0.01/0.0091) yens to acquire 0.01 dollars. Thus, the dollar has appreciated while the yen has depreciated. Now, your return realized in dollars is only 10.92%. The adverse movement in the foreign exchange rate—the dollar’s appreciation—reduced your actual yield.
EXHIBIT 32
Exchange Risk and Foreign Investment Yield
Transaction Yens
Exchange Rate:
No. of Dollars
per 1 Yen Dollars On 1/1/20X1
Purchased one German bond
with a 12% coupon rate 500 $0.01* $5.00
On 12/31/20X1
Expected interest received 60 0.01 0.60
Expected yield 12% 12%
(Continued) CURRENCY RISK
74
Note, however, that currency swings work both ways. A weak dollar would boost foreign returns of U.S. investors. Exhibit 33 is a quick reference to judge how currency swings affect your foreign returns.
CURRENCY RISK MANAGEMENT
Foreign exchange rate risk exists when the contract is written in terms of the foreign currency or denominated in the foreign currency. The exchange rate fluctuations increase the riskiness of the investment and incur cash losses. The financial manager must not only seek the highest return on temporary investments but must also be concerned about changing values of the currencies invested. You do not necessarily eliminate foreign exchange risk. You may only try to contain it. In countries where currency values are likely to drop, financial managers of the subsidiaries should:
• Avoid paying advances on purchase orders unless the seller pays interest on the advances sufficient to cover the loss of purchasing power.
• Not have excess idle cash. Excess cash can be used to buy inventory or other real assets.
• Buy materials and supplies on credit in the country in which the foreign subsidiary is operating, extending the final payment date as long as possible.
• Avoid giving excessive trade credit. If accounts receivable balances are outstanding for an extended time period, interest should be charged to absorb the loss in purchasing power.
• Borrow local currency funds when the interest rate charged does not exceed U.S.
rates after taking into account expected devaluation in the foreign country.