fOptions (version 251.70)

CurrencyTranslatedOptions: Valuation of Currency Translated Options

Description

This is a collection of functions to valuate currency translated options. Currency translated options are options on foreign assets where the payoff is exchanged into domestic currency at expiration. For example, a US investor is interested in buying an option that is linked to the Nikkei index that is priced in yen. There are two types or risks, changing prices and exchange rates, to consider when valuing currency-translated options. The functions are:

ll{ FEInDomesticFXOption Foreign Exchange In Domestic Currency Option, QuantoOption Quanto Option, EquityLinkedFXOption Equity Linked FX Option, TakeoverFXOption Takeover FX Option. }

Usage

FEInDomesticFXOption(TypeFlag, S, E, X, Time, r, q, sigmaS, 
    sigmaE, rho, title = NULL, description = NULL)
QuantoOption(TypeFlag, S, Ep, X, Time, r, rf, q, sigmaS, 
    sigmaE, rho, title = NULL, description = NULL) 
EquityLinkedFXOption(TypeFlag, E, S, X, Time, r, rf, q, 
    sigmaS, sigmaE,rho, title = NULL, description = NULL)
TakeoverFXOption(V, B, E, X, Time, r, rf, sigmaV, sigmaE, 
    rho, title = NULL, description = NULL)

Arguments

B

[TakeoverFX*] - the value of the foreign firm in the foreign currency at the option expiration, a numeric value.

description

a character string which allows for a brief description.

E

[FEInDomesticFX*] - the spot exchange rate specified in units of the domestic currency per unit of the foreign currency, a numeric value. [TakeoverFX*] - the currency price quoted in units of the domestic currency per unit of the foreign

Ep

[Quanto*] - the predetermined exchange rate specified in units of domestic currency per unit of foreign currency.

q

[FEInDomesticFX*][EquityLinkedFX*] - the instantaneous proportional dividend payout rate of the underlying asset, a numerical value.

r

[FEInDomesticFX*][TakeoverFX*] - the domestic interest rate, a numeric value. E.g. 0.25 means 25% p.a.

rf

[TakeoverFX*] - the foreign interest rate, a numeric value.

rho

[TakeoverFX*] - the correlation between annualized volatility of the currency price quoted in units of the domestic currency per unit of the foreign currency and the annualized volatility of the value of the foreign firm, a num

S

[FEInDomesticFX*][EquityLinkedFX*] - the underlying asset price in foreign currency, a numeric value.

sigmaE

[TakeoverFX*] - the annualized volatility of the currency price quoted in units of the domestic currency per unit of the foreign currency, a numeric value; e.g. 0.3 means 30% volatility pa.

sigmaS

[Quanto*] - the annualized volatility of the underlying asset, a numeric value; e.g. 0.3 means 30% volatility pa.

sigmaV

[TakeoverFX*] - the annualized volatility of the value of the foreign firm, a numeric value; e.g. 0.3 means 30% volatility pa.

Time

the time to maturity, a numeric value.

title

a character string which allows for a project title.

TypeFlag

a character string either "c" for a call option or a "p" for a put option.

V

[TakeoverFX*] - the value of the foreign firm in the foreign currency, a numeric value.

X

[FEInDomesticFX*] - the strike (delivery) price in domestic currency, a numeric value. [TakeoverFX*] - the strike price quoted in units of the domestic currency per unit of the foreign currency.

Value

• The option price, a numeric value.

Details

Equity Linked Foreign Exchange Options: An equity-linked foreign-exchange option is an option on the foreign exchange rate and is linked to the forward price of a stock or equity index. This option can be priced analytically using a model introduced by Reiner (1992). Quanto Options: A fixed exchange-rate foreign-equity option (Quanto) is denominated in another currency than that of the underlying equity exposure. The face value of the currency protection expands or contracts to cover changes in the foreign currency value of the underlying asset. Quanto options can be priced analytically using a model published by Dravid, Richardson, and Sun (1993). Foreign Equity Options: A foreign equity option is an option on a foreign asset where the strike price is specified in either domestic or foreign currency and the payoff at expiration is valued in domestic currency. Foreign equity options can be priced analytically using a model introduced by Reiner (1992). Takeover Foreign Exchange Options: A takeover foreign exchange call option gives the buyer the right purchase a specified number of units of foreign currency at a strike price if the corporate takeover is successful. This option can be priced analytically using a model introduced by Schnabel and Wei (1994). [Haug's Book, Chapter 2.13.4]

References

Haug E.G. (1997); The Complete Guide to Option Pricing Formulas, Chapter 2.13, McGraw-Hill, New York.

Examples

## Examples from Chapter 2.13 in E.G. Haug's Option Guide (1997)

## Foreign Equity Options Struck in Domestic Currency [2.13.1]:
   FEInDomesticFXOption(TypeFlag = "c", S = 100, E = 1.5, 
     X = 160, Time = 0.5, r = 0.08, q = 0.05, sigmaS = 0.20, 
     sigmaE = 0.12, rho = 0.45)

## Fixed Exchange-Rate Foreign-Equity Option [2.13.2]: 
   QuantoOption(TypeFlag = "c", S = 100, Ep = 1.5, X = 105, 
     Time = 0.5, r = 0.08, rf = 0.05, q = 0.04, sigmaS= 0.2, 
     sigmaE = 0.10, rho = 0.30) 

## Equity Linked Foreign Exchange Option [2.13.3]:
   EquityLinkedFXOption(TypeFlag = "p", E = 1.5, S = 100, 
     X = 1.52, Time = 0.25, r = 0.08, rf = 0.05, q = 0.04, 
     sigmaS = 0.20, sigmaE = 0.12, rho = -0.40)

## Takeover Foreign-Exchange Option [2.13.4]:
   TakeoverFXOption(V = 100, B = 100, E = 1.5, X = 1.55, Time = 1, 
     r = 0.08, rf = 0.06, sigmaV = 0.20, sigmaE = 0.25, rho = 0.1)