CurrencyTranslatedOptions | R Documentation |
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:
FEInDomesticFXOption | Foreign Exchange In Domestic Currency Option, |
QuantoOption | Quanto Option, |
EquityLinkedFXOption | Equity Linked FX Option, |
TakeoverFXOption | Takeover FX Option. |
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)
B |
[TakeoverFX*] - |
description |
a character string which allows for a brief description. |
E |
[FEInDomesticFX*] - |
Ep |
[Quanto*] - |
q |
[FEInDomesticFX*][EquityLinkedFX*] - |
r |
[FEInDomesticFX*][TakeoverFX*] - |
rf |
[TakeoverFX*] - |
rho |
[TakeoverFX*] - |
S |
[FEInDomesticFX*][EquityLinkedFX*] - |
sigmaE |
[TakeoverFX*] - |
sigmaS |
[Quanto*] - |
sigmaV |
[TakeoverFX*] - |
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*] - |
X |
[FEInDomesticFX*] - |
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]
The option price, a numeric value.
The functions implement the algorithms to valuate plain vanilla options as described in Chapter 1 of Haug's Book (1997).
Diethelm Wuertz for the Rmetrics R-port.
Haug E.G. (1997); The Complete Guide to Option Pricing Formulas, Chapter 2.13, McGraw-Hill, New York.
## 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)
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