Garman Kohlhagen Model and VBA

Get VBA and an Excel spreadsheet for the Garman Kohlhagen model, a method of pricing European foreign exchange options.

The Garman Kohlhagen model generalizes the standard Black-Scholes model to include two interest rates – one for a domestic currency, and one for a foreign currency. The dividend yield is replaced by the foreign currency interset rate. The size of the interest rate gap between a foreign and domestic currency affects the pricing of these options.

The model was published in 1976 by Mark Garman and Steven Kohlhagen, and predicts that foreign exchange options are cheaper than standard European option for a call but more expensive for a put.

The Garman Kohlhagen model assumes

European-style options with a pre-determined expiration date,
foreign and domestic interest rates and the exchange rate are constant,
the market is efficient (i.e. no arbitrage),
there are no transaction costs,
and the exchange rate has a log-normal price distribution

The governing equations are

r_d and r_f are the domestic and foreign interest rates
S₀ is the spot rate (i.e. foreign exchange rate)
K is the strike
T is the maturity time
σ is the foreign exchange rate volatility
N is the cumulative normal distribution

Garman Kohlhagen Model in VBA

This VBA implements the equations above, and can be used in Excel. However, you can just download the Excel spreadsheet which uses this code at the bottom of this article.

Function GarmanKohlhagen(CallOrPut As String, SpotRate As Double, Strike As Double, TimeToMaturity As Double, DomesticInterestRate As Double, ForeignInterestRate As Double, Volatility As Double) As Double
 
Dim d1 As Double, d2 As Double
 
d1 = (Log(SpotRate / Strike) + (DomesticInterestRate - ForeignInterestRate + Volatility ^ 2 / 2) * TimeToMaturity) / (Volatility * Sqr(TimeToMaturity))
d2 = d1 - Volatility * Sqr(TimeToMaturity)
 
If CallOrPut = "Call" Then
    GarmanKohlhagen = SpotRate * Exp(-ForeignInterestRate * TimeToMaturity) * Application.NormSDist(d1) - Strike * Exp(-DomesticInterestRate * TimeToMaturity) * Application.NormSDist(d2)
ElseIf CallOrPut = "Put" Then
    GarmanKohlhagen = Strike * Exp(-DomesticInterestRate * TimeToMaturity) * Application.NormSDist(-d2) - SpotRate * Exp(-ForeignInterestRate * TimeToMaturity) * Application.NormSDist(-d1)
End If
 
End Function