Garman Kohlhagen Currency Model

To estimate the premium of a call option on a currency contract, one can use the Garman Kohlhagen model, shown here:

(1)\begin{align} C = \frac{S}{e^{r_ft}} \cdot N(d) - \frac{K}{e^{r_dt}}} \cdot N(d - \sigma\sqrt{t}) \end{align}

where

(2)\begin{align} d = \frac {{ln(\frac{S}{K})+(r_d-r_f+ \frac{\sigma^2}{2})t}} {\sigma\sqrt{t}} \end{align}

C | call premium |

S | spot exchange rate underlying option |

K | Exercise exchange rate |

t | Time until call expires |

$\sigma$ | underlying asset's standard deviation |

r_{d} |
Domestic interest rate |

r_{f} |
Foreign interest rate |

The first step in estimating the call premium is to calculate the value for $d.$ After you have this value you may use a spreadsheet such as Excel to find $N(d)$ or you may look up the value for $N(d)$ in a statistical table. $N(d)$ is the cumulative normal distribution from negative infinity to $d.$ You can find $N(d)$ as the NORMSDIST function in Excel, or read it from Cumulative Normal Distribution tables.

page revision: 0, last edited: 03 Sep 2008 16:42