Biger And Hull

# Currency call option pricing model for premium estimation

First the value of d is calculated

(1)\begin{align} d=\frac{\ln\frac{S}{X}+(r-f+\frac{\sigma^2}{2})T}{\sigma\sqrt{T}} \end{align}

Next the d value is inserted with other terms as shown below into the following equation

(2)\begin{align} C=\frac{S}{e^f^T}N(d)-\frac{X}{e^r^T}N(d-\sigma\sqrt{T}) \end{align}

The symbols are defined as follows:

C= Currency call option premium

S = Spot exchange rate of underlying foreign currency

X = eXercise price of call option

r = rate of domestic interest

f = foreign rate of interest

\sigma = Standard deviation rate of underlying foreign currency

T = Time until option expires measured in years

N(.) = Cumulative area under the standard normal distribution function from negative infinity to d

Bibliography

1. Nahum Biger and John Hull, "The valuation of currency options,"

*Financial Management*(Spring 1983), 24-28page revision: 0, last edited: 29 Apr 2009 19:26