Biger And Hull

Currency call option pricing model for premium estimation

First the value of d is calculated

\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

\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

1. Nahum Biger and John Hull, "The valuation of currency options," Financial Management (Spring 1983), 24-28
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