Black And Scholes Call Premium Model

To estimate the premium of a call option, one can use the Black & Scholes model, shown here:

(1)
\begin{align} C = S \cdot N(d) - PV(K) \cdot N(d - \sigma\sqrt{T}) \end{align}

where

(2)
\begin{align} d = \frac{ln(\frac{S}{PV(K)})}{\sigma\sqrt{T}}+ \frac{\sigma\sqrt{T}}{2} \end{align}
C call premium
S stock underlying option
K Exercise price
T Time until call expires
$\sigma$ underlying asset's standard deviation
PV present value

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.

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