Ty Rakestraw

### Computing Black and Shoels Call Options

I had some problems understanding the Black and Shoels models and we didnt have an example. So I put together the following example. Hopefully it helps.

(Pg. 279-280) Using the Black and Scholes model predict the call option on a stock with a standard deviation of 30%, which has a a $55 per share market price, the current present value of the exercise price is$45, the time remaining until maturity is 4 months.

S = 55
PV(K) = 45
${\sigma}$ =.3
T = .33 (4 months / 12 months)

(1)
\begin{align} d_1=\frac{ln(\frac{S}{PV(K)})}{\sigma\sqrt{T}}+\frac{\sigma\sqrt{T}}{2} \end{align}
(2)
\begin{align} d_1=\frac{ln\frac{55}{45}}{0.17}+\frac{.17}{2} \end{align}

$d_{1}$ = 1.26
$d_{1}$ = 1.26-.17 = 1.09 *Simply take d1 less the 0.17 we found above

$N$ = NORMSDIST(1.26) = .896 *Plug into an excel spreedsheet as shown
$N$ = NORMSDIST(1.09) = .862 *Plug into an excel spreedsheet as shown

$55(.896) -$45(.862) = $10.49 Call Option Premium is$10.49

page revision: 2, last edited: 16 Feb 2009 03:50