### 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)

$d_{1}$ = 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