How to Calculate Black Scholes Option Pricing Model - Tutorial

Calculate Black Scholes Option Pricing Model Tutorial with Definition, Formula, Example

Definition:

The Black-Scholes model is used to calculate the theoretical price of European put and call options, ignoring any dividends paid during the option's lifetime.

Formula:

C = SN(d1)-Ke(-rt)N(d2) where,

C = Theoretical call premium S = Current stock price t = time K = option striking price r = risk free interest rate N = Cumulative standard normal distribution e = exponential term (2.7183) d1 = ( ln(S/K) + (r + (s2/2))t ) / s√t d2 = d1 - s√t s = standard deviation of stock returns

Example :

A company currently sells for $210.59 per share. The annual stock price volatility is 14.04%, and the annual continuously compounded risk-free interest rate is 0.2175%. Find the value of d1 in the Black-Scholes formula for the price of a call on a company's stock with strike price $205 and time for expiration of 4 days.

Given,

S= $210.59, K= $205 t = 4 days r = 0.2175% s = 14.04%

To Find,

Call option priced1

Solution :
Step 1:

Substitute the given value in the formula, d1 = ( ln(210.59/205) + (0.002175+(0.14042) / 2)(0.01096) ) / 0.1404*√(0.01096) d1 = 1.8394

Step 2:

d2 = 1.8394 - 0.1404*√(0.01096) d2 = 1.8247

Step 3:

Substitute the value of d1 and d2 in the Call option (C) formula C = 210.59 * - 205 * SN(d1)-Ke(-rt)N(d2) C = -8.1313

This tutorial explains you how to calculate the call values using Black sholes model.

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