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Options Pricing Models- Black Scholes & Binomial Models

Published on Wednesday, April 4, 2018 by Chittorgarh.com Team | Modified on Friday, November 8, 2019

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Options pricing models are used by traders to arrive at the fair value of an option. The two most popular option pricing models are the Black Scholes Model and the Binomial Model.

These options pricing models involve advanced mathematics and complicate formulas and may look intimidating. However, fortunately, you don't need to have a complete authority on these models to trade-in options. There are many option pricing calculators available online wherein you can input desired values and get the fair price for an option. The online options pricing calculators are built using these models. So some knowledge of the models is helpful but not necessary.

The Black-Scholes Pricing Model

The Black-Scholes pricing model was developed in 1973 by Fisher Black and Myron Scholes. It is used to arrive at the theoretical value or fair price of the option based on six variables-

  • Volatility
  • Type of option
  • Price of the underlying instrument
  • Time to expiration
  • Strike price of the Option
  • Risk-free interest rate.

Black Scholes Formula Explained

The formula used for computing option price is:

Option Premium C = SN(d1) - Xe-rt N(d2)

d1 = [ln (S / X) + (r + s2 / 2)t]/vt

d2= d1- vt

Here,

ln= algorithm

e= exponential function

N= standard normal distribution with mean = 0 and standard deviation = 1

C = price of an option

S = price of the underlying instrument

X = the strike price of the option

r = risk-free interest rate

t = time to expiration

s = volatility

N represents a standard normal distribution with mean = 0 and standard deviation = 1

Black Scholes Pricing Model- Advantages & Disadvantages

Advantages Disadvantages
  1. Calculates a high number of options prices in short time.
  1. Dividend announcements are ignored as a variable while calculating price.
  2. Cannot be used to determine prices of American Options that allow option traders to exercise the option at any time before expiration

The Binomial Option Pricing Model

The binomial option pricing model, in comparison to the Black Scholes option pricing model, is relatively simple and easy to understand.

What is the binomial option pricing model?

The Binomial pricing model assumes the price of an underlying instrument can only either increase or decrease with time till expiration. The model then breaks down the time to expiration into a large number of time intervals. A binomial price tree is built by calculating the value of an option at each time interval.

Binomial Option Pricing Model- Advantages & Disadvantages

Advantages Disadvantages
  1. Calculates American options, unlike the Black Scholes formula that is used only for European options.
  1. Cannot calculate a large number of prices at high speed.
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