 # What are different pricing models for options?

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Traders use Options pricing models to calculate the fair value of an option. Black Scholes Model and the Binomial Model are two of the most popular models used.

The Black-Scholes pricing model uses 5 key factors affecting an option's price like stock price, strike price, volatility, time to expiration, and risk free interest rate to calculate the fair value of an option. The model assumes that percentage change in the price of the underlying follows a lognormal distribution. The formula is-

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

The Black-Scholes option pricing model is popular for its effectiveness in calculating a large number of options prices in short time. However, it doesn’t take into consideration dividends announced by the company while calculating Option prices. Also, it is not suitable to calculate American options.

The Binomial Option Pricing Model is popular as it is simple and easy to understand. The model works on the assumption that the underlying price only decreases or increases. It breaks down the time to expiration into smaller time intervals and calculates price for each interval. A tree of different prices is produced on working from present to the day of expiration.

The Binomial Pricing model while admired for its simplicity but it is slow in calculating prices of a large number of options. However, it is useful in calculating the price of American Options.