What are various pricing models for Options ?

Options pricing models are used by traders to determine the fair value of options. Two of the most common models are the Binomial Model and Black Scholes Model.

 

Black-Scholes' pricing model considers five key factors that affect an option's value: stock price, strike price volatility, expiration time, risk free interest rate, and volatility. This is used to calculate an option's fair value. The model assumes that the percentage change in price of the underlying follows the lognormal distribution. This formula is:

 

The following formula is used to calculate the option price:

 

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

 

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

 

d2=d1-vt

 

This is where you can find:

 

Algorithm ln=

 

e= exponential function

 

N is equals to Normal Distribution of Standard with Mean = 0 , Standard Deviation = 1

 

C = Price of an Option

 

S is Instrument's underlying price 

 

X = strike price (for the option)

 

r = Risk-free interest rate

 

T = Time to Expire

 

s = volatility

 

Black-Scholes' option pricing model is well-known for its ability to quickly calculate a large number options prices. It does not take into account dividends that the company has announced when calculating Option prices. It is also not appropriate to calculate American options.

 

Because it is easy to understand, the Binomial Option Pricing Model is very popular. It assumes that the underlying price does not change or increase. The model breaks down the expiration time into smaller intervals and calculates the price for each interval. It creates a tree with different prices by working from the present to expiration.

 

While the Binomial Pricing model is simple and well-liked, it can be slow at calculating prices for a large number options. It is however useful for calculating American Options' prices.