Black Scholes Model in Python for Predicting Options Premiums

Black Scholes in Python by Suhail Saqan

A stock option is the right to buy or sell a stock at an agreed price and date. The two types of options used for different situations are either calls, betting a stock will increase in value , or puts, betting a stock will decrease in value (however this is not always true, discussed at the end). Each options contract represents 100 shares of that stock.

There are also two different styles for options: American and European. The calculations that will be done here are for European options.

The Black Scholes model is considered to be one of the best ways of determining fair prices of options. It requires five variables: the strike price of an option, the current stock price, the time to expiration, the risk-free rate, and the volatility.

C = call option price
N = CDF of the normal distribution
St= spot price of an asset
K = strike price
r = risk-free interest rate
t = time to maturity
σ = volatility of the asset

Assumptions Made for this Calculator

For the Black Scholes formula, we need to calculate the probability of receiving the stock at the expiration of the option as well a the risk-adjusted probability that the option will be exercised. In order to do that we need a function for calculating d1 and d2. After that we could input them into a Normal distribution cumulative distribution function using scipy which will give us the probabilities. Each will require 5 inputs: S, K, T, r, and sigma.

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