Black Scholes Model in Python

Alex Habegger

This is a Python implementation of the Black Scholes Model for option pricing and a collection of helper functions for calculating option Greeks and implied volatility. The code also includes an essential MySQL database interaction to upload option data.

Overview

The Black-Scholes Model is a mathematical model for pricing European options. It makes certain assumptions:

• No dividends are paid out during the life of the option.
• Markets are random (i.e., market movements cannot be predicted).
• There are no transaction costs in buying the option.
• The risk-free rate and volatility of the underlying asset are known and constant.
• The returns on the underlying asset are log-normally distributed.
• The option is European and can only be exercised at expiration.

Usage

The main functions provided by this code are:

• black_scholes(s, k, t, v, rf, div, cp): Price an option using the Black-Scholes model.
• call_price(s, k, t, v, rf, div): Calculate the price of a call option.
• put_price(s, k, t, v, rf, div): Calculate the price of a put option.
• call_delta, call_gamma, call_vega, call_theta, call_rho: Calculate the Greeks for call options.
• put_delta, put_gamma, put_vega, put_theta, put_rho: Calculate the Greeks for put options.
• call_implied_volatility(Price, S, K, T, r): Calculate the implied volatility for call options.
• put_implied_volatility(Price, S, K, T, r): Calculate the implied volatility for put options.

Database Interaction

The code includes functions to interact with a MySQL database:

• sql_upload(ticker): Upload options data for a given ticker to a MySQL database.
• clear_all_tables(): Clear all tables in the MySQL database.
• clear_table(tablename): Clear a specific table in the MySQL database.

Disclaimer

This project is part of an academic exercise and is not intended for commercial use.