Master Option Pricing: The Complete Python Toolkit

Unlock the core of financial engineering with this comprehensive Python script. Go from theory to practice by implementing the binomial and trinomial tree models used by top financial institutions. This isn't just code; it's a complete, hands-on project that calculates, analyzes, and visualizes option prices.

Perfect for students, aspiring quants, and finance professionals looking to sharpen their computational skills.

Bonus:

Extended version file with additional features including:
- Complete Greeks calculation (Delta, Gamma, Theta, Vega, Rho)
- Enhanced visualizations including 3D plots and heatmaps
- Performance analysis and model comparison
- Dividend support
- Implied volatility calculation
- Black-Scholes comparison
- Interactive parameter analysis

For theoretical Foundation of the concepts visit SimplifiedZone

Introduction & Motivation

This project will provide you with hands-on experience in the fascinating world of financial engineering, where we use computational methods to price financial derivatives. Derivatives are financial securities with a value that is reliant upon or derived from an underlying asset or group of assets. In this project, you will be pricing options, a common type of derivative that gives the holder the right, but not the obligation, to buy or sell an underlying asset at a predetermined price.

You will be implementing binomial and trinomial tree models, which are powerful numerical methods for valuing options. These models are widely used in the financial industry due to their flexibility in handling a variety of option types and their intuitive representation of the underlying asset's price movements. By the end of this project, you will have a deeper understanding of the theoretical concepts of option pricing and the practical skills to implement these models in Python.

Learning Objectives

By successfully completing this project, you will be able to:

• Implement binomial and trinomial tree models for option pricing.
• Price both European and American style options.
• Calculate and interpret the "Greeks," specifically the delta of an option.
• Analyze the sensitivity of option prices to changes in volatility.
• Verify the put-call parity relationship for European options.
• Visualize and interpret the convergence of option prices.

Step-by-Step Project Plan

Milestone 1: European Option Pricing using Binomial Trees

1. Implement the Binomial Tree Model: Write a Python function to price a European call and put option using a binomial tree.
2. Determine Optimal Number of Steps: Test for convergence of the option price by varying the number of steps (N) in your binomial tree.
3. Verify Put-Call Parity: For a given number of steps, verify that the put-call parity relationship holds for your calculated European call and put prices.
4. Calculate Delta: Compute the delta of the European call and put options at time t=0.
5. Sensitivity Analysis: Analyze the sensitivity of the option prices to an increase in volatility.

Milestone 2: American Option Pricing using Binomial Trees

1. Implement the American Option Pricing Model: Modify your binomial tree model to price American call and put options.
2. Determine Optimal Number of Steps: Find the optimal number of steps for the American options by checking for convergence.
3. Calculate Delta: Compute the delta of the American call and put options at time t=0.
4. Sensitivity Analysis: Analyze the sensitivity of the American option prices to an increase in volatility.

Milestone 3: European Option Pricing using Trinomial Trees

1. Implement the Trinomial Tree Model: Write a Python class for a trinomial tree model to price European call and put options.
2. Price Options for Various Strike Prices: Use your trinomial tree model to calculate the prices of European call and put options for five different strike prices (deep OTM, OTM, ATM, ITM, and deep ITM).
3. Verify Put-Call Parity: Verify the put-call parity for the calculated European option prices.

Milestone 4: American Option Pricing using Trinomial Trees

1. Implement the American Option Pricing Model: Modify your trinomial tree model to price American call and put options.
2. Price Options for Various Strike Prices: Calculate the prices of American call and put options for the same five strike prices as in Milestone 3.

Milestone 5: Analysis and Visualization

1. Visualize Option Prices: Create plots to visualize the relationship between European/American call and put prices versus stock prices and strike prices.
2. Compare European and American Options: Create plots to confirm that the European call is less than or equal to the American call, and the European put is less than or equal to the American put.

Technical Requirements

• Programming Language: Python 3.x
• Mandatory Libraries:
  • numpy for numerical operations.
  • matplotlib for plotting and visualizations.

Python Script Output Screenshots: