Options Pricing and Analytics Tool

This project provides a comprehensive quantitative finance tool for pricing European options. It implements multiple pricing models to allow for cross-verification and includes a numerical engine for calculating option Greeks.

Features

• Black-Scholes Model: Analytical pricing for European calls and puts.
• Binomial Tree Model: Cox-Ross-Rubinstein implementation for discrete step pricing.
• Monte Carlo Simulation: Stochastic pricing using Geometric Brownian Motion.
• Greeks Calculation: Numerical estimation of Delta, Gamma, Theta, Vega, and Rho using finite difference methods.
• Interactive Interface: A Streamlit dashboard for visualizing price sensitivities and comparing model outputs.

Mathematical Underpinnings

The core of this tool relies on the Black-Scholes-Merton differential equation. For a European call option, the price $C$ is calculated as:

$$C(S,t) = N(d_1)S - N(d_2)Ke^{-r(T-t)}$$

Where: $$d_1 = \frac{\ln(S/K) + (r + \frac{\sigma^2}{2})(T-t)}{\sigma\sqrt{T-t}}$$ $$d_2 = d_1 - \sigma\sqrt{T-t}$$

Installation

Ensure you have Python 3.8 or higher installed. Install the required dependencies:

pip install numpy scipy pandas matplotlib streamlit

Usage

Run the interactive dashboard locally:

streamlit run app.py