Monte Carlo

Welcome to the Monte Carlo Option Pricer – a Python-based GUI application designed to simulate and price options using Monte Carlo methods.

Table of Contents

• Overview
• Features
• Screenshot
• Installation

Overview

The Monte Carlo Option Pricer uses simulation techniques to estimate the price of European-style options. It supports multiple models, including:

• Geometric Brownian Motion (GBM): The standard model for simulating stock prices. The GBM model assumes that prices follow a log-normal distribution.

  • dSₜ = μ Sₜ dt + σ Sₜ dWₜ
  • Sₜ = Stock price at time t
  • μ = Expected return (drift term)
  • σ = Volatility (standard deviation of returns)
  • dWₜ = Wiener process (Brownian motion)

• Jump Diffusion Model: Incorporates sudden jumps, capturing events like earnings surprises or market shocks.

  • dSₜ = μ Sₜ dt + σ Sₜ dWₜ + Jₜ dNₜ
  • Jₜ = Jump size (log-normally distributed)
  • dNₜ = Poisson-distributed jump occurrences

• Built with:

  • Tkinter: Interactive GUI
  • Matplotlib: Visualizations (Histograms, Heatmaps, Simulations)
  • NumPy: Fast numerical calculations

Features

• Interactive GUI: User-friendly input with tooltips and themed styling.
• Real-time Simulations: Visualize simulated stock price paths.
• Option Pricing: Calculate call/put option prices with confidence intervals.
• Distribution Analysis: View histograms of the final stock prices.
• Heatmap Visualization: Examine the density of stock prices over time.
• Customizable Parameters: Adjust simulations, jump diffusion parameters, and more.
• Save Plots: Save your simulation plots for reporting or further analysis.

Screenshot

Below is a preview of the Monte Carlo Option Pricer in action:

Installation

Ensure you have Python 3.7 or above installed. Then, install the required packages using pip:

pip install numpy matplotlib tk