mc-option-pricing

A Monte Carlo option pricing engine with path simulation written in Rust and a Python interface for pricing, Greeks, and visualization.

Built as a learning project to explore the intersection of quantitative finance and systems programming.

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Features

• Path simulation in Rust – fast, parallelized Monte Carlo simulation using Geometric Brownian Motion
• European Call & Put pricing – with discounted payoff averaging
• Greeks – Delta and Gamma via central finite differences
• Black-Scholes validation – analytical benchmark to verify MC results
• Visualizations – simulated paths, end-price distribution, payoff distribution, Delta curve
• Benchmark – 16x speedup over pure Python (using 4 threads, Rayon)

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Project Structure

mc-option-pricing/
├── src/
│   └── lib.rs                  # Rust: Path simulation (PyO3 + Rayon)
├── mc_option_pricing/
│   ├── pricing.py              # European Call & Put pricing
│   ├── black_scholes.py        # Analytical Black-Scholes formulas
│   ├── greeks.py               # Delta & Gamma via finite differences
│   └── python_sim.py        # Pure Python simulation (benchmark baseline)
├── notebooks/
│   └── demo.ipynb              # Visualizations & examples
├── Cargo.toml
└── pyproject.toml

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Methodology

Geometric Brownian Motion

Stock prices are simulated using GBM:

$$S_{t+\Delta t} = S_t \cdot \exp\left(\left(\mu - \frac{\sigma^2}{2}\right)\Delta t + \sigma\sqrt{\Delta t}, Z\right)$$

where $Z \sim \mathcal{N}(0, 1)$ is a standard normal random variable.

Monte Carlo Pricing

The fair price of a European Call option is the discounted expected payoff under the risk-neutral measure:

$$C = e^{-rT} \cdot \frac{1}{N} \sum_{i=1}^{N} \max(S_T^{(i)} - K,, 0)$$

Installation

Requirements: Python 3.8+, Rust toolchain

# Clone the repository
git clone https://github.com/NiklasK3R/mc-option-pricing.git
cd mc-option-pricing

# Create and activate virtual environment
python3 -m venv .venv
source .venv/bin/activate

# Install Python dependencies
pip install -r requirements.txt

# Compile Rust extension and install package
maturin develop

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Usage

CLI

# Price an at-the-money call option
python -m mc_option_pricing

# Custom parameters
python -m mc_option_pricing --start 100 --strike 110 --sigma 0.3 --maturity 0.5 --type both

# All options
python -m mc_option_pricing --help

Example Results

At-the-money call option (S=100, K=100, r=5%, σ=20%, T=1yr):

Method	Price
Black-Scholes	10.4506
Monte Carlo	10.4281
Difference	0.0225

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Tech Stack

• Rust – path simulation engine
• PyO3 – Rust/Python bindings
• Rayon – data parallelism in Rust
• maturin – build system for Rust Python extensions
• Python – pricing logic, Greeks, visualization
• matplotlib / numpy – plots and numerical utilities

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License

MIT