European Option Pricing with Black-Scholes

This project implements the Black-Scholes model to price European call and put options and analyze sensitivity using the Greeks (Delta, Gamma, Vega).

Features

• Price European call and put options
• Visualize how price changes with strike price
• Analyze Delta and Vega as a function of stock price

How to Run

1. Clone the repo and navigate into it:

   git clone https://github.com/sensor-aae/European-Option-Pricing.git
   cd European-Option-Pricing

2. Create a virtual environment and activate it:

   python3 -m venv .venv
   source .venv/bin/activate

3. Install dependencies:

   pip install -r requirements.txt

4. Run the notebook:

   jupyter notebook notebooks/black_scholes_pricing.ipynb

📁 Project Structure

european-option-pricing/
├── .venv/                  # Python virtual environment
├── notebooks/              # Jupyter notebooks
│   └── black_scholes_pricing.ipynb
├── outputs/                # Plots and generated output
│   └── surfaces.png        # Sensitivity plots, price graphs
├── utils/                  # Custom pricing and Greeks code
│   └── bs_functions.py
├── requirements.txt        # Python packages list
├── README.md               # Project documentation

📈 Sample Output

Interpretation

The Option Greeks plot above illustrates how option sensitivities vary with strike price for a call option.

• Delta — the rate of change of the option price with respect to the underlying stock price — is high when the call option is deep in the money and decreases as the strike price increases.
• Vega — the sensitivity of the option price to changes in volatility — peaks when the option is at the money and diminishes for deep in- or out-of-the-money options.

These sensitivities help traders understand how option values respond to movements in the underlying asset price and volatility.

👤 Author

Amanda Achiangia
BSc Applied Mathematics (Financial Mathematics), York University
Aspiring Quantitative Finance Professional
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