Volatility Surface Calibration & Option Pricing Model

A quantitative finance project implementing a full pipeline from live market data to implied volatility extraction and volatility surface calibration, written in Python.

Built independently as a self-directed learning project, using an AI mentor (Claude) for guided instruction on quantitative finance concepts and Python implementation. All code written and understood by the author; AI used in a teaching capacity rather than for code generation.

Motivation

Options markets imply a different volatility for every strike and expiry — the so-called volatility surface. This project builds the tooling to extract, calibrate, and visualise that surface from live SPY options data, then uses it to price exotic options via Monte Carlo simulation.

Project Structure

• data.py — Fetches and cleans SPY options data via yfinance
• models.py — Black-Scholes pricing, Vega, and implied volatility
• main.py — Runs the full pipeline

Testing

Tests are written using pytest and cover individual components in isolation.

Run all tests with:

pytest tests/

Phases

• Phase 1: Data pipeline (fetch, clean, filter options data)
• Phase 2: Black-Scholes implementation and implied volatility extraction
• Phase 3: Volatility surface fitting
• Phase 4: Monte Carlo simulation and exotic pricing
• Phase 5: Analysis and documentation

Results

Volatility Smile

SVI parameterisation fitted to synthetic SPY options data, capturing the characteristic left skew observed in equity markets — higher implied volatility at lower strikes reflecting demand for downside protection.

Monte Carlo Validation

European call prices produced by Monte Carlo simulation converge to Black-Scholes analytical prices as path count increases, consistent with the theoretical 1/√n convergence rate.

Exotic Pricing

Asian call option priced at approximately 45% below the equivalent European call, reflecting the variance-reducing effect of price averaging over the path.

Known Limitations

• Real market data pipeline limited by yfinance data quality; synthetic data used for surface fitting
• Single expiry fitted; full surface requires multiple maturities
• No variance reduction techniques implemented (antithetic variates etc.)

Concepts Covered

• Call/put options, strike price, expiry, moneyness, bid-ask spread
• Black-Scholes formula: derivation intuition, inputs, and limitations
• Implied volatility extraction via Newton-Raphson root-finding
• Volatility smile and skew; SVI (Stochastic Volatility Inspired) parameterisation
• Geometric Brownian Motion (GBM) and risk-neutral pricing
• Monte Carlo simulation: path generation, convergence, and variance
• Exotic option pricing: Asian options (no closed-form solution)
• Sensitivity analysis and model validation

Dependencies

Install all dependencies with:

pip install -r requirements.txt