Heston Stochastic Volatility Model

A quantitative finance repository focused on implementing the Heston stochastic volatility model for equity derivatives.

This project develops the Heston (1993) framework, calibrates its parameters to market option prices, and applies the model to the pricing of equity variance and volatility swaps.

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Repository Structure

Heston-Stochastic-Volatility-Model/
├── Heston Stochastic Volatility Model.ipynb

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Project Overview

This notebook focuses on the Heston stochastic volatility model for equity derivatives.

It starts from the standard risk-neutral dynamics of the Heston model, where the underlying price follows a diffusion with stochastic variance governed by a mean-reverting square-root process. On this basis, the notebook derives the semi-analytical pricing formula for European vanilla options through the model’s characteristic function and a Fourier inversion approach.

The model is then calibrated to market option prices by optimizing the five Heston parameters — κ, θ, V₀, ρ, and σ — through a weighted pricing-error objective. The calibration procedure relies on SciPy’s differential evolution algorithm, includes a Feller constraint to promote strictly positive variance dynamics, and uses several runtime controls to improve numerical efficiency and robustness.

Once calibrated, the framework is applied to the pricing of equity variance swaps and equity volatility swaps.

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Example Output

CAC40 10-Month Listed Options:

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Best use case

Use this notebook when working with equity option market data and calibrating the Heston model to vanilla option prices, as well as pricing equity variance swaps and equity volatility swaps.

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How to Use

Clone the repository:

git clone https://github.com/Idriss-Afra/Heston-Stochastic-Volatility-Model.git
cd Heston-Stochastic-Volatility-Model
jupyter notebook

Then open:

• Heston Stochastic Volatility Model.ipynb

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Author

Idriss Afra