Local Volatility Model

A quantitative finance repository focused on stripping the equity local volatility surface from listed equity option data.

This project combines SVI total variance calibration, Dupire local volatility extraction, and PDE-based option pricing under the local volatility framework.

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Repository Structure

Local-Volatility-Model/
├── Local Volatility Model.ipynb

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Project Overview

This notebook focuses on the Local Volatility model for equity derivatives.

It starts by constructing a smooth implied total variance surface from market option data through the SVI model. Beyond fitting the market smile, the SVI layer helps remove arbitrage inconsistencies, regularize the implied variance surface, and provide the smooth derivatives required for a more stable stripping of the local volatility surface through the Dupire formula.

The resulting local volatility surface is then embedded in a PDE pricing framework.

The local volatility PDE repricing of market quotes provides a direct measure of calibration quality. In this implementation, all repriced options differ by less than 5% from their market prices, while 128 out of 142 options (about 90%) show an error below 1%.

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Market Data

The MarketData/ folder includes the market inputs required for the calibration and repricing workflow.

• CAC40_MarketData_12022025.csv — market option data
• CAC40_SVI_12022025.csv — SVI-calibrated parameters
• EURIBOR6M_ZCRates_12022025.csv — zero-coupon rates used for discounting and forward-related calculations

Users can replace the sample input files with their own market data, provided that the CSV files keep the same structure as the ones included in MarketData/.
To run the notebook correctly, the current column layout and overall file format must be respected.

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Example Output

CAC40 Local Volatility Surface:

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Best use case

Use this notebook when working with equity option market data and building a local volatility surface for calibration, analysis, or local volatility PDE-based pricing.

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How to Use

Clone the repository:

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

Then open:

• Local Volatility Model.ipynb

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Author

Idriss Afra