SABR Implied Volatility

A quantitative finance repository focused on constructing the equity implied volatility surface under the SABR model.

This project calibrates the SABR model to market implied volatilities across quoted expiries in order to construct a fitted implied volatility surface.

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Repository Structure

SABR-Implied-Volatility/
├── SABR Volatility Model.ipynb
└── MarketData/
    ├── CAC40_MarketData_12022025.csv
    └── EURIBOR6M_ZCRates_12022025.csv

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Project Overview

This notebook focuses on fitting the equity implied volatility surface using the SABR model.

Under the log-normal SABR specification, the model describes the joint dynamics of the forward and its instantaneous volatility through four parameters:

• β — CEV elasticity parameter
• σ₀ — initial volatility level
• α — volatility of volatility
• ρ — correlation between the forward and its volatility

The workflow includes:

• Hagan’s 2002 log-normal volatility expansion
• SABR slice-by-slice calibration
• volatility surface construction

The notebook also highlights an important modelling limitation: while SABR is effective for fitting the implied volatility smile, it does not guarantee arbitrage-free market prices and may even introduce arbitrages at low strikes. As a result, arbitrage correction on market prices and volatility extrapolation at extreme strikes remain important practical considerations.

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Market Data

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

• CAC40_MarketData_12022025.csv — market option data
• 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 Implied SABR Volatility Surface:

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Best use case

Use this notebook when working with equity option market data and calibrating the SABR model to market implied volatilities in order to fit an implied volatility surface.

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How to Use

Clone the repository:

git clone https://github.com/Idriss-Afra/SABR-Implied-Volatility.git
cd SABR-Implied-Volatility
jupyter notebook

Then open:

• SABR Volatility Model.ipynb

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Author

Idriss Afra