Stochastic Volatility Inspired Model

A quantitative finance repository focused on constructing the equity implied volatility surface under the Stochastic Volatility Inspired (SVI) model.

This project calibrates the SVI parameterization to market implied volatilities while enforcing practical no-arbitrage conditions across strikes and maturities.

---

Repository Structure

Stochastic-Volatility-Inspired-Model/
├── Stochastic Volatility Inspired Model.ipynb
└── MarketData/
    ├── CAC40_MarketData_12022025.csv
    └── EURIBOR6M_ZCRates_12022025.csv

---

Project Overview

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

For each expiry, the model represents total implied variance as a function of log-moneyness through five parameters:

• a — overall variance level
• b — wing slope intensity
• rho — skew asymmetry
• m — horizontal shift
• sigma — local curvature scale

The workflow includes:

• SVI slice-by-slice calibration
• constrained optimization of the five SVI parameters
• butterfly arbitrage checks
• calendar arbitrage checks
• parameter bounds for numerical stability
• smart initial guess construction for calibration efficiency

---

Arbitrage Constraints

The notebook is not limited to fitting market quotes. It also checks that the calibrated surface remains consistent with standard no-arbitrage conditions.

Butterfly Arbitrage

For each expiry slice, the calibration verifies that the implied total variance curve is free of butterfly arbitrage, meaning the associated risk-neutral density remains non-negative across strikes.

Calendar Arbitrage

Across maturities, the notebook verifies that total variance is non-decreasing with expiry, preventing calendar spread arbitrage.

---

Market Data

The MarketData/ folder includes:

• CAC40_MarketData_12022025.csv — market option data used for the SVI calibration
• 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.

---

Example Output

CAC40 Implied SVI Volatility Surface:

CAC40 Implied SVI Total Variance Surface:

---

Best use case

Use this notebook when working with equity option market data and building a smooth, arbitrage-free implied volatility surface under the SVI framework.

---

How to Use

Clone the repository:

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

Then open:

• Stochastic Volatility Inspired Model.ipynb

---

Author

Idriss Afra