UnifiedVol

UnifiedVol is a C++20 quantitative finance library for volatility surface modeling and calibration.

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Current Capabilities

Arbitrage-Free SVI Calibration

• Full enforcement of static no-arbitrage conditions:

  • Calendar arbitrage
  • Butterfly spread arbitrage
  • Positive minimum variance
  • Roger Lee’s asymptotic wing slope bounds

• Calibration methodology:

  • Sequential Quadratic Programming (SQP) with constraint handling via NLopt
  • Closed-form analytical gradients for improved speed and numerical stability
  • Post-calibration validation to confirm absence of arbitrage violations

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Examples

• SVI Calibration Fits (PDF)
• Market implied volatilities vs fitted SVI curves (SPY 2025-04-07) :

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Roadmap

Planned extensions include:

• SSVI (Stochastic Volatility Inspired) parameterization
• SABR stochastic volatility model
• Heston stochastic variance model
• Stochastic Local Volatility (SLV) frameworks
• Integration with PDE solvers for local volatility pricing

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References

• Roger W. Lee (2003), The Moment Formula for Implied Volatility at Extreme Strikes
• Jim Gatheral & Antoine Jacquier (2014), Arbitrage-Free SVI Volatility Surfaces
• Zeliade Systems (2012), Quasi-Explicit Calibration of Gatheral’s SVI Model (White Paper)
• Tahar Ferhati (2020), Robust Calibration for SVI Model Arbitrage-Free

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Data

Sample surfaces calibrated in this project are derived from publicly available option data:

• CBOE Volatility Surface Data

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Dependencies

• C++20 STL
• NLopt — nonlinear optimization library for SQP calibration, constraint enforcement, and stopping criteria

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Status

This repository is under active development. Interfaces, APIs, and model implementations are subject to further changes.