Magic strikes for variance and gamma contracts, and other attainable claims

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Highly relevant for desks trading variance and gamma swaps. Provides a fast, accurate, and model-independent way to price these instruments directly from market implied volatility surfaces without complex numerical integration or full model calibration.

Moderate. Requires implementing the forest expansion coefficients (provided in Mathematica file) and solving a fixed-point equation. The core logic is algebraic and efficient, but deriving the coefficients for arbitrary orders requires symbolic computation tools.

Code and tutorial notebooks are available in the GitHub repository https://github.com/fbourgey/bergomi-guyon/. The paper provides explicit formulae and algorithmic steps (Algorithm 1) for the approximations.