A Wiener Chaos Approach to Martingale Modelling and Implied Volatility Calibration

Battle Count: 113

Highly relevant to quantitative trading in the derivatives space. The model provides a flexible, arbitrage-free framework for calibrating to implied volatility surfaces, which is fundamental to options trading, hedging, and risk management. The ability to price path-dependent exotics consistently with the calibrated European surface is particularly valuable for market-making and structured product desks. However, it is more of a modeling/calibration tool than a direct trading signal generator.

Requires understanding of Wiener chaos expansions, Hermite polynomials, Malliavin calculus, and conditional expectations of chaos basis elements. The piecewise-constant basis simplifies computation significantly. Calibration involves gradient-based optimization with Monte Carlo pricing and control variates. The mathematical framework is sophisticated but the resulting expressions are closed-form and implementable. Dimensionality of the parameter space (up to 1,770) requires careful optimization setup.

The paper provides detailed hyperparameters (learning rate, weight decay, number of iterations, MC samples, quadrature nodes), explicit mathematical formulations, and states that code will be made publicly available in a future release. However, the code is not yet available at the time of publication. SPX data is from OptionMetrics (commercial). Synthetic data generation parameters are fully specified.