Linking Path-Dependent and Stochastic Volatility Models

Battle Count: 138

Highly relevant for quantitative trading. The paper provides a practical, lightweight method for volatility estimation and forecasting that improves both in-sample fit and out-of-sample predictions. The joint SPX/VIX smile calibration capability is directly applicable to options trading and hedging. The connection between SV and PDV models enables practitioners to use PDV models for fast calibration while leveraging SV models for Monte Carlo pricing. The ADF-based parameter estimation with standard errors supports robust model calibration for trading strategies. However, the paper is more theoretical/methodological than directly implementing a trading strategy.

Moderate complexity. The ADF algorithm is described as 'lightweight' and avoids storing weighted sums of historical returns, updating quantities stepwise. The core algorithm (Algorithm 1) is straightforward: prediction step computes conditional moments, correction step updates Inverse Gamma parameters. However, implementing the full framework requires: (1) discrete-time SDE discretization, (2) moment matching for the assumed density, (3) back-propagation for PDV representation, (4) optimization for parameter calibration, and (5) parametric bootstrap for standard errors. The mathematical derivations are involved but the computational implementation is manageable.

The paper provides detailed algorithmic pseudocode (Algorithm 1 in Appendix D), explicit parameter values for simulations (Gatheral's Heston parameters), and mathematical derivations. However, no code repository is provided. The Oxford-Man Institute's Realized Library is referenced for real data. Standard errors are computed via parametric bootstrap, which is described but not fully reproducible without code. The theoretical framework is well-specified with all equations provided.