A Four-Factor Markovian Path-Dependent Volatility Model as a Pricing Engine

The paper develops pricing and calibration for the four-factor Markovian path-dependent volatility (PDV) model — the low-dimensional approximation behind Guyon–Lekeufack — and demonstrates a joint SPX/VIX fit using neural-network pricing of the relevant functionals. We read it as the operational counterpart to the PDV thesis: a model that is both path-faithful and computationally usable.

Volatility is driven by four Markovian factors approximating the trend feature R_1 and the activity feature R_2 under exponential kernels; option values are learned as functions of the factor state to enable fast calibration.

The significance is feasibility: a genuinely path-dependent model with a four-dimensional Markov state that still calibrates jointly to SPX and VIX. It moves PDV from an explanatory regression to a pricing engine.

Indicates that path-conditioning is compatible with a small Markov state the desk could actually maintain, supporting treatment of the recent path as a maintainable model input rather than an intractable history.

The neural pricing layer inherits training-distribution dependence; the four-factor exponential approximation is a deliberate compression of the true power-law memory.