Conditional Deep Levy Models for Exotic Derivatives: History-Aware Path Generation and P-Q Payoff Diagnostics

Helin Zhao and Junchi Shen

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Abstract: We develop and audit a history-aware financial path generator based on Denoising Levy Probabilistic Models (DLPMs) for conditional equity-index path generation. The model combines symmetric alpha-stable diffusion noise with a conditional U-Net observing the contract state, 60- and 252-day return histories, and pre-start trend, drawdown, and volatility state. A chronological protocol evaluates one frozen model on 6,824 untouched windows from eight Chinese and U.S. equity indices. The generator attains terminal CRPS 0.0485, path energy score 0.3368, and a generated-to-realized volatility ratio of 0.882, improving on contract-only DLPM and Gaussian diffusion controls. An unconditional historical block bootstrap remains competitive on pooled marginal metrics; against a stronger state-matched empirical control using the same index, tenor, volatility, trend, and drawdown information, DLPM lowers terminal CRPS from 0.0633 to 0.0485 (23.3%), with joint calendar-block confidence intervals below zero from 20 to 150 days. We then embed the learned physical-measure distribution in a transparent P-Q payoff diagnostic against an independently fitted, martingale-corrected Student-t GARCH(1,1) benchmark. At a pre-specified 0.05 dealer spread and a 1%-of-spot materiality threshold, the aligned unconditional diagnostic is 0.91% of initial spot for vanilla calls and 0.36% for Asian calls. Drift-neutral and one-time-delta counterfactuals decompose this gap: physical direction is a large component, leaving a 0.33% vanilla residual and a near-zero Asian residual. The P-Q framework is a belief-based payoff diagnostic, distinct from an option-surface-calibrated pricing engine.

Date: 2025-09, Revised 2026-08
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