Synthetic American Option Pricing via Jump-HMM-Driven Heston Implied Volatility

Paper: arXiv 2605.13998

Authors: Julia Sun, Zheyu Jin, Jiawei Zhang, Jeffrey D. Varner

Abstract

Generating realistic synthetic option prices requires implied volatility as an input, yet implied volatility is itself derived from observed option prices, creating a circular dependency that limits synthetic data for machine-learning and risk-analysis applications. We break this circularity with a pipeline in which implied volatility emerges as an output of a structural model of equity returns. A Jump Hidden Markov Model produces multi-asset price paths with realistic stylized facts and cross-asset tail dependence; a modified Heston variance process, whose mean-reversion target depends on regime state, days to expiration, moneyness, and a market-mood indicator, converts those paths into implied-volatility paths; and a recombining binomial lattice prices American options from the resulting surface. Initializing variance at its mean-reversion target for each strike-expiration pair lets smile, skew, and term structure emerge without external calibration. We calibrate the shape function through a hierarchy spanning a parametric baseline, a globally shared neural surrogate, and a sector-specific neural surrogate fit to a multi-ticker, multi-sector option ladder. A temporal holdout on a multi-day capture isolated scheduled corporate events as the dominant source of test-time generalization error, and calendar-derived earnings-distance and same-sector peer-coupling features recovered the anticipatory portion of that signal. We then apply the framework as a synthetic-data generator on real near-the-money put and call contracts, forward-simulating price paths, and recovering path-conditional implied volatility, finite-difference American Greeks, and terminal short-premium profit and loss from one coherent simulation, and confirm cross-ticker robustness by re-running on a second underlying from a different sector and volatility regime. The framework is released as an open-source Julia package.

Complexity vs Empirical Score

• Math Complexity: 7.5/10
• Empirical Rigor: 8.0/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper integrates advanced stochastic processes (Jump-HMM, Heston) and numerical pricing methods (binomial lattices) with high-density empirical work, including neural surrogate calibration, temporal holdout testing, and the release of a production-ready Julia package.

Research Flowchart

  flowchart TD
    A[<b>Goal:</b> Synthetic American Option Pricing without Circularity] --> B[<b>Data/Input:</b> Asset price paths via Jump-HMM]
    B --> C[<b>Process:</b> Regime-dependent Heston variance model]
    C --> D[<b>Process:</b> Recombining binomial lattice pricing]
    D --> E[<b>Validation:</b> Hierarchical neural surrogate calibration]
    E --> F[<b>Outcomes:</b> Coherent Greeks, P&L, and open-source Julia framework]

Cited References (34)

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0 of 34 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.