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

2026-05-13

AI Summary

This work addresses the circular dependency between implied volatility and market prices that hinders high-fidelity synthetic option data generation. The authors propose an end-to-end framework that integrates a jump hidden Markov model to simulate multi-asset price paths and a state-dependent extension of the Heston model to intrinsically generate implied volatility surfaces without external calibration. American options are priced via a recombinant binomial tree, thereby breaking the circularity. By innovatively coupling the jump HMM with the state-dependent Heston process, the model naturally reproduces volatility smiles, skews, and term structures. A hierarchical neural surrogate further enhances cross-asset generalization. Experiments demonstrate robust generation of realistic synthetic data across diverse market regimes, accurately capturing implied volatility surfaces, path-conditioned Greeks, and short-dated premium dynamics. The implementation is publicly released as a Julia package.

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.

Problem

• synthetic option pricing
• implied volatility
• circular dependency
• American options
• machine learning

Innovation

• Jump Hidden Markov Model
• Heston model
• implied volatility surface
• American option pricing
• synthetic data generation