Synthetic American Option Pricing from Regime-Based Return Paths
Summary
The framework addresses the circularity in synthetic option generation: implied volatility is usually inferred from observed option prices, yet synthetic prices need an implied volatility input. It first generates multi-asset equity paths with a Jump Hidden Markov Model, then derives implied-volatility paths through a modified Heston variance process. The variance target varies with regime, time to expiration, moneyness, and a market-mood indicator. A recombining binomial lattice then prices American options, with strike and expiration-specific initialization intended to produce a volatility smile, skew, and term structure without external calibration.
The shape function is developed from a parametric baseline through globally shared and sector-specific neural surrogates. In a temporal holdout, scheduled corporate events were the main source of generalization error; earnings-distance and same-sector peer features recovered some anticipatory signal. The authors apply the approach to real near-the-money contracts and report generating path-conditional volatility, American Greeks, and short-premium outcomes, with a second underlying used to examine robustness. Evidence is limited to the described captures and underlyings, so broader performance is not established.
Key ideas
- A Jump Hidden Markov Model generates equity paths with regime changes and cross-asset tail dependence.
- A modified Heston process derives implied-volatility paths from return regimes and option characteristics.
- A binomial lattice prices American options from the resulting volatility surface.
- Neural surrogates estimate the volatility shape at global and sector levels.
- A temporal holdout identifies scheduled corporate events as a major source of forecast error.
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# Synthetic American Option Pricing via Jump-HMM-Driven Heston Implied Volatility # Synthetic American Option Pricing via Jump-HMM-Driven Heston Implied Volatility 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.
Shown in full with attribution under the source's licence. Licence: abstract CC0
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