Marketron Through the Looking Glass: From Equity Dynamics to Option Pricing in Incomplete Markets

TL;DR

This paper extends the Marketron model to option markets, developing a utility-based pricing approach for incomplete markets, and demonstrates efficient calibration and the model's ability to replicate key statistical properties of asset returns.

Contribution

It introduces a novel utility-based option pricing framework within the Marketron model, addressing market incompleteness and enabling efficient calibration on standard hardware.

Findings

Successfully calibrated the model to option prices

Reproduces statistical properties of underlying asset returns

Provides a unified framework for equity and option dynamics

Abstract

The Marketron model, introduced by [Halperin, Itkin, 2025], describes price formation in inelastic markets as the nonlinear diffusion of a quasiparticle (the marketron) in a multidimensional space comprising the log-price $x$, a memory variable $y$ encoding past money flows, and unobservable return predictors $z$. While the original work calibrated the model to S\&P 500 time series data, this paper extends the framework to option markets - a fundamentally distinct challenge due to market incompleteness stemming from non-tradable state variables. We develop a utility-based pricing approach that constructs a risk-adjusted measure via the dual solution of an optimal investment problem. The resulting Hamilton-Jacobi-Bellman (HJB) equation, though computationally formidable, is solved using a novel methodology enabling efficient calibration even on standard laptop hardware. Having done that, we look at the additional question to answer: whether the Marketron model, calibrated to market option prices, can simultaneously reproduce the statistical properties of the underlying asset's log-returns. We discuss our results in view of the long-standing challenge in quantitative finance of developing an unified framework capable of jointly capturing equity returns, option smile dynamics, and potentially volatility index behavior.