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

Speaker: Prof. Andrey Itkin, Department of Finance and Risk Engineering, Tandon School of Engineering, NYU

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.