Equity Options

Marketron Through the Looking Glass: From Equity Dynamics to Option Pricing in Incomplete Markets ArXiv ID: 2508.09863 “View on arXiv” Authors: Igor Halperin, Andrey Itkin 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. ...

Analytic estimation of parameters of stochastic volatility diffusion models with exponential-affine characteristic function for currency option pricing ArXiv ID: 2507.11868 “View on arXiv” Authors: Mikołaj Łabędzki Abstract This dissertation develops and justifies a novel method for deriving approximate formulas to estimate two parameters in stochastic volatility diffusion models with exponentially-affine characteristic functions and single- or two-factor variance. These formulas aim to improve the accuracy of option pricing and enhance the calibration process by providing reliable initial values for local minimization algorithms. The parameters relate to the volatility of the stochastic factor in instantaneous variance dynamics and the correlation between stochastic factors and asset price dynamics. The study comprises five chapters. Chapter one outlines the currency option market, pricing methods, and the general structure of stochastic volatility models. Chapter two derives the replication strategy dynamics and introduces a new two-factor volatility model: the OUOU model. Chapter three analyzes the distribution and surface dynamics of implied volatilities using principal component and common factor analysis. Chapter four discusses calibration methods for stochastic volatility models, particularly the Heston model, and presents the new Implied Central Moments method to estimate parameters in the Heston and Schöbel-Zhu models. Extensions to two-factor models, Bates and OUOU, are also explored. Chapter five evaluates the performance of the proposed formulas on the EURUSD options market, demonstrating the superior accuracy of the new method. The dissertation successfully meets its research objectives, expanding tools for derivative pricing and risk assessment. Key contributions include faster and more precise parameter estimation formulas and the introduction of the OUOU model - an extension of the Schöbel-Zhu model with a semi-analytical valuation formula for European options, previously unexamined in the literature. ...

Predicting Realized Variance Out of Sample: Can Anything Beat The Benchmark? ArXiv ID: 2506.07928 “View on arXiv” Authors: Austin Pollok Abstract The discrepancy between realized volatility and the market’s view of volatility has been known to predict individual equity options at the monthly horizon. It is not clear how this predictability depends on a forecast’s ability to predict firm-level volatility. We consider this phenomenon at the daily frequency using high-dimensional machine learning models, as well as low-dimensional factor models. We find that marginal improvements to standard forecast error measurements can lead to economically significant gains in portfolio performance. This makes a case for re-imagining the way we train models that are used to construct portfolios. ...

Deep Learning for Options Trading: An End-To-End Approach ArXiv ID: 2407.21791 “View on arXiv” Authors: Unknown Abstract We introduce a novel approach to options trading strategies using a highly scalable and data-driven machine learning algorithm. In contrast to traditional approaches that often require specifications of underlying market dynamics or assumptions on an option pricing model, our models depart fundamentally from the need for these prerequisites, directly learning non-trivial mappings from market data to optimal trading signals. Backtesting on more than a decade of option contracts for equities listed on the S&P 100, we demonstrate that deep learning models trained according to our end-to-end approach exhibit significant improvements in risk-adjusted performance over existing rules-based trading strategies. We find that incorporating turnover regularization into the models leads to further performance enhancements at prohibitively high levels of transaction costs. ...

Enhancing Deep Hedging of Options with Implied Volatility Surface Feedback Information ArXiv ID: 2407.21138 “View on arXiv” Authors: Unknown Abstract We present a dynamic hedging scheme for S&P 500 options, where rebalancing decisions are enhanced by integrating information about the implied volatility surface dynamics. The optimal hedging strategy is obtained through a deep policy gradient-type reinforcement learning algorithm. The favorable inclusion of forward-looking information embedded in the volatility surface allows our procedure to outperform several conventional benchmarks such as practitioner and smiled-implied delta hedging procedures, both in simulation and backtesting experiments. The outperformance is more pronounced in the presence of transaction costs. ...