From Arbitrage Removal to Density Extraction: A Model-Free Framework for Short-Dated Options

TL;DR

This paper introduces a model-free, two-step pipeline for extracting risk-neutral densities from short-dated options, effectively handling bid-ask spreads and arbitrage constraints, with robust results on synthetic and real market data.

Contribution

It develops a novel, practical framework combining arbitrage removal and density extraction that improves stability and robustness in short-dated options analysis.

Findings

The pipeline accurately recovers densities on synthetic Heston data.

It produces stable densities on real SPX options near expiry.

The method is computationally fast and effective under various market conditions.

Abstract

We study risk-neutral density extraction from short-dated option chains. As expiry approaches, option premia decline and bid--ask spreads can be large relative to prices, making mid quotes particularly uninformative. Stale or asynchronous quotes may also generate potential static arbitrages, rendering standard procedures infeasible or unstable. We develop a model-free pipeline that treats bid-ask quotes as the primitive market constraint. The pipeline consists of two steps. First, a procedure called ``Arbitrage Removal Iterative Executable Strategy'' (ARIES) filters executable static arbitrage at quoted bid and ask prices under market-depth constraints. Second, the ``Smooth Entropic Density EXtraction'' (SEDEx) then recovers the density through a criterion leveraging smoothness and entropy under bid-ask constraints. We test the pipeline on synthetic Heston panels and short-dated SPX option data, sampled from a few hours to one week before expiry. Computation is fast and returns robust densities across various market conditions, including scheduled macroeconomic announcements. As an empirical application, we use the recovered densities to construct short dated implied-volatility smiles.