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

2026-05-21

AI Summary

This study addresses the challenge of robustly extracting risk-neutral densities from near-expiry options, which is hindered by low premiums, wide bid–ask spreads, and asynchronous quotes that undermine conventional approaches. To overcome these issues, the authors propose a model-free two-stage framework: first, the ARIES strategy eliminates static arbitrage opportunities under market depth constraints; second, the SEDEx method recovers the density by incorporating smoothness and maximum entropy principles while respecting bid–ask bounds. Notably, this approach explicitly treats the bid–ask spread as a fundamental market constraint and uniquely integrates executable arbitrage filtering with entropy regularization, substantially enhancing stability in processing short-dated option data. Empirical validation on both synthetic Heston-generated data and real-world SPX options demonstrates the method’s ability to reconstruct stable and accurate implied volatility smiles.

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.

Problem

• risk-neutral density
• short-dated options
• bid-ask spreads
• static arbitrage
• option quotes

Innovation

• model-free
• risk-neutral density
• static arbitrage removal
• bid-ask constraints
• entropy-based smoothing