Empirical Analysis of the Model-Free Valuation Approach: Hedging Gaps, Conservatism, and Trading Opportunities

ArXiv ID: 2508.16595 “View on arXiv”

Authors: Zixing Chen, Yihan Qi, Shanlan Que, Julian Sester, Xiao Zhang

Abstract

In this paper we study the quality of model-free valuation approaches for financial derivatives by systematically evaluating the difference between model-free super-hedging strategies and the realized payoff of financial derivatives using historical option prices from several constituents of the S&P 500 between 2018 and 2022. Our study allows in particular to describe the realized gap between payoff and model-free hedging strategy empirically so that we can quantify to which degree model-free approaches are overly conservative. Our results imply that the model-free hedging approach is only marginally more conservative than industry-standard models such as the Heston-model while being model-free at the same time. This finding, its statistical description and the model-independence of the hedging approach enable us to construct an explicit trading strategy which, as we demonstrate, can be profitably applied in financial markets, and additionally possesses the desirable feature with an explicit control of its downside risk due to its model-free construction preventing losses pathwise.

Keywords: Model-Free Hedging, Super-Hedging, Derivatives Valuation, Pathwise Risk Control, Statistical Arbitrage, Equities

Complexity vs Empirical Score

• Math Complexity: 6.0/10
• Empirical Rigor: 8.0/10
• Quadrant: Holy Grail
• Why: The paper employs advanced mathematical tools like semi-static trading strategies and linear programming for model-free valuation, reflecting high mathematical complexity. It demonstrates high empirical rigor through the use of five years of historical S&P 500 options data and the construction of a backtest-ready trading strategy.

  flowchart TD
    A["Research Goal:<br>Quantify conservatism of<br>Model-Free vs. Model-Based<br>Derivative Hedging"] --> B["Methodology:<br>Super-Hedging Comparison"]
    B --> C["Data Input:<br>S&P 500 Historical Option Prices<br>(2018-2022)"]
    C --> D["Computational Process:<br>Calculate Payoff vs.<br>Super-Hedge Payoff Gap<br>for Model-Free & Heston"]
    D --> E{"Key Findings/Outcomes"}
    E --> F["Outcome 1:<br>Model-Free is only<br>marginally more conservative<br>than Heston Model"]
    E --> G["Outcome 2:<br>Statistical description of<br>the hedging gap"]
    E --> H["Outcome 3:<br>Explicit Trading Strategy:<br>Profitable & Pathwise<br>Risk Controlled"]