Paper: arXiv 2610.06168

Authors: Paul McCloud

Abstract

Entropic risk optimisation is a general framework for pricing and hedging financial derivatives in incomplete markets that can be used to decompose P&L into market and model risk contributions. When the prices are quadratic Gaussian, the coupled equations for price and hedge ratios are solved in closed form. This enables comprehensive analysis of trading P&L, with a decomposition of the model value-at-risk into convexity, dimension and funding contributions that are attributed in the explanation of realised P&L. The equations of the quadratic Gaussian model are directly applicable when the underlying prices follow Gaussian processes, such as fractional Ornstein-Uhlenbeck processes. The model also provides simple parametric expressions for hedge ratios that can be used for regressions in deep hedging.

Complexity vs Empirical Score

  • Math Complexity: 9.0/10
  • Empirical Rigor: 3.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: This paper presents a highly mathematical framework for entropic hedging, with extensive derivations and theorems. While the theoretical novelty is strong, it lacks empirical validation or backtesting, placing it in the ‘Lab Rats’ quadrant. The clarity is generally good for a technical paper, but the lack of empirical application limits its immediate practical rigor.

Research Flowchart

  flowchart TD
    A[Research Goal: Analyze Model Risk for Entropic Hedging] --> B{Key Methodology: Entropic Risk Optimization Framework};
    B --> C[Data/Inputs: Financial Derivatives, Incomplete Markets];
    C --> D{Computational Process: Solve Coupled Equations for Price/Hedge Ratios};
    D --> E[Computational Process: Quadratic Gaussian Model Application];
    E --> F[Outcomes: P&L Decomposition, Model VaR Contributions, Parametric Hedge Ratios];