Paper: arXiv 2301.05333

Authors: Yoshihiro Shirai

Abstract

The purpose of this paper is to utilize statistical methodologies to infer from market prices of assets and their derivatives the magnitude of the set of a measure M that defines acceptance sets of risky future cash flows. Specifically, we estimate upper and lower boundaries of the compensation needed for a given bilateral gamma distributed future cash flow to be acceptable. We show that prospects theory provides a natural interpretation of the behaviors implied by such boundaries, which are not compatible with expected utility theory over terminal wealth. Boundaries for bilateral gamma risk neutral scale parameters for given speed parameters are also estimated and tested against market data and, in particular, comparisons are made with known empirical facts about the magnitude of the acceptance set of a common class of risk measures.

Complexity vs Empirical Score

  • Math Complexity: 7.5/10
  • Empirical Rigor: 6.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper presents a mathematically rigorous framework bridging acceptability indices, risk measures, and the Bilateral Gamma process. It successfully links structural risk measure parameters to behavioral economics concepts like prospect theory, backed by calibration to market option data.

Research Flowchart

  flowchart TD
    A["Research Goal:<br>Infer Acceptance Set Boundaries (M)<br>for Bilateral Gamma Cash Flows"] --> B["Inputs:<br>Market Prices of Assets & Derivatives"]
    B --> C["Statistical Estimation:<br>Compute Upper & Lower Compensation<br>Boundaries & Scale/Speed Parameters"]
    C --> D["Empirical Validation:<br>Test Risk-Neutral Parameters Against<br>Market Data & Known Risk Measures"]
    D --> E["Key Finding:<br>Boundaries Match Prospect Theory,<br>Incompatible with Expected Utility"]