Paper: arXiv 2610.37171

Authors: Saeid Safarveisi

Abstract

This paper presents a framework for pricing catastrophe (CAT) bonds in incomplete markets through Riemannian geometric optimization of financial entropy. We formulate pricing-measure selection as a maximum financial entropy problem on a finite-dimensional manifold of equivalent measures, parameterized by the non-hedgeable market prices of catastrophe frequency and severity risk, with discounting fixed by the default-free term structure. Since unconstrained entropy maximization recovers the physical measure, we incorporate observed secondary-market spreads, both pooled and date by date. For a compound Poisson-generalized Pareto loss model with Wang distortion, we derive closed-form expressions for financial entropy and the Riemannian metric. We show that CAT bond prices depend on frequency and severity premia primarily through the risk-neutral trigger intensity, making the two premia unidentifiable from market data alone; the entropy criterion resolves this ambiguity. Using a hypothetical earthquake CAT bond calibrated to quarterly spreads of Golden State Re II Ltd. (Series 2014-1), we obtain risk-neutral trigger intensities of 6.58 to 10.45 times the physical intensity (9.20 pooled and 18.26 at the end of 2015). The model-implied risk multiple aligns with the market spread-to-expected-loss ratio (8.87 versus 8.81 at issuance). The minimal-entropy measure attributes 53.5% to 63.7% of the log risk multiple to frequency risk, reflecting the selection principle rather than market identification. Finally, equating the coupon with the quoted spread understates the risk multiple by approximately half.

Complexity vs Empirical Score

  • Math Complexity: 9.0/10
  • Empirical Rigor: 7.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: This paper demonstrates a high level of mathematical sophistication, particularly with Riemannian geometry and financial entropy. It also exhibits strong empirical rigor through calibration to real market data and robust analysis of risk premia. The novelty lies in its unique approach to resolving identification issues in incomplete markets.

Research Flowchart

  flowchart TD
    A[Research Goal: Price CAT Bonds in Incomplete Markets & Unbundle Risk Premia] --> B{Methodology: Riemannian Geometric Optimization of Financial Entropy};
    B --> C{Model: Compound Poisson-Generalized Pareto Loss with Wang Distortion};
    C --> D[Inputs: Hypothetical Earthquake CAT Bond, Quarterly Spreads of Golden State Re II Ltd. (Series 2014-1)];
    D --> E[Computation: Derive Closed-Form Expressions for Entropy & Metric, Optimize for Risk-Neutral Trigger Intensity];
    E --> F[Outcome 1: Risk-neutral Trigger Intensities (6.58x to 10.45x physical; 9.20x pooled)];
    F --> G[Outcome 2: Model-implied risk multiple (8.87) aligns with market spread-to-expected-loss ratio (8.81)];
    G --> H[Outcome 3: Minimal-entropy measure attributes 53.5%-63.7% of log risk multiple to frequency risk];
    H --> I[Outcome 4: Equating coupon with quoted spread understates risk multiple by ~half];