An Application of Geometric Riemannian Pricing Algorithm for Valuing Catastrophe Bonds in Incomplete Markets: Market-Consistent Financial Entropy and the Split of Frequency and Severity Risk Premia
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.
Read the AI summary and key takeaways for traders on WOBR Quant Research.