Pricing Excess-of-Loss Reinsurance and CAT Bonds under Climate Uncertainty: A Cox Process Framework with Temperature-Dependent Stochastic Intensity

Battle Count: 57

The paper is primarily focused on insurance/reinsurance pricing and regulatory capital assessment rather than quantitative trading. However, CAT bond pricing and spread analysis have tangential relevance to fixed-income trading and ILS (Insurance-Linked Securities) market making. The stochastic intensity modeling techniques could inform credit risk or event-driven trading strategies.

Implementation requires: (1) MLE calibration of OU process with time-varying mean, (2) exact discretization of Gaussian mean-reverting process, (3) Monte Carlo simulation of Cox process with path-dependent intensity, (4) compound Poisson loss generation with lognormal severities, (5) Common Random Numbers for variance reduction, (6) tail risk estimation (VaR/TVaR). The mathematical framework is well-specified with explicit formulas, but the multi-layer stochastic structure and scenario-based pricing add complexity.

The paper provides detailed calibration methodology (MLE for OU process), specifies random seed (42), reports Monte Carlo parameters (M=50,000 paths), and includes full algorithm pseudocode. However, simulation code is only available upon request from the corresponding author, and catastrophe intensity parameters (λ₀, β) are scenario-based rather than empirically estimated. NASA GISTEMP data is publicly available.