Rationale and mechanics for peak natural catastrophe variance swaps in insurance

Abstract

The geospatial variability, clustering and dependence of natural catastrophe loss for (re)insured risks are well-known physical realities for insurance industry practitioners and academics. These realities create complex underlying risks for (re)insurance policy underwriting, capital reserving and portfolio management, all of which are reasonably hard to measure and difficult to quantify. The quantitative measurements of such underlying risk factors are also known as second order risks. They are traditionally evaluated and hedged using statistical models for variance and volatility and involve specific complexities in modelling and managing both, volatility and correlation. This technical study explores the motivation, structuring and detailed mechanics for using what we call a 'peak natural catastrophe risk variance swap contract' adapted to provide reinsurance cover for a property and business interruption insurance portfolio. We use known natural catastrophe event historical and modelled loss data to structure, price and test the sensitivities of the swap contract.