Frequency and Severity Modelling Using Multifractal Processes: An Application to Tornado Occurrence in the USA and CAT Bonds

摘要

This paper proposes a statistical model for claims related to climatic events that exhibit huge volatility both in frequency and intensity, such these caused by tornadoes hitting the US. To duplicate this volatility and the seasonality, we introduce a new claim arrival process modeled by a Poisson process of intensity equal to the product of a periodic function with a multifractal process. The amplitudes of claims are modeled in a similar way, with gamma random variables. We show that this method allows simulation of the peaks of damage. The two dimension multifractal model is also investigated. The work concludes with an analysis of the impact of the model on spreads of weather bonds related to claims caused by tornadoes.