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

Abstract

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.

Multifractal analysis of financial markets: a review

“…Other extensions include the Copula-MSM model for characterizing spot and weekly futures price dynamics and more generally other pairs of financial assets [520], the MSM-t model in which the innovations i follow the Student distribution [521], the MSM-skewed t model in which the innovations follow a skewed Student distribution [522], the level-MSM model for interest rates which incorporates the well-known level effect observed in interest rates [523], the modified Hull-White model of interest rates in which the volatility of the short term rate is driven by an MSM model [524], the cyclic MSM model for insurance claims arising from climatic events in which the term i is set to the smoothed average of claims observed during the corresponding month of the year [525], the realized volatility lognormal MSM (RV-LMSM) model in which the non-RV σ i in equation ( 284) is replaced by the realized volatility [526], and the MSM duration (MSMD) model for the analysis of intertrade durations in financial markets [527][528][529].…”

Multifractal analysis of financial markets

“…Other extensions include the Copula-MSM model for characterizing spot and weekly futures price dynamics and more generally other pairs of financial assets [481], the MSM-t model in which the innovations ǫ i follow the Student distribution [482], the MSM-skewed t model in which the innovations follow a skewed Student distribution [483], the level-MSM model for interest rates which incorporates the well-known level effect observed in interest rates [484], the modified Hull-White model of interest rates in which the volatility of the short term rate is driven by an MSM model [485], the cyclic MSM model for insurance claims arising from climatic events in which the term ǫ i is set to the smoothed average of claims observed during the corresponding month of the year [486], the realized volatility lognormal MSM (RV-LMSM) model in which the non-RV σ i in Eq. ( 281) is replaced by the realized volatility [487], and the MSM duration (MSMD) model for the analysis of inter-trade durations in financial markets [488][489][490].…”

Nuclear Catastrophe Risk Bonds in a Markov-Dependent Environment

“…Despite the rising popularity, the number of previous studies devoted to CAT risk bond modeling and pricing is relatively limited. Some notable models have been based on: quasi Monte Carlo (Vaugirard 2003;Albrecher et al 2004) and indifference pricing techniques (Young 2004), entropy based models (Ling and Jun 2009), a simple robust model (Jarrow 2010), a representative agent pricing approach (Cox and Pedersen 2000;Shao et al 2015), premium calculation models (Galeotti et al 2013), a mixed approximation method (Ma and Ma 2013), a Bayesian pricing model (Ahrens et al 2014), a cluster analysis approach (Constantin et al 2014), a multifactor pricing model (Gomez and Carcamo 2014), modeling using multifractal processes (Hainaut and Boucher 2014), fuzzy based approaches (Nowak and Romaniuk 2013b;Nowak and Romaniuk 2017), and with Cox-Ingersoll-Ross interest rate models (Nowak and Romaniuk 2016).…”

“…Some notable applications have included: modeling of tropical cyclones (Daneshvaran and Morden 2004), systemic risks in agriculture for the case of Georgia cotton (Vedenov et al 2006), transportation assets and feasibility analysis for bridges (Sircar et al 2009), calibration using Chinese earthquake loss data (Wu and Zhou 2010), models for earthquakes (Penalva Zuast 2002;Zimbidis et al 2007;Tao et al 2009;Härdle and Cabrera 2010;Ahrens et al 2014;Shao et al 2015), modeling of tornado occurrence in the USA (Hainaut and Boucher 2014), exposure to currency exchange risk (Lai et al 2014), seismic risk management of insurance portfolio (Goda 2015), hedging of flood losses (Tetu et al 2015), and temperature-based agricultural applications (Karagiannis et al 2016) among others.…”