Stable Weak Approximation at Work in Index-Linked Catastrophe Bond Pricing

Abstract

Abstract:We consider the subject of approximating tail probabilities in the general compound renewal process framework, where severity data are assumed to follow a heavy-tailed law (in that only the first moment is assumed to exist). By using the weak convergence of compound renewal processes to α-stable Lévy motion, we derive such weak approximations. Their applicability is then highlighted in the context of an existing, classical, index-linked catastrophe bond pricing model, and in doing so, we specialize these approximations to the case of a compound time-inhomogeneous Poisson process. We emphasize a unique feature of our approximation, in that it only demands finiteness of the first moment of the aggregate loss processes. Finally, a numerical illustration is presented. The behavior of our approximations is compared to both Monte Carlo simulations and first-order single risk loss process approximations and compares favorably.

How to Price Catastrophe Bonds for Sustainable Earthquake Funding? A Systematic Review of the Pricing Framework

“…This has become known as earthquake-insurance-linked securities (EILS). The most successful financial instruments in EILS are bonds [19][20][21]. Compared to other financial instruments, bonds can raise significant funds quickly; however, they also involve moderate levels of risk [14].…”

Application of Compound Poisson Process in Pricing Catastrophe Bonds: A Systematic Literature Review

“…Homogeneous 17 [3,9,[19][20][21][22]25,[27][28][29][30][31][32][33][34][35][36] Nonhomogeneous 13 [23,24,26,[37][38][39][40][41][42][43][44][45][46] Table 3 shows that homogeneous CPP is more widely used in pricing CAT bonds than nonhomogeneous CPP. The catastrophe intensity is not always constant in every unit of time, but homogeneous CPP is the most widely used.…”

The Exponential Estimate of the Ultimate Ruin Probability for the Non-Homogeneous Renewal Risk Model

“…Some of them investigated non-homogeneous renewal risk models with independent, identically distributed claims and inter-arrival times, but mutual independence of these two sequences is no longer required (see, for instance, Albrecher and Teugels (2006); Li et al (2010); Liu et al (2017b)). Other authors worked with the claim sizes, which have a common distribution function and not necessarily identically distributed inter-arrival times (see Šiaulys 2015, 2017;Burnecki and Giuricich 2017;Mao et al 2017). Other authors dealt with identically distributed claims and inter-arrival times, but there may be some kind of dependence between them (see Chen and Ng 2007;Huang et al 2017;Constantinescu et al 2016;Liu and Gao 2016;Li and Sendova 2015;Shen et al 2016;Yang and Yuen 2016;Yang and Konstantinides 2015;Yang et al 2014;Wang et al 2013).…”