Market-Consistent Valuation of Natural Catastrophe Risk

Abstract

Natural catastrophe risk is increasingly covered through alternative capital instead of classical reinsurance. As most instruments in this space do not trade in a secondary market, their ongoing valuation poses a challenge to investors. We suggest extracting pricing information contained in regularly observed catastrophe bond quotes by means of a reduced form model. The resulting implied Poisson intensities are shown to materially depend on the time to maturity and modeled probability of first loss. Along these two dimensions, we estimate smooth hazard rate surfaces that allow investors to mark illiquid catastrophe risk contracts to market.

Pricing industry loss warranties in a Lévy–Frailty framework

“…We aim to contribute to the resolution of this disarray by advancing the debate in favor of the latter category. The general applicability of arbitrage methods in the context of catastrophe-linked instruments has already been evaluated by Balbás et al (1999) and, more recently, Gatzert et al (2017) as well as Beer and Braun (2019). Notable attempts to derive risk-neutral pricing formulas were, amongst others, undertaken by Bakshi and Madan (2002) as well as Jarrow (2010).…”

“…Although, at first glance, cat bonds are a natural subject matter for our study, their lack of standardization makes them less suitable for calibration purposes. More specifically, the wide variety of terms and conditions leads to a high-dimensional setting with only few observations for each case (Beer and Braun, 2019). In addition to this data scarcity problem, cat bond issuances with more than one tranche are generally quite rare (see, e.g., Guy Carpenter, 2016).…”