An exploration of parametric earthquake risk transfer solutions that dynamically adapt to seismicity changes

Abstract

(Re)insurance companies rely on earthquake risk models to estimate the frequency and severity of their potential financial losses. To protect themselves, they sometimes use parametric risk transfer solutions, which are derivative-form agreements that provide compensation as a function of routine measurable earthquake characteristics. These mechanisms typically remain in force for one to three years and assume seismic conditions—and our estimates of them—remain unchanged during this period. However, seismic risk estimates evolve continuously due to changes in nearby seismicity, sudden ruptures, slower redistributions of stress, or improvements in our own understanding of these phenomena. As a consequence, the likelihood of some loss-causing events might decrease and make the protection superfluous (wasted money), or, more problematically, it might increase and render the protection insufficient (increased risk). This paper explores the construction of parametric earthquake risk transfer mechanisms that adapt efficiently (i.e., near real-time) to changes in seismicity throughout the lifetime of the transaction. The mechanism proposes the periodic adjustment of the payment conditions of the parametric agreement in harmony with the evolving probabilities of event occurrence. This, we hypothesize, may result in a more efficient allocation of premiums that reflects the changing nature of seismic risk. To build the proposed dynamic risk transfer mechanism, we first employ one of the earthquake models commonly used in the (re)insurance industry to assess the risk of a portfolio of assets. The modeling exercise yields the expected frequency distribution of loss, which a standard (re)insurance transaction would typically consider constant for the entire coverage period. Here, we use these results simply as a baseline for the initial time step of reference. Next, we construct a retrospective update loop, which consists of two parts: (1) we obtain the earthquake occurrence rate conditions at a previous time step taking into account the changes in seismicity observed in the interim period; and (2) we use the modeled losses and adjusted frequencies at the new time step to build a parametric risk transfer solution. This parametric solution remains in force until it is updated at the next iteration. We also track the effects on the efficiency of the risk transfer solution and its premium if these continuous updates were not implemented. We apply the proposed mechanism to California and find that changes in seismicity can cause swings in the frequency of parametric payments (which is related to the premium paid for the cover) in average of 16% and up to 36% in any three-year period from 1986 to 2020. We also find that avoiding an update of the parametric solution on a yearly basis to match the new risk profile can decrease the efficiency of the cover (measured as the relative contribution to the average annual loss of the events covered) in the same time period by 13% on average and up to 35%.