GNGTS 2021 - Atti del 39° Convegno Nazionale

GNGTS 2021 S essione 2.2 288 level are considered respectively ranging between [0.25, 5] years and [0.1, 10] bn €, guaranteeing in this way a sufficiently broad T - D domain for showing the variation of CAT bond price for a wide range of possible combinations. The bond for a zone is triggered when the accumulated losses caused by earthquakes occurred within the zone are greater than the set threshold before the set expiration time. Fig. 2 shows the probability of failure P f surfaces for Zones 1, 2 and 3, together with the bounds deriving from considering the parameters uncertainties and containing the 80% of the probability. Two cross sections of the surface are also shown, corresponding to planes with T = 2, and D = 3 bn €. As a general behaviour common for all the three zones, for a given expiration time T , P f decreases as the threshold level D increases, whereas for a given threshold level D , P f increases from 0 to 1 over time. P f of Zone 1 and Zone 2 are comparable since despite a slightly lower expected loss, Zone 2 has a higher Poisson intensity due to a wider zone area and consequently more events inside. Zone 3 has the lowest P f due to a combination of lower expected losses and less expected events. Fig. 3a shows the zero-coupon CAT bond pricing surfaces V ZC associated with the threshold D paying Z = 1.06 € at maturity, for each Zone. In this case, for a given threshold level D , the CAT bond value decreases over time, whereas for a set expiration time T , the CAT bond value increases as the threshold level D increases. The prices reflect the related failure probabilities: price of Zone 3 is the highest since it is associated with the lowest probability of exceeding the money threshold of 3 bn €. Higher gains provided by the bonds are associated to higher failure probabilities. Finally, Fig. 3b illustrates the case of the coupon CAT bond, evidencing how the overall trend is similar to the zero-coupon one due to the high ratio intercurrent between the principal and the entity of coupons. Numerical results are the combination of two contributions: as time passes, the chance of receiving more coupon payments is bigger, but at the same time, the possibility of losing the principal increases. Both the zero-coupon CAT bond and the coupon CAT bond price reflect the different seismic risk-levels of the three zones. For a given T-D combination, the price for a bond in Zone 1 and Zone 2 is the lowest while the price in Zone 3 is the highest. This work can be considered the first original attempt currently retrievable in scientific literature aimed at a rational management of significant losses induced to the Italian residential building stock by seismic events. Italian authorities can directly use results, reducing in this way the burden of reconstruction processes on the public finances. Fig. 3 - Zero-coupon (a) and coupon (b) CAT bond price for the three Zones.