A traceable grid-based framework for earthquake parametric insurance pricing: methodology and case studies in Indonesia

Abstract. We propose F_g, a portable and end-to-end traceable framework for pricing earthquake parametric insurance contracts on a fixed grid, and apply it to Indonesia as a case study. Three persistent gaps motivate the framework. National PSHA delivers a single value per return period, not the full annual distribution that contract calibration requires; existing risk metrics are reported at portfolio level and lose grid-level traceability; and basis risk is evaluated post hoc rather than as a design feedback. F_g closes these gaps by combining four established components on a single 1° × 1° spatial unit: (i) annual hazard via Gutenberg–Richter recurrence with a Boore–Atkinson 2008 baseline GMPE, (ii) a Grid Loss Table from Monte Carlo simulation (N = 20000), (iii) parametric contract calibration via local AEP inversion, and (iv) a basis-risk vector fed back into the contract before the premium is set. The resulting premium Π_g is a deterministic function of just four catalogue inputs Applying F_g to the USGS catalogue for Indonesia (1925–2025; 84 774 events; 623 active grids; the Gardner–Knopoff dispersion index drops from 111.4 to 4.2 after declustering) produces national maps of the seismicity parameters and average annual loss, plus end-to-end pricing on five representative grids spanning the national variation. The actuarial loading ratio Π_g/E[Y_g] falls in a 5.87–6.13 band across the four high- to medium-hazard grids – a property that, as we show analytically, follows directly from the AEP-inversion calibration combined with the fixed loading scheme. Two independent sensitivity experiments on grid G1 confirm this structural prediction numerically. Substituting the BC Hydro subduction GMPE for the BA08 baseline shifts the loading ratio by only 1.7 %, and substituting either the Reasenberg or the Zaliapin–Ben-Zion declustering algorithm for the Gardner–Knopoff baseline shifts it by less than 1 % – three substitutions in total across the two experiments, all of them moving the absolute premium by 22–94 % but leaving the loading ratio essentially unchanged. The very-low-hazard reference grid never reaches its parametric trigger, yielding an explicit segmentation criterion that separates regions suitable for parametric protection from those better served by indemnity coverage. Every premium is auditable end- to-end from catalogue to tariff, and the four-module structure transfers to any seismic region by substituting the catalogue, GMPE, vulnerability curve, and exposure database.