Catastrophe Reinsurance Single Premium Valuation Model Based on Indonesia's Earthquake Data

Abstract

Indonesia's position along the Pacific Ring of Fire makes it highly vulnerable to catastrophic earthquakes, creating significant financial exposure for insurers through simultaneous surges in life, health, and property insurance claims.  This study develops a comprehensive valuation model for catastrophe reinsurance contracts using advanced statistical techniques to assess extreme risks and their interdependencies. The model integrates three key approaches: (1) the Peaks Over Threshold method with Generalized Pareto Distribution to analyze extreme losses from fatalities and injuries, (2) copula theory (Clayton and Gumbel) to capture dependence structures between different claim types, and (3) Monte Carlo simulations to project future event frequencies and financial impacts. Using Indonesian seismic data from 1979 to 2025 while excluding extreme outlier events, we model extreme losses in fatalities and injuries. While also employing the Fundamental Theorem of Asset Pricing to determine reinsurance premiums as the expected present value of potential claims. , with the Gumbel copula demonstrating superior fit for upper-tail dependence between variables. The model implements realistic assumptions, including: a retention limit of Rp15 billion for the primary insurer, average claims of Rp500 million per life and Rp15 million per injury, and coverage of 5% and 7% of the population for life and health policies, respectively. Applying a 5.75% discount rate (BI rate 2025) through 10,000 Monte Carlo simulations, we calculate a single reinsurance premium of Rp17,395,932,554. The results demonstrate how advanced statistical methods can effectively quantify catastrophe risk transfer, providing insurers with an actuarially sound pricing framework for managing low-frequency, high-severity earthquake exposures. However, a limitation of this study includes the exclusion of the 2004 mega-disaster, which may lead to an underestimation of worst-case scenarios, and the use of fixed assumptions for insurance coverage and claim values, which may not fully reflect real-world variability. Despite these limitations, this approach offers a valuable framework for managing earthquake-related risks in Indonesia’s reinsurance market.