Earthquake Bond Pricing Model Involving the Inconstant Event Intensity and Maximum Strength

Riza Andrian Ibrahim, Sukono (), Herlina Napitupulu and Rose Irnawaty Ibrahim
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Riza Andrian Ibrahim: Doctoral Program of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Padjadjaran, Sumedang 45363, Indonesia
Sukono: Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Padjadjaran, Sumedang 45363, Indonesia
Herlina Napitupulu: Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Padjadjaran, Sumedang 45363, Indonesia
Rose Irnawaty Ibrahim: Faculty of Science and Technology, Universiti Sains Islam Malaysia, Nilai 71800, Malaysia

Mathematics, 2024, vol. 12, issue 6, 1-21

Abstract: Traditional insurance’s earthquake contingency costs are insufficient for earthquake funding due to extreme differences from actual losses. The earthquake bond (EB) links insurance to capital market bonds, enabling higher and more sustainable earthquake funding, but challenges persist in pricing EBs. This paper presents zero-coupon and coupon-paying EB pricing models involving the inconstant event intensity and maximum strength of extreme earthquakes under the risk-neutral pricing measure. Focusing on extreme earthquakes simplifies the modeling and data processing time compared to considering infinite earthquake frequency occurring over a continuous time interval. The intensity is accommodated using the inhomogeneous Poisson process, while the maximum strength is modeled using extreme value theory (EVT). Furthermore, we conducted model experiments and variable sensitivity analyses on EB prices using earthquake data from Indonesia’s National Disaster Management Authority from 2008 to 2021. The sensitivity analysis results show that choosing inconstant intensity rather than a constant one implies significant EB price differences, and the maximum strength distribution based on EVT matches the data distribution. The presented model and its experiments can guide EB issuers in setting EB prices. Then, the variable sensitivities to EB prices can be used by investors to choose EB according to their risk tolerance.

Keywords: earthquake bonds; inconstant event intensity; maximum strength; inhomogeneous Poisson process; extreme value theory; risk-neutral pricing measure (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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