Modeling earthquake bond prices with correlated dual trigger indices and the approximate solution using the Monte Carlo algorithm

• Published in: AIMS mathematics Vol. 10; no. 2; pp. 2223 - 2253
• Main Authors: Ibrahim, Riza Andrian, Sukono, Napitupulu, Herlina, Ibrahim, Rose Irnawaty
• Format: Journal Article
• Language: English
• Published: AIMS Press 01.01.2025
• Subjects: depth; earthquake bond; intensity; maximum magnitude; monte carlo method; price; risk-neutral pricing measure
• ISSN: 2473-6988; 2473-6988
• DOI: 10.3934/math.2025103

Countries prone to earthquakes face increasing seismic activity, often resulting in losses that exceed national budgets. To mitigate these losses, earthquake bonds present a promising alternative funding source; however, pricing them is complex, requiring simultaneous accounting for financial and seismic risks. Therefore, this study aimed to model earthquake bond pricing. The model incorporates earthquake intensity to account for rising seismic activity. It also includes depth and maximum magnitude as correlated dual trigger indices, making the bonds more attractive to investors, as claims are generated if both events occur. These three factors were modeled together as a compound stochastic process. The bond price was then formulated using a risk-neutral pricing measure with a stochastic interest rate under the Cox-Ingersoll-Ross model. Since the model lacks a closed-form solution, we employed an algorithm based on the Monte Carlo method for estimation. Through this algorithm, we showed that bond prices for terms of one to six years follow a normal distribution. The use of stochastic interest rates becomes significant as the bond term increases. We also found that earthquake intensity and bond terms negatively correlate with bond prices, while annual coupons positively correlate. Additionally, including dual triggers lowers claim probability and increases the bond demand, but is compensated by higher prices. This study can assist issuers in pricing earthquake bonds based on earthquake severity-maximum magnitude, depth, and intensity-and aid geological institutions in estimating earthquake risk in observed areas.