CAT Bond Pricing in Uncertain Environment

Document Type : Research Paper


Department of Applied Mathematics, Faculty of Basic Sciences, Azarbaijan Shahid Madani University, Tabriz, Iran


Catastrophe bonds are among the essential instruments in providing a financial hedge for insurance companies and their policyholders. Catastrophic events are rare, and the shortage of data turns using probability theory indefensible. On the other hand, uncertainty theory is a reliable alternative to deal with these kinds of indeterminacies. We model the problem of pricing catastrophe bonds as an uncertain optimization problem where the maximization of the cedent insurance company’s profit is constrained to the uncertain measure of ruin defined for the investors. Consequently, one could provide a tradeoff between being profitable for the ceding company and having reasonable protection for the investors. A solution to the optimization problem will be considered as the spread over the LIBOR, leading to a complete determination of the bond price. The results suggest the practicality of the model, especially the application of uncertainty theory in pricing catastrophe bonds. Finally, the uncertain ruin index is calculated for a real-world problem, and the results are compared with those obtained by probability theory.


Main Subjects

Aase, K. (1999). An equilibrium model of catastrophe insurance futures and spreads. The Geneva Papers on Risk and Insurance Theory, 24(1), 69-96.
Artemis, D. D. (2020). Catastrophe bonds, insurance linked securities, reinsurance capital & investment, risk transfer intelligence. Artemis.
Baryshnikov, Y., Mayo, A., & Taylor, D. R. (2001). Pricing of CAT bonds. Mimeo, University of Illinois.
Benckert, L. G., & Jung, J. (1974). Statistical models of claim distributions in fire insurance. ASTIN Bulletin: The Journal of the IAA, 8(1), 1-25.
Bodoff, N. M., & Gan, Y. (2009). An analysis of the market price of cat bonds. CAS E-Forum.
Braun, A. (2016). Pricing in the primary market for cat bonds: New empirical evidence. Journal of Risk and Insurance, 83(4), 811-847.
Cox, S. H., & Pedersen, H. W. (2000). Catastrophe risk bonds. North American Actuarial Journal, 4(4), 56-82.
Cummins, J.. (2012). cat bonds and other risk-linked securities: Product design and evolution of the market. SSRN Electronic Journal.
Duffie, D., & Singleton, K. J. (1999). Modeling term structures of defaultable bonds. The Review of Financial Studies, 12(4), 687-720.
Ermoliev, Y. M., Ermolieva, T. Y., MacDonald, G. J., & Norkin, V. I. (2000). Stochastic optimization of insurance portfolios for managing exposure to catastrophic risks. Annals of Operations Research, 99(1-4), 207-225.
Galeotti, M., Gürtler, M., & Winkelvos, C. (2013). Accuracy of premium calculation models for CAT bonds—An empirical analysis. Journal of Risk and Insurance, 80(2), 401-421.
Henkind, S. J., & Harrison, M. C. (1988). An analysis of four uncertainty calculi. IEEE Transactions on Systems, Man, and Cybernetics, 18(5), 700-714.
Kickert, W. J. (1979). Fuzzy theories on decision making: A critical review (vol. 3). Springer Science & Business Media.
Krutov, A. (2010). Investing in insurance risk: Insurance-linked securities: A practitioner’s perspective. Risk Books.
Lakdawalla, D., & Zanjani, G. (2012). Catastrophe bonds, reinsurance, and the optimal collateralization of risk transfer. Journal of Risk and Insurance, 79(2), 449-476.
Lane, M., & Mahul, O. (2008). Catastrophe risk pricing: An empirical analysis. The World Bank.
Lane, M. N. (2000). Pricing risk transfer transactions 1. ASTIN Bulletin: The Journal of the IAA, 30(2), 259-293.
Lei, D. T., Wang, J.-H., & Tzeng, L. Y. (2008). Explaining the spread premiums on catastrophe bonds [paper presentation]. NTU International Conference on Finance, Taiwan,
Liu, B. (2007). Uncertainty theory. In  (Eds.), Uncertainty theory (pp.  ). Springer.
Liu, B. (2008). Fuzzy process, hybrid process and uncertain process. Journal of Uncertain Systems, 2(1), 3-16.
Liu, B. (2009). Some research problems in uncertainty theory. Journal of Uncertain Systems, 3(1), 3-10.
Liu, B. (2010a). Uncertain risk analysis and uncertain reliability analysis. Journal of Uncertain Systems, 4(3), 163-170.
 . In   (Eds.), Uncertainty theory (pp.  ). Springer.
Liu, B. (2012). Why is there a need for uncertainty theory. Journal of Uncertain Systems, 6(1), 3-10.
Liu, B. (2013). Extreme value theorems of uncertain process with application to insurance risk model. Soft Computing, 17(4), 549-556.
 .  (Eds.), In Uncertainty theory (pp.  ). Springer.
Nowak, P., & Romaniuk, M. (2013). Pricing and simulations of catastrophe bonds. Insurance: Mathematics and Economics, 52(1), 18-28.
Nowak, P., & Romaniuk, M. (2014). Catastrophe bond pricing with fuzzy volatility parameters. In   (Eds.), Issues and challenges of intelligent systems and computational intelligence (pp. 27-44). Springer.
Nowak, P., & Romaniuk, M. (2017). Catastrophe bond pricing for the two-factor Vasicek interest rate model with automatized fuzzy decision making. Soft Computing, 21(10), 2575-2597.
Tajeddini, K., & Mueller, S. (2019). Moderating effect of environmental dynamism on the relationship between a firm’s entrepreneurial orientation and financial performance. Entrepreneurship Research Journal, 9(4),  .
Tajeddini, K., & Trueman, M. (2016). Environment-strategy and alignment in a restricted, transitional economy: Empirical research on its application to Iranian state-owned enterprises. Long Range Planning, 49(5), 570-583.
Thorin, O., & Wikstad, N. (1977). Calculation of ruin probabilities when the claim distribution is lognormal. ASTIN Bulletin: The Journal of the IAA, 9(1-2), 231-246.
Vakili, W., & Ghaffari-Hadigheh, A. (2021). Optimal reinsurance: A ruin-related uncertain programming approach. arXiv:2101.06470.
Vasicek, O. (1977). An equilibrium characterization of the term structure. Journal of Financial Economics, 5(2), 177-188.
Vaugirard, V. E. (2003). Pricing catastrophe bonds by an arbitrage approach. The Quarterly Review of Economics and Finance, 43(1), 119-132.
Wang, S. S. (2002). A universal framework for pricing financial and insurance risks. ASTIN Bulletin: The Journal of the IAA, 32(2), 213-234.
Zhou, C. (1997). A jump-diffusion approach to modeling credit risk and valuing defaultable securities. Finance and Economics Discussion Series 1997-15, Board of Governors of the Federal Reserve System (U.S.).
Zimbidis, A. A., Frangos, N. E., & Pantelous, A. A. (2007). Modeling earthquake risk via extreme value theory and pricing the respective catastrophe bonds. ASTIN Bulletin: The Journal of the IAA, 37(1), 163-183.