The optimal write-down coefficients in a percentage for a catastrophe bond.(English)Zbl 1393.91102

Summary: Catastrophe bonds, also known as CAT bonds, are insurance-linked securities that help to transfer catastrophe risks from insurance industry to bond holders. When the aggregate catastrophe loss exceeds a specified amount by the maturity, the CAT bond is triggered and the future bond payments are reduced. This article first presents a general pricing formula for a CAT bond with coupon payments, which can be adapted to various assumptions for a catastrophe loss process. Next, it gives formulas for the optimal write-down coefficients in a percentage, implemented by Monte Carlo simulations, which maximize two measurements of risk reduction, hedge effectiveness rate (HER) and hedge effectiveness (HE), respectively, and examines how the optimal write-down coefficients in a percentage help reinsurance or insurance companies to mitigate extreme catastrophe losses. Last, it demonstrates how the number of coupon payments, loss share, retention level, strike price, maturity, frequency, and severity parameters of the catastrophe loss process and different interest rate models affect the optimal write-down coefficients in a percentage with numerical examples for illustrations.

MSC:

 91B30 Risk theory, insurance (MSC2010) 91G20 Derivative securities (option pricing, hedging, etc.)
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 [1] Baryshnikov, Y.; Mayo, A.; Taylor, D. R., Pricing of CAT bonds, (1998) [2] Blake, D.; MacMinn, R.; Li, J. S. H.; Hardy, M. R., Longevity risk and capital markets: the 2012–2013 update, North American Actuarial Journal, 18, 1, 1-13, (2014) [3] Burnecki, K.; Kukla, G., Pricing of zero-coupon and coupon CAT bonds, Applicationes Mathematicae, 30, 3, 315-324, (2003) · Zbl 1051.62105 [4] Chan, K. C.; Karolyi, G. A.; Longstaff, F. A.; Sanders, A. B., An empirical comparison of alternative models of the short-term interest rate, Journal of Finance, 47, 3, 1209-1227, (1992) [5] Chang, C. C.; Lin, S. K.; Yu, M. T., Valuation of catastrophe equity puts with Markov-modulated Poisson processes, Journal of Risk and Insurance, 78, 2, 447-473, (2011) [6] Chang, C. W.; Chang, J. S. K.; Yu, M. T., Pricing catastrophe insurance futures call spreads: A randomized operational time approach, Journal of Risk and Insurance, 63, 4, 599-617, (1996) [7] Cox, S. H.; Pedersen, H. W., Catastrophe risk bonds, North American Actuarial Journal, 4, 4, 56-82, (2000) · Zbl 1083.91534 [8] Egami, M.; Young, V. R., Indifference prices of structured catastrophe (CAT) bonds, Insurance: Mathematics and Economics, 42, 2, 771-778, (2008) · Zbl 1152.91442 [9] Jarrow, R., A simple robust model for CAT bond valuation, Finance Research Letters, 7, 2, 72-79, (2010) [10] Kuczinski, T., and Irvin, K. 2012. Severe Weather in North America: Perils, Risks, Insurance. Munich, Germany: Munich Re. Available at [11] Laster, D. S., Capital market innovation in the insurance industry, Sigma, (Vol. 3), (2001) [12] Lee, J. P.; Yu, M. T., Pricing default-risky CAT bonds with moral hazard and basis risk, Journal of Risk and Insurance, 69, 1, 25-44, (2002) [13] Lee, J. P.; Yu, M. T., Valuation of catastrophe reinsurance with catastrophe bonds, Insurance: Mathematics and Economics, 41, 2, 264-278, (2007) · Zbl 1193.91067 [14] Li, J. S. H.; Hardy, M. R., Measuring basis risk in longevity hedges, North American Actuarial Journal, 15, 2, 177-200, (2011) · Zbl 1228.91042 [15] Li, J. S. H.; Luo, A., Key q-duration: A framework for hedging longevity risk, ASTIN Bulletin, 42, 413-452, (2012) · Zbl 1277.91089 [16] Lo, C. L.; Lee, J. P.; Yu, M. T., Valuation of insurersâ€™ contingent capital with counterparty risk and price endogeneity, Journal of Banking and Finance, 37, 12, 5025-5035, (2013) [17] Ma, Z. G.; Ma, C. Q., Pricing catastrophe risk bonds: A mixed approximation method, Insurance: Mathematics and Economics, 52, 2, 243-254, (2013) · Zbl 1284.91551 [18] Nowak, P.; Romaniuk, M., Pricing and simulations of catastrophe bond, Insurance: Mathematics and Economics, 52, 1, 18-28, (2013) · Zbl 1291.91208 [19] Tsai, C. C. L.; Yang, S., A linear regression approach to modeling mortality rates of different forms, North American Actuarial Journal, 19, 1, 1-23, (2015) [20] Vaugirard, V. E., Pricing catastrophe bonds by an arbitrage approach, Quarterly Review of Economics and Finance, 43, 1, 119-132, (2003) [21] Vaugirard, V. E., Valuing catastrophe bonds by Monte Carlo simulations, Applied Mathematical Finance, 10, 1, 75-90, (2003) · Zbl 1060.91088
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