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The valuation of contingent capital with catastrophe risks

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  • Lin, Shih-Kuei
  • Chang, Chia-Chien
  • Powers, Michael R.

Abstract

The Intergovernmental Panel on Climate Change Fourth Assessment Report (2007) indicates that unanticipated catastrophic events could increase with time because of global warming. Therefore, it seems inadequate to assume that arrival process of catastrophic events follows a pure Poisson process adopted by most previous studies (e.g. [Louberge, H., Kellezi, E., Gilli, M., 1999. Using catastrophe-linked securities to diversify insurance risk: A financial analysis of lCAT bonds. J. Risk Insurance 22, 125-146; Lee, J.-P., Yu, M.-T., 2002. Pricing default-risky CAT bonds with moral hazard and basis risk. J. Risk Insurance 69, 25-44; Cox, H., Fairchild, J., Pedersen, H., 2004. Valuation of structured risk management products. Insurance Math. Econom. 34, 259-272; Jaimungal, S., Wang, T., 2006. Catastrophe options with stochastic interest rates and compound Poisson losses. Insurance Math. Econom., 38, 469-483]. In order to overcome this shortcoming, this paper proposes a doubly stochastic Poisson process to model the arrival process for catastrophic events. Furthermore, we generalize the assumption in the last reference mentioned above to define the general loss function presenting that different specific loss would have different impacts on the drop in stock price. Based on modeling the arrival rates for catastrophe risks, the pricing formulas of contingent capital are derived by the Merton measure. Results of empirical experiments of contingent capital prices as well as sensitivity analyses are presented.

Suggested Citation

  • Lin, Shih-Kuei & Chang, Chia-Chien & Powers, Michael R., 2009. "The valuation of contingent capital with catastrophe risks," Insurance: Mathematics and Economics, Elsevier, vol. 45(1), pages 65-73, August.
    • Handle: RePEc:eee:insuma:v:45:y:2009:i:1:p:65-73
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    References listed on IDEAS

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    1. Liu, Liang-Chih & Dai, Tian-Shyr & Zhou, Lei, 2024. "On the design of bail-in-able bonds from the perspective of non-financial firms," International Review of Economics & Finance, Elsevier, vol. 89(PA), pages 1136-1155.
    2. Yang‐Che Wu & Ming Jing Yang, 2018. "The effectiveness of asset, liability and equity hedging against catastrophe risk: the cases of winter storms in North America and Europe," European Financial Management, European Financial Management Association, vol. 24(5), pages 893-918, November.
    3. Gunther Leobacher & Philip Ngare, 2014. "Utility indifference pricing of derivatives written on industrial loss indexes," Papers 1404.0879, arXiv.org.
    4. Tang, Chao & Chen, Peimin & Zhang, Shu, 2025. "Valuing catastrophe equity put options with liquidity risk, default risk and jumps," The North American Journal of Economics and Finance, Elsevier, vol. 76(C).
    5. Andreas Eichler & Gunther Leobacher & Michaela Szolgyenyi, 2016. "Utility Indifference Pricing of Insurance Catastrophe Derivatives," Papers 1607.01110, arXiv.org, revised May 2017.
    6. Eckhard Platen & David Taylor, 2016. "Loading Pricing of Catastrophe Bonds and Other Long-Dated, Insurance-Type Contracts," Papers 1610.09875, arXiv.org.
    7. Wang, Xingchun, 2016. "Catastrophe equity put options with target variance," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 79-86.
    8. Lo, Chien-Ling & Lee, Jin-Ping & Yu, Min-Teh, 2013. "Valuation of insurers’ contingent capital with counterparty risk and price endogeneity," Journal of Banking & Finance, Elsevier, vol. 37(12), pages 5025-5035.
    9. Kim, Hwa-Sung & Kim, Bara & Kim, Jerim, 2014. "Pricing perpetual American CatEPut options when stock prices are correlated with catastrophe losses," Economic Modelling, Elsevier, vol. 41(C), pages 15-22.
    10. Wang, Xingchun, 2020. "Catastrophe equity put options with floating strike prices," The North American Journal of Economics and Finance, Elsevier, vol. 54(C).
    11. Xingchun Wang, 2016. "The Pricing of Catastrophe Equity Put Options with Default Risk," International Review of Finance, International Review of Finance Ltd., vol. 16(2), pages 181-201, June.
    12. Yu, Jun, 2015. "Catastrophe options with double compound Poisson processes," Economic Modelling, Elsevier, vol. 50(C), pages 291-297.
    13. Wu, Yang-Che, 2015. "Reexamining the feasibility of diversification and transfer instruments on smoothing catastrophe risk," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 54-66.
    14. Têtu Alexandre & Lai Van Son & Soumaré Issouf & Gendron Michel, 2015. "Hedging Flood Losses Using Cat Bonds," Asia-Pacific Journal of Risk and Insurance, De Gruyter, vol. 9(2), pages 149-184, July.
    15. Wang, Xingchun, 2019. "Valuation of new-designed contracts for catastrophe risk management," The North American Journal of Economics and Finance, Elsevier, vol. 50(C).
    16. Chen, Jun-Home & Lian, Yu-Min & Liao, Szu-Lang, 2022. "Pricing catastrophe equity puts with counterparty risks under Markov-modulated, default-intensity processes," The North American Journal of Economics and Finance, Elsevier, vol. 61(C).
    17. Truong, Chi & Trück, Stefan & Mathew, Supriya, 2018. "Managing risks from climate impacted hazards – The value of investment flexibility under uncertainty," European Journal of Operational Research, Elsevier, vol. 269(1), pages 132-145.

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