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Catastrophe Bond Pricing with Fuzzy Volatility Parameters

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Issues and Challenges of Intelligent Systems and Computational Intelligence

Part of the book series: Studies in Computational Intelligence ((SCI,volume 530))

Abstract

The number of natural catastrophes and losses caused by them increase in time. The damages caused by natural disasters are difficult to handle for insurers. Therefore catastrophe bonds were introduced to transfer the catastrophic risk to financial markets. In this paper we continue our research concerning catastrophe bond pricing. In our approach we use stochastic analysis and fuzzy sets theory in order to obtain catastrophe bond pricing formulas. To model the short interest rate we use the one- and two-factor Vasicek model. We take into account different sources of uncertainty, not only the stochastic one. In particular, we treat the volatility of the interest rate and market price of risk as fuzzy numbers. We use Monte Carlo simulations for data describing natural catastrophic events in the United States to illustrate the obtained results.

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References

  1. Buckley, J.J., Eslami, E.: Pricing stock options using fuzzy sets. Iran. J. Fuzzy Syst. 4(2), 1–14 (2007)

    MATH  MathSciNet  Google Scholar 

  2. Chernobai, A., Burnecki, K., Rachev, S., Trueck, S., Weron, R.: Modeling catastrophe claims with left-truncated severity distributions. HSC, Research Reports, HSC/05/01 (2005)

    Google Scholar 

  3. Ermolieva, T., Romaniuk, M., Fischer, G., Makowski, M.: Integrated model-based decision support for management of weather-related agricultural losses. In: Hryniewicz, O., Studziński, J., Romaniuk, M. (eds.), Enviromental informatics and systems research. Vol. 1: Plenary and session papers—EnviroInfo 2007, Shaker Verlag, IBS PAN (2007)

    Google Scholar 

  4. Ermolieva, T., Ermoliev, Y.: Catastrophic risk management: flood and seismic risks case studies. In: Wallace, S.W., Ziemba, W.T. (eds.) Applications of Stochastic Programming. MPS-SIAM Series on Optimization, Philadelphia (2005)

    Google Scholar 

  5. George, J.B.: Alternative reinsurance: using catastrophe bonds and insurance derivatives as a mechanism for increasing capacity in the insurance markets. CPCU J. 52(1), 50–54 (1999)

    Google Scholar 

  6. Gil-Lafuente, A.M.: Fuzzy Logic in Financial Analysis. Springer, Berlin (2005)

    Google Scholar 

  7. Hewitt, Ch. C., Lefkowitz, B.: Methods for fitting distributions to insurance loss data. In: Proceedings of the Casualty Actuarial Society Casualty Actuarial Society, vol. LXVI, pp. 139–160. Arlington, Virginia (1979)

    Google Scholar 

  8. Hogg, R.V., Klugman, S.A.: On the estimation of long-tailed skewed distributions with actuarial applications. J. Econom. 23, 91–102 (1983)

    Article  Google Scholar 

  9. Muermann, A.: Market price of insurance risk implied by catastrophe derivatives. N. Am. Actuarial J. 12(3), 221–227 (2008)

    Article  MathSciNet  Google Scholar 

  10. Niedzielski J.: USAA places catastrophe bonds, National Underwriter, Jun 16 (1997)

    Google Scholar 

  11. Nowak, P., Romaniuk, M.: On pricing formula and numerical analysis of catastrophe bond with some payment function. In: Wilimowska, Z., Borzemski, L., Grzech, A., Swiatek, J. (eds.) Information Systems Architecture and Technology. The Use of IT Models for Organization Management, Wrocław (2012)

    Google Scholar 

  12. Nowak, P., Romaniuk, M.: Computing option price for Levy process with fuzzy parameters. Eur. J. Oper. Res. 201(1), 206–210 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  13. Nowak, P., Romaniuk, M.: Analiza wlasnosci portfela zlozonego z instrumentow finansowych i ubezpieczeniowych. In: STUDIA I MATERIALY POLSKIEGO STOWARZYSZENIA ZARZADZANIA WIEDZA, vol. 31, 65–76 (2010)

    Google Scholar 

  14. Nowak, P., Romaniuk, M.: Pricing and simulation of catastrophe bonds. Insurance: Mathematics and Economics, 52(1), 18–28 (2013)

    Google Scholar 

  15. Nowak, P., Romaniuk, M.: Catastrophe bond pricing for the one- and two-factor Vasicek interest rate model. Research Report, RB/3/2012, SRI PAS, Warszawa (2012)

    Google Scholar 

  16. Nowman, K.B.: Gaussian estimation of single-factor continuous time models of the term structure of interest rates. J. Finance 52(4), 1695–1706 (1997)

    Article  Google Scholar 

  17. Papush, D.E., Patrik, G.S., Podgaits, F.: Approximations of the aggregate loss distribution. Casualty Actuarial Society Forum Casualty Actuarial Society. Arlington, Virginia 2001 (Winter), 175–186 (2001)

    Google Scholar 

  18. Vaugirard, V.E.: Pricing catastrophe bonds by an arbitrage approach. Q. Rev. Econ. Finance 43, 119–132 (2003)

    Article  Google Scholar 

  19. Wu, H-Ch.: Pricing European options based on the fuzzy pattern of Black-Scholes formula. Comput. Oper. Res. 31, 1069–1081 (2004)

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. Systems Research Institute Polish Academy of Sciences, ul. Newelska 6, 01-447, Warszawa, Poland

    Piotr Nowak & Maciej Romaniuk

  2. The John Paul II Catholic University of Lublin, Lublin, Poland

    Maciej Romaniuk

Authors
  1. Piotr Nowak
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  2. Maciej Romaniuk
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Corresponding author

Correspondence to Piotr Nowak .

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Editors and Affiliations

  1. Department of Automation, Széchenyi István University, Győr, Hungary

    László T. Kóczy

  2. Department of Information Technology, Széchenyi István University, Győr, Hungary

    Claudiu R. Pozna

  3. Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland

    Janusz Kacprzyk

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Nowak, P., Romaniuk, M. (2014). Catastrophe Bond Pricing with Fuzzy Volatility Parameters. In: Kóczy, L., Pozna, C., Kacprzyk, J. (eds) Issues and Challenges of Intelligent Systems and Computational Intelligence. Studies in Computational Intelligence, vol 530. Springer, Cham. https://doi.org/10.1007/978-3-319-03206-1_3

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  • DOI: https://doi.org/10.1007/978-3-319-03206-1_3

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-03205-4

  • Online ISBN: 978-3-319-03206-1

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