IDEAS home Printed from https://ideas.repec.org/a/eee/insuma/v89y2019icp171-181.html
   My bibliography  Save this article

Pricing industry loss warranties in a Lévy–Frailty framework

Author

Listed:
  • Beer, Simone
  • Braun, Alexander
  • Marugg, Andrin

Abstract

We propose a novel risk-neutral pricing approach for industry loss warranties. In doing so, we explicitly take into account the statistical dependence of the losses on individual policies in the underlying insurance portfolio, caused by the occurrence of a natural catastrophe. Inspired by recent advances in the structured credit literature, we model joint claim events in a Lévy–Frailty framework with a stochastic time change. Event time is driven by rare and large jumps of a compound Poisson subordinator and thus elapses more quickly when a natural catastrophe has struck, leading to a clustering of losses. We estimate the model on historical ILW quotes and obtain encouraging fit statistics.

Suggested Citation

  • Beer, Simone & Braun, Alexander & Marugg, Andrin, 2019. "Pricing industry loss warranties in a Lévy–Frailty framework," Insurance: Mathematics and Economics, Elsevier, vol. 89(C), pages 171-181.
    • Handle: RePEc:eee:insuma:v:89:y:2019:i:c:p:171-181
    DOI: 10.1016/j.insmatheco.2019.09.008
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167668719303968
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.insmatheco.2019.09.008?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Alexander Braun & Hato Schmeiser & Florian Schreiber, 2017. "Portfolio Optimization Under Solvency II: Implicit Constraints Imposed by the Market Risk Standard Formula," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 84(1), pages 177-207, March.
    2. Alexander Braun & Hato Schmeiser & Florian Schreiber, 2015. "Solvency II's Market Risk Standard Formula: How Credible Is the Proclaimed Ruin Probability," Journal of Insurance Issues, Western Risk and Insurance Association, vol. 38(1), pages 1-30.
    3. Alexander Braun & Sarah Affolter & Hato Schmeiser, 2016. "Life Settlement Funds: Current Valuation Practices and Areas for Improvement," Risk Management and Insurance Review, American Risk and Insurance Association, vol. 19(2), pages 173-195, September.
    4. Walter Kielholz & Alex Durrer, 1997. "Insurance Derivatives and Securitization: New Hedging Perspectives for the US Cat Insurance Market," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan;The Geneva Association, vol. 22(1), pages 3-16, January.
    5. Robert A. Jarrow & Stuart M. Turnbull, 2008. "Pricing Derivatives on Financial Securities Subject to Credit Risk," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 17, pages 377-409, World Scientific Publishing Co. Pte. Ltd..
    6. Geman, Helyette & Yor, Marc, 1997. "Stochastic time changes in catastrophe option pricing," Insurance: Mathematics and Economics, Elsevier, vol. 21(3), pages 185-193, December.
    7. Jan-Frederik Mai & Matthias Scherer, 2009. "A Tractable Multivariate Default Model Based On A Stochastic Time-Change," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 12(02), pages 227-249.
    8. Alexander Braun & Hato Schmeiser & Florian Schreiber, 2018. "Return on Risk-Adjusted Capital Under Solvency II: Implications for the Asset Management of Insurance Companies," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan;The Geneva Association, vol. 43(3), pages 456-472, July.
    9. Alexander Braun, 2016. "Pricing in the Primary Market for Cat Bonds: New Empirical Evidence," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 83(4), pages 811-847, December.
    10. J. David Cummins & Mary A. Weiss, 2009. "Convergence of Insurance and Financial Markets: Hybrid and Securitized Risk‐Transfer Solutions," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 76(3), pages 493-545, September.
    11. Bakshi, Gurdip & Madan, Dilip, 2002. "Average Rate Claims with Emphasis on Catastrophe Loss Options," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 37(1), pages 93-115, March.
    12. Xu, Xinzhong & Taylor, Stephen J., 1995. "Conditional volatility and the informational efficiency of the PHLX currency options market," Journal of Banking & Finance, Elsevier, vol. 19(5), pages 803-821, August.
    13. J. David Cummins, 2006. "Should the government provide insurance for catastrophes?," Review, Federal Reserve Bank of St. Louis, vol. 88(Jul), pages 337-380.
    14. Clark, Peter K, 1973. "A Subordinated Stochastic Process Model with Finite Variance for Speculative Prices," Econometrica, Econometric Society, vol. 41(1), pages 135-155, January.
    15. Geman, Helyette, 2002. "Pure jump Levy processes for asset price modelling," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1297-1316, July.
    16. Alexander Braun & Katja Müller & Hato Schmeiser, 2013. "What Drives Insurers’ Demand for Cat Bond Investments? Evidence from a Pan-European Survey," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan;The Geneva Association, vol. 38(3), pages 580-611, July.
    17. Jarrow, Robert A., 2010. "A simple robust model for Cat bond valuation," Finance Research Letters, Elsevier, vol. 7(2), pages 72-79, June.
    18. Alexander Braun & Daliana Luca & Hato Schmeiser, 2019. "Consumption‐Based Asset Pricing in Insurance Markets: Yet Another Puzzle?," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 86(3), pages 629-661, September.
    19. Braun, Alexander, 2011. "Pricing catastrophe swaps: A contingent claims approach," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 520-536.
    20. Cummins, J. David & Danzon, Patricia M., 1997. "Price, Financial Quality, and Capital Flows in Insurance Markets," Journal of Financial Intermediation, Elsevier, vol. 6(1), pages 3-38, January.
    21. Dwight M. Jaffee & Thomas Russell, 1996. "Catastrophe Insurance, Capital Markets and Uninsurable Risks," Center for Financial Institutions Working Papers 96-12, Wharton School Center for Financial Institutions, University of Pennsylvania.
    22. Braun, Alexander & Ben Ammar, Semir & Eling, Martin, 2019. "Asset pricing and extreme event risk: Common factors in ILS fund returns," Journal of Banking & Finance, Elsevier, vol. 102(C), pages 59-78.
    23. Mary A. Weiss & Joon‐Hai Chung, 2004. "U.S. Reinsurance Prices, Financial Quality, and Global Capacity," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 71(3), pages 437-467, September.
    24. Carr, Peter & Wu, Liuren, 2004. "Time-changed Levy processes and option pricing," Journal of Financial Economics, Elsevier, vol. 71(1), pages 113-141, January.
    25. Mai, Jan-Frederik & Scherer, Matthias, 2009. "Lévy-frailty copulas," Journal of Multivariate Analysis, Elsevier, vol. 100(7), pages 1567-1585, August.
    26. Borovkova, Svetlana & Schmeck, Maren Diane, 2017. "Electricity price modeling with stochastic time change," Energy Economics, Elsevier, vol. 63(C), pages 51-65.
    27. Alexander Braun & Nadine Gatzert & Hato Schmeiser, 2012. "Performance and Risks of Open‐End Life Settlement Funds," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 79(1), pages 193-230, March.
    28. Balbás, Alejandro & Longarela, Iñaki R. & Lucia, Julio J., 1999. "How does financial theory apply to catastrophe-linked derivatives? En empirical test of several princing models," DEE - Working Papers. Business Economics. WB 6521, Universidad Carlos III de Madrid. Departamento de Economía de la Empresa.
    29. Lindskog, Filip & McNeil, Alexander J., 2003. "Common Poisson Shock Models: Applications to Insurance and Credit Risk Modelling," ASTIN Bulletin, Cambridge University Press, vol. 33(2), pages 209-238, November.
    30. Chang, Carolyn W. & Chang, Jack S.K. & Lu, WeLi, 2010. "Pricing catastrophe options with stochastic claim arrival intensity in claim time," Journal of Banking & Finance, Elsevier, vol. 34(1), pages 24-32, January.
    31. Armstrong, J. Scott & Collopy, Fred, 1992. "Error measures for generalizing about forecasting methods: Empirical comparisons," International Journal of Forecasting, Elsevier, vol. 8(1), pages 69-80, June.
    32. Chang, Carolyn W. & Chang, Jack S.K. & Lu, WeiLi, 2008. "Pricing catastrophe options in discrete operational time," Insurance: Mathematics and Economics, Elsevier, vol. 43(3), pages 422-430, December.
    33. Salah Amraoui & Laurent Cousot & Sebastien Hitier & Jean-Paul Laurent, 2012. "Pricing CDOs with state-dependent stochastic recovery rates," Quantitative Finance, Taylor & Francis Journals, vol. 12(8), pages 1219-1240, February.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Wu, Yang-Che, 2020. "Equilibrium in natural catastrophe insurance market under disaster-resistant technologies, financial innovations and government interventions," Insurance: Mathematics and Economics, Elsevier, vol. 95(C), pages 116-128.
    2. Peter Carayannopoulos & Olga Kanj & M. Fabricio Perez, 2022. "Pricing dynamics in the market for catastrophe bonds," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan;The Geneva Association, vol. 47(1), pages 172-202, January.
    3. Beer, Simone & Braun, Alexander, 2022. "Market-consistent valuation of natural catastrophe risk," Journal of Banking & Finance, Elsevier, vol. 134(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Beer, Simone & Braun, Alexander, 2022. "Market-consistent valuation of natural catastrophe risk," Journal of Banking & Finance, Elsevier, vol. 134(C).
    2. Peter Carayannopoulos & Olga Kanj & M. Fabricio Perez, 2022. "Pricing dynamics in the market for catastrophe bonds," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan;The Geneva Association, vol. 47(1), pages 172-202, January.
    3. Ben Ammar, Semir & Braun, Alexander & Eling, Martin, 2015. "Alternative Risk Transfer and Insurance-Linked Securities: Trends, Challenges and New Market Opportunities," I.VW HSG Schriftenreihe, University of St.Gallen, Institute of Insurance Economics (I.VW-HSG), volume 56, number 56.
    4. Braun, Alexander, 2011. "Pricing catastrophe swaps: A contingent claims approach," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 520-536.
    5. Burnecki, Krzysztof & Giuricich, Mario Nicoló & Palmowski, Zbigniew, 2019. "Valuation of contingent convertible catastrophe bonds — The case for equity conversion," Insurance: Mathematics and Economics, Elsevier, vol. 88(C), pages 238-254.
    6. Wu, Yang-Che, 2020. "Equilibrium in natural catastrophe insurance market under disaster-resistant technologies, financial innovations and government interventions," Insurance: Mathematics and Economics, Elsevier, vol. 95(C), pages 116-128.
    7. Eckhard Platen & David Taylor, 2016. "Loading Pricing of Catastrophe Bonds and Other Long-Dated, Insurance-Type Contracts," Research Paper Series 379, Quantitative Finance Research Centre, University of Technology, Sydney.
    8. Lim, Terence & Lo, Andrew W. & Merton, Robert C. & Scholes, Myron S., 2006. "The Derivatives Sourcebook," Foundations and Trends(R) in Finance, now publishers, vol. 1(5–6), pages 365-572, April.
    9. Alexander Braun, 2016. "Pricing in the Primary Market for Cat Bonds: New Empirical Evidence," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 83(4), pages 811-847, December.
    10. Krzysztof Burnecki & Mario Nicoló Giuricich, 2017. "Stable Weak Approximation at Work in Index-Linked Catastrophe Bond Pricing," Risks, MDPI, vol. 5(4), pages 1-19, December.
    11. Faias, José Afonso & Guedes, José, 2020. "The diffusion of complex securities: The case of CAT bonds," Insurance: Mathematics and Economics, Elsevier, vol. 90(C), pages 46-57.
    12. Tobias Götze & Marc Gürtler & Eileen Witowski, 2020. "Improving CAT bond pricing models via machine learning," Journal of Asset Management, Palgrave Macmillan, vol. 21(5), pages 428-446, September.
    13. Riza Andrian Ibrahim & Sukono & Herlina Napitupulu & Rose Irnawaty Ibrahim, 2024. "Earthquake Bond Pricing Model Involving the Inconstant Event Intensity and Maximum Strength," Mathematics, MDPI, vol. 12(6), pages 1-21, March.
    14. Beaulieu, Marie-Claude & Dufour, Jean-Marie & Khalaf, Lynda & Melin, Olena, 2023. "Identification-robust beta pricing, spanning, mimicking portfolios, and the benchmark neutrality of catastrophe bonds," Journal of Econometrics, Elsevier, vol. 236(1).
    15. Charpentier, Arthur & Le Maux, Benoît, 2014. "Natural catastrophe insurance: How should the government intervene?," Journal of Public Economics, Elsevier, vol. 115(C), pages 1-17.
    16. Perrakis, Stylianos & Boloorforoosh, Ali, 2013. "Valuing catastrophe derivatives under limited diversification: A stochastic dominance approach," Journal of Banking & Finance, Elsevier, vol. 37(8), pages 3157-3168.
    17. Georges Dionne & Denise Desjardins, 2022. "A re‐examination of the US insurance market's capacity to pay catastrophe losses," Risk Management and Insurance Review, American Risk and Insurance Association, vol. 25(4), pages 515-549, December.
    18. Braun, Alexander & Ben Ammar, Semir & Eling, Martin, 2019. "Asset pricing and extreme event risk: Common factors in ILS fund returns," Journal of Banking & Finance, Elsevier, vol. 102(C), pages 59-78.
    19. Carolyn W. Chang & Jack S. K. Chang & Min‐Teh Yu & Yang Zhao, 2020. "Portfolio optimization in the catastrophe space," European Financial Management, European Financial Management Association, vol. 26(5), pages 1414-1448, November.
    20. Roy Kouwenberg, 2018. "Strategic asset allocation for insurers under Solvency II," Journal of Asset Management, Palgrave Macmillan, vol. 19(7), pages 447-459, December.

    More about this item

    Keywords

    Natural catastrophe risk; Industry loss warranties; Risk-neutral valuation; Lévy–Frailty model; Stochastic time change;
    All these keywords.

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:insuma:v:89:y:2019:i:c:p:171-181. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/505554 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.