IDEAS home Printed from https://ideas.repec.org/a/eee/insuma/v51y2012i2p271-281.html
   My bibliography  Save this article

Computing bounds on the expected payoff of Alternative Risk Transfer products

Author

Listed:
  • Villegas, Andrés M.
  • Medaglia, Andrés L.
  • Zuluaga, Luis F.

Abstract

The demand for integrated risk management solutions and the need for new sources of capital have led to the development of innovative risk management products that mix the characteristics of traditional insurance and financial products. Such products, usually referred as Alternative Risk Transfer (ART) products include: (re)insurance contracts that bundle several risks under a single policy; multi-trigger products where the payment of benefits depends upon the occurrence of several events; and insurance linked securities that place insurance risks in the capital market. Pricing of these complex products usually requires tailor-made complex valuation methods that combine derivative pricing and actuarial science techniques for each product, as well as strong distributional assumptions on the ART’s underlying risk factors. We present here an alternative methodology to compute bounds on the price of ART products when there is limited information on the distribution of the underlying risk factors. In particular, we develop a general optimization-based method that computes upper and lower price bounds for different ART products using market data and possibly expert information about the underlying risk factors. These bounds are useful when the structure of the product is too complex to develop analytical or simulation valuation methods, or when the scarcity of data makes it difficult to make strong distributional assumptions on the risk factors. We illustrate our results by computing bounds on the price of a floating retention insurance contract, and a catastrophe equity put (CatEPut) option.

Suggested Citation

  • Villegas, Andrés M. & Medaglia, Andrés L. & Zuluaga, Luis F., 2012. "Computing bounds on the expected payoff of Alternative Risk Transfer products," Insurance: Mathematics and Economics, Elsevier, vol. 51(2), pages 271-281.
  • Handle: RePEc:eee:insuma:v:51:y:2012:i:2:p:271-281
    DOI: 10.1016/j.insmatheco.2012.03.012
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167668712000479
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.insmatheco.2012.03.012?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. James E. Smith, 1995. "Generalized Chebychev Inequalities: Theory and Applications in Decision Analysis," Operations Research, INFORMS, vol. 43(5), pages 807-825, October.
    2. Cox, Samuel H. & Fairchild, Joseph R. & Pedersen, Hal W., 2004. "Valuation of structured risk management products," Insurance: Mathematics and Economics, Elsevier, vol. 34(2), pages 259-272, April.
    3. Kaas, R. & Goovaerts, M. J., 1986. "Extremal values of stop-loss premiums under moment constraints," Insurance: Mathematics and Economics, Elsevier, vol. 5(4), pages 279-283, October.
    4. J David Cummins, 2005. "Convergence in Wholesale Financial Services: Reinsurance and Investment Banking," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan;The Geneva Association, vol. 30(2), pages 187-222, April.
    5. Jansen, K. & Haezendonck, J. & Goovaerts, M. J., 1986. "Upper bounds on stop-loss premiums in case of known moments up to the fourth order," Insurance: Mathematics and Economics, Elsevier, vol. 5(4), pages 315-334, October.
    6. Møller, T., 2002. "On Valuation and Risk Management at the Interface of Insurance and Finance," British Actuarial Journal, Cambridge University Press, vol. 8(4), pages 787-827, October.
    7. Jaimungal, Sebastian & Wang, Tao, 2006. "Catastrophe options with stochastic interest rates and compound Poisson losses," Insurance: Mathematics and Economics, Elsevier, vol. 38(3), pages 469-483, June.
    8. Hobson, David & Laurence, Peter & Wang, Tai-Ho, 2005. "Static-arbitrage optimal subreplicating strategies for basket options," Insurance: Mathematics and Economics, Elsevier, vol. 37(3), pages 553-572, December.
    9. 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.
    10. Phelim Boyle & Brian Ding, 2005. "Portfolio Selection with Skewness," Springer Books, in: Michèle Breton & Hatem Ben-Ameur (ed.), Numerical Methods in Finance, chapter 0, pages 227-240, Springer.
    11. Hiroshi Konno & Hiroaki Yamazaki, 1991. "Mean-Absolute Deviation Portfolio Optimization Model and Its Applications to Tokyo Stock Market," Management Science, INFORMS, vol. 37(5), pages 519-531, May.
    12. Dimitris Bertsimas & Ioana Popescu, 2002. "On the Relation Between Option and Stock Prices: A Convex Optimization Approach," Operations Research, INFORMS, vol. 50(2), pages 358-374, April.
    13. Javier Pena & Juan Vera & Luis Zuluaga, 2010. "Static-arbitrage lower bounds on the prices of basket options via linear programming," Quantitative Finance, Taylor & Francis Journals, vol. 10(8), pages 819-827.
    14. Schepper, Ann De & Heijnen, Bart, 2007. "Distribution-free option pricing," Insurance: Mathematics and Economics, Elsevier, vol. 40(2), pages 179-199, March.
    15. Lo, Andrew W., 1987. "Semi-parametric upper bounds for option prices and expected payoffs," Journal of Financial Economics, Elsevier, vol. 19(2), pages 373-387, December.
    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. 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.
    2. Yin-Yee Leong & Yen-Chih Chen, 0. "Cyber risk cost and management in IoT devices-linked health insurance," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan;The Geneva Association, vol. 0, pages 1-23.
    3. Yin-Yee Leong & Yen-Chih Chen, 2020. "Cyber risk cost and management in IoT devices-linked health insurance," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan;The Geneva Association, vol. 45(4), pages 737-759, October.
    4. Qiaoming Han & Donglei Du & Luis F. Zuluaga, 2014. "Technical Note---A Risk- and Ambiguity-Averse Extension of the Max-Min Newsvendor Order Formula," Operations Research, INFORMS, vol. 62(3), pages 535-542, June.
    5. Christian Biener & Martin Eling, 2013. "Recent Research Developments Affecting Nonlife Insurance—The CAS Risk Premium Project 2012 Update," Risk Management and Insurance Review, American Risk and Insurance Association, vol. 16(2), pages 219-231, September.
    6. Hanbali, Hamza & Dhaene, Jan & Linders, Daniël, 2022. "Dependence bounds for the difference of stop-loss payoffs on the difference of two random variables," Insurance: Mathematics and Economics, Elsevier, vol. 107(C), pages 22-37.

    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. Zuluaga, Luis F. & Peña, Javier & Du, Donglei, 2009. "Third-order extensions of Lo's semiparametric bound for European call options," European Journal of Operational Research, Elsevier, vol. 198(2), pages 557-570, October.
    2. Robert Howley & Robert Storer & Juan Vera & Luis F. Zuluaga, 2016. "Computing semiparametric bounds on the expected payments of insurance instruments via column generation," Papers 1601.02149, arXiv.org.
    3. 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.
    4. van Eekelen, Wouter, 2023. "Distributionally robust views on queues and related stochastic models," Other publications TiSEM 9b99fc05-9d68-48eb-ae8c-9, Tilburg University, School of Economics and Management.
    5. Derek Singh & Shuzhong Zhang, 2020. "Tight Bounds for a Class of Data-Driven Distributionally Robust Risk Measures," Papers 2010.05398, arXiv.org, revised Oct 2020.
    6. Evangelia Dragazi & Shuaiqiang Liu & Antonis Papapantoleon, 2024. "Improved model-free bounds for multi-asset options using option-implied information and deep learning," Papers 2404.02343, arXiv.org.
    7. Giuricich, Mario Nicoló & Burnecki, Krzysztof, 2019. "Modelling of left-truncated heavy-tailed data with application to catastrophe bond pricing," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 498-513.
    8. Peña, Javier & Vera, Juan C. & Zuluaga, Luis F., 2012. "Computing arbitrage upper bounds on basket options in the presence of bid–ask spreads," European Journal of Operational Research, Elsevier, vol. 222(2), pages 369-376.
    9. Kirschner, Felix, 2023. "Conic optimization with applications in finance and approximation theory," Other publications TiSEM e9bef4a5-ee46-45be-90d7-9, Tilburg University, School of Economics and Management.
    10. 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.
    11. Karthik Natarajan & Melvyn Sim & Joline Uichanco, 2018. "Asymmetry and Ambiguity in Newsvendor Models," Management Science, INFORMS, vol. 64(7), pages 3146-3167, July.
    12. J. A. Primbs, 2010. "SDP Relaxation of Arbitrage Pricing Bounds Based on Option Prices and Moments," Journal of Optimization Theory and Applications, Springer, vol. 144(1), pages 137-155, January.
    13. Ioana Popescu, 2005. "A Semidefinite Programming Approach to Optimal-Moment Bounds for Convex Classes of Distributions," Mathematics of Operations Research, INFORMS, vol. 30(3), pages 632-657, August.
    14. Peter Laurence & Tai-Ho Wang, 2008. "Distribution-free upper bounds for spread options and market-implied antimonotonicity gap," The European Journal of Finance, Taylor & Francis Journals, vol. 14(8), pages 717-734.
    15. Carole Bernard & Ludger Rüschendorf & Steven Vanduffel, 2017. "Value-at-Risk Bounds With Variance Constraints," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 84(3), pages 923-959, September.
    16. Braun, Alexander, 2011. "Pricing catastrophe swaps: A contingent claims approach," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 520-536.
    17. Georgia Perakis & Guillaume Roels, 2008. "Regret in the Newsvendor Model with Partial Information," Operations Research, INFORMS, vol. 56(1), pages 188-203, February.
    18. 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.
    19. Javier Pena & Juan Vera & Luis Zuluaga, 2010. "Static-arbitrage lower bounds on the prices of basket options via linear programming," Quantitative Finance, Taylor & Francis Journals, vol. 10(8), pages 819-827.
    20. Viet Anh Nguyen & Fan Zhang & Shanshan Wang & Jose Blanchet & Erick Delage & Yinyu Ye, 2021. "Robustifying Conditional Portfolio Decisions via Optimal Transport," Papers 2103.16451, arXiv.org, revised Apr 2024.

    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:51:y:2012:i:2:p:271-281. 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.