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Combining fair pricing and capital requirements for non-life insurance companies

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  • Gatzert, Nadine
  • Schmeiser, Hato

Abstract

The aim of this article is to identify fair equity-premium combinations for non-life insurers that satisfy solvency capital requirements imposed by regulatory authorities. In particular, we compare target capital derived using the value at risk concept as planned for Solvency II in the European Union with the tail value at risk concept as required by the Swiss Solvency Test. The model framework uses Merton's jump-diffusion process for the market value of liabilities and a geometric Brownian motion for the asset process; fair valuation is conducted using option pricing theory. We show that even if regulatory requirements are satisfied under different risk measures and parameterizations, the associated costs of insolvency - measured with the insurer's default put option value - can differ substantially.

Suggested Citation

  • Gatzert, Nadine & Schmeiser, Hato, 2008. "Combining fair pricing and capital requirements for non-life insurance companies," Journal of Banking & Finance, Elsevier, vol. 32(12), pages 2589-2596, December.
    • Handle: RePEc:eee:jbfina:v:32:y:2008:i:12:p:2589-2596
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    References listed on IDEAS

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    1. Nadine Gatzert & Hato Schmeiser, 2011. "On the risk situation of financial conglomerates: does diversification matter?," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 25(1), pages 3-26, March.
    2. Eckert, Christian & Gatzert, Nadine, 2017. "Modeling operational risk incorporating reputation risk: An integrated analysis for financial firms," Insurance: Mathematics and Economics, Elsevier, vol. 72(C), pages 122-137.
    3. Hato Schmeiser & Caroline Siegel & Joël Wagner, 2012. "The risk of model misspecification and its impact on solvency measurement in the insurance sector," Journal of Risk Finance, Emerald Group Publishing, vol. 13(4), pages 285-308, August.
    4. Wang, Guanying & Wang, Xingchun & Shao, Xinjian, 2022. "Exchange options for catastrophe risk management," The North American Journal of Economics and Finance, Elsevier, vol. 59(C).
    5. de Haan, Leo & Kakes, Jan, 2010. "Are non-risk based capital requirements for insurance companies binding?," Journal of Banking & Finance, Elsevier, vol. 34(7), pages 1618-1627, July.
    6. Tsai, Ming-Shann & Chen, Lien-Chuan, 2011. "The calculation of capital requirement using Extreme Value Theory," Economic Modelling, Elsevier, vol. 28(1), pages 390-395.
    7. McShane, Michael K. & Cox, Larry A. & Butler, Richard J., 2010. "Regulatory competition and forbearance: Evidence from the life insurance industry," Journal of Banking & Finance, Elsevier, vol. 34(3), pages 522-532, March.
    8. Lo, Chien-Ling & Chang, Carolyn W. & Lee, Jin-Ping & Yu, Min-Teh, 2021. "Pricing catastrophe swaps with default risk and stochastic interest rates," Pacific-Basin Finance Journal, Elsevier, vol. 68(C).
    9. Berdin, Elia & Pancaro, Cosimo & Kok Sørensen, Christoffer, 2016. "A stochastic forward-looking model to assess the profitability and solvency of European insurers," ICIR Working Paper Series 21/16, Goethe University Frankfurt, International Center for Insurance Regulation (ICIR).
    10. George Zanjani, 2010. "An Economic Approach to Capital Allocation," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 77(3), pages 523-549, September.
    11. Mao Hong & Carson James M. & Ostaszewski Krzysztof M., 2018. "Optimal Price Setting and Insurer Capital Management in a Multiple Line Context," Asia-Pacific Journal of Risk and Insurance, De Gruyter, vol. 12(1), pages 1-22, January.
    12. Buch, Arne & Dorfleitner, Gregor & Wimmer, Maximilian, 2011. "Risk capital allocation for RORAC optimization," Journal of Banking & Finance, Elsevier, vol. 35(11), pages 3001-3009, November.
    13. Jahani, Hamed & Abbasi, Babak & Alavifard, Farzad & Talluri, Srinivas, 2018. "Supply chain network redesign with demand and price uncertainty," International Journal of Production Economics, Elsevier, vol. 205(C), pages 287-312.
    14. Martin Eling, 2012. "What Do We Know About Market Discipline in Insurance?," Risk Management and Insurance Review, American Risk and Insurance Association, vol. 15(2), pages 185-223, September.
    15. Stoyanova, Rayna & Schlütter, Sebastian, 2012. "Safety versus affordability as targets of insurance regulation in an opaque market: A welfare approach," ICIR Working Paper Series 10/12, Goethe University Frankfurt, International Center for Insurance Regulation (ICIR).
    16. Schlütter, Sebastian, 2011. "The role of frictional costs for insurance pricing and insurer default risk," ICIR Working Paper Series 07/11, Goethe University Frankfurt, International Center for Insurance Regulation (ICIR).
    17. Janko Gorter & Jacob A. Bikker, 2013. "Investment risk taking by institutional investors," Applied Economics, Taylor & Francis Journals, vol. 45(33), pages 4629-4640, November.
    18. Tsai, Ming-Shann & Chen, Lien-Chuan, 2011. "The calculation of capital requirement using Extreme Value Theory," Economic Modelling, Elsevier, vol. 28(1-2), pages 390-395, January.
    19. 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.
    20. Schlütter, Sebastian, 2011. "Capital requirements or pricing constraints? An economic analysis of measures for insurance regulation," ICIR Working Paper Series 03/11, Goethe University Frankfurt, International Center for Insurance Regulation (ICIR).
    21. Gatzert, Nadine & Kellner, Ralf, 2011. "The influence of non-linear dependencies on the basis risk of industry loss warranties," Insurance: Mathematics and Economics, Elsevier, vol. 49(1), pages 132-144, July.

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