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MARKET VALUE MARGIN VIA MEAN–VARIANCE HEDGING

  • Andreas Tsanakas (a1), Mario V. Wüthrich (a2) and Aleš Černý (a3)
Abstract

We use mean–variance hedging in discrete time in order to value an insurance liability. The prediction of the insurance liability is decomposed into claims development results, that is, yearly deteriorations in its conditional expected values until the liability is finally settled. We assume the existence of a tradeable derivative with binary pay-off written on the claims development result and available in each development period. General valuation formulas are stated and, under additional assumptions, these valuation formulas simplify to resemble familiar regulatory cost-of-capital-based formulas. However, adoption of the mean–variance framework improves upon the regulatory approach by allowing for potential calibration to observed market prices, inclusion of other tradeable assets, and consistent extension to multiple periods. Furthermore, it is shown that the hedging strategy can also lead to increased capital efficiency.

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E-Mail: a.tsanakas.1@city.ac.uk
References
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[1]Černý, A. (2009) Mathematical Techniques in Finance. Princeton: Princeton University Press.
[2]Černý, A. and Kallsen, J. (2007) On the structure of general mean-variance hedging strategies. Annals of Probability, 35 (4), 14791531.
[3]Černý, A. and Kallsen, J. (2009) Hedging by sequential regression revisited. Mathematical Finance, 19 (4), 591617.
[4]Cummins, J.D. (2008) CAT bonds and other risk-linked securities: State of the market and recent developments. Risk Management and Insurance Review, 11 (1), 2347.
[5]Dahl, M., Møller, T. (2006) Valuation and hedging of life insurance liabilities with systematic mortality risk. Insurance: Mathematics and Economics, 39 (2), 193217.
[6]Denuit, M., Dhaene, J., Goovaerts, M. and Kaas, R. (2005) Actuarial Theory for Dependent Risks: Measures, Orders and Models. England: Wiley.
[7]Delong, Ł. (2012) No-good-deal, local mean-variance and ambiguity risk pricing and hedging for an insurance payment process. ASTIN Bulletin, 42 (1), 203232.
[8]Delong, Ł. and Gerrard, R. (2007) Mean-variance portfolio selection for a non-life insurance company. Mathematical Methods of Operations Research, 66, 339367.
[9]Doherty, N.A. (1997) Innovations in managing catastrophe risk. Journal of Risk and Insurance, 64 (4), 713718.
[10]European Commission (2010) QIS 5 Technical Specifications, Annex to Call for Advice from CEIOPS on QIS5.
[11]Föllmer, H. and Schweizer, M. (1988) Hedging by sequential regression: An introduction to the mathematics of option trading. ASTIN Bulletin, 18 (2), 147160.
[12]Haslip, G.G. and Kaishev, V. K. (2010) Pricing of reinsurance contracts in the presence of catastrophe bonds. ASTIN Bulletin, 40 (1), 307329.
[13]McNeil, A.J., Frey, R. and Embrechts, P. (2005) Quantitative Risk Management: Concepts, Techniques and Tools. Princeton: Princeton University Press.
[14]Merz, M. and Wüthrich, M.V. (2008) Modelling the claims development result for solvency purposes. Casualty Actuarial Society E-Forum, Fall 2008, 542568.
[15]Merz, M., Wüthrich, M.V. and Hashorva, E. (2013) Dependence modeling in multivariate claims run-off triangles. Annals of Actuarial Science, 7 (1), 325.
[16]Möhr, C. (2011) Market-consistent valuation of insurance liabilities by cost of capital. ASTIN Bulletin, 41 (2), 315341.
[17]Møller, T. (1998) Risk-minimizing hedging strategies for unit-linked life insurance contracts. ASTIN Bulletin, 28 (1), 1747.
[18]Møller, T. (2001) Risk-minimizing hedging strategies for insurance payment processes. Finance and Stochastics, 5 (4), 419446.
[19]Papachristou, D. (2011) Statistical analysis of the spreads of catastrophe bonds at the time of issue. ASTIN Bulletin, 41 (1), 251277.
[20]Salzmann, R. and Wüthrich, M.V. (2010) Cost-of-capital margin for a general insurance liability runoff. ASTIN Bulletin, 40 (2), 415451.
[21]Schweizer, M. (2001) A guided tour through quadratic hedging approaches. In Option Pricing, Interest Rates and Risk Management (eds. Jouini, E., Cvitanić, J. and Musiela, M.), pp. 538574. Cambridge, UK: Cambridge University Press.
[22]Schweizer, M. (2001) From actuarial to financial valuation principles. Insurance: Mathematics and Economics, 28 (1), 3147.
[23]Swiss Solvency Test (2006) FINMA SST Technisches Dokument, Version 2. October 2006.
[24]Thomson, R.J. (2005) The pricing of liabilities in an incomplete market using dynamic mean-variance hedging. Insurance: Mathematics and Economics, 36 (3), 441455.
[25]Venter, G.G. (2004) Capital allocation survey with commentary. North American Actuarial Journal, 8 (2), 96107.
[26]Wüthrich, M.V., Merz, M. (2013) Financial Modeling, Actuarial Valuation and Solvency in Insurance. Berlin: Springer.
[27]Zanjani, G. (2002) Pricing and capital allocation in catastrophe insurance. Journal of Financial Economics, 65, 283305.
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ASTIN Bulletin: The Journal of the IAA
  • ISSN: 0515-0361
  • EISSN: 1783-1350
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