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MARKET VALUE MARGIN VIA MEAN–VARIANCE HEDGING

Published online by Cambridge University Press:  18 July 2013

Andreas Tsanakas ,
Mario V. Wüthrich  and
Aleš Černý
Andreas Tsanakas*
Affiliation:
Cass Business School, City University London, 106 Bunhill Row, London EC1Y 8TZ, UK
Mario V. Wüthrich
Affiliation:
Department of Mathematics, ETH Zurich, RiskLab, 8092 Zurich, Switzerland
Aleš Černý
Affiliation:
Cass Business School, City University London, 106 Bunhill Row, London EC1Y 8TZ, UK
*
E-Mail: a.tsanakas.1@city.ac.uk
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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.

Keywords

Market value marginmean–variance hedgingmarket consistent valuationcost-of-capitalSolvency II
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 43 , Issue 3 , September 2013 , pp. 301 - 322
Copyright
Copyright © ASTIN Bulletin 2013 

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References

[1]Černý, A. (2009) Mathematical Techniques in Finance. Princeton: Princeton University Press.CrossRefGoogle Scholar
[2]Černý, A. and Kallsen, J. (2007) On the structure of general mean-variance hedging strategies. Annals of Probability, 35 (4), 1479–1531.CrossRefGoogle Scholar
[3]Černý, A. and Kallsen, J. (2009) Hedging by sequential regression revisited. Mathematical Finance, 19 (4), 591–617.CrossRefGoogle Scholar
[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), 23–47.CrossRefGoogle Scholar
[5]Dahl, M., Møller, T. (2006) Valuation and hedging of life insurance liabilities with systematic mortality risk. Insurance: Mathematics and Economics, 39 (2), 193–217.Google Scholar
[6]Denuit, M., Dhaene, J., Goovaerts, M. and Kaas, R. (2005) Actuarial Theory for Dependent Risks: Measures, Orders and Models. England: Wiley.CrossRefGoogle Scholar
[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), 203–232.Google Scholar
[8]Delong, Ł. and Gerrard, R. (2007) Mean-variance portfolio selection for a non-life insurance company. Mathematical Methods of Operations Research, 66, 339–367.CrossRefGoogle Scholar
[9]Doherty, N.A. (1997) Innovations in managing catastrophe risk. Journal of Risk and Insurance, 64 (4), 713–718.CrossRefGoogle Scholar
[10]European Commission (2010) QIS 5 Technical Specifications, Annex to Call for Advice from CEIOPS on QIS5.Google Scholar
[11]Föllmer, H. and Schweizer, M. (1988) Hedging by sequential regression: An introduction to the mathematics of option trading. ASTIN Bulletin, 18 (2), 147–160.CrossRefGoogle Scholar
[12]Haslip, G.G. and Kaishev, V. K. (2010) Pricing of reinsurance contracts in the presence of catastrophe bonds. ASTIN Bulletin, 40 (1), 307–329.CrossRefGoogle Scholar
[13]McNeil, A.J., Frey, R. and Embrechts, P. (2005) Quantitative Risk Management: Concepts, Techniques and Tools. Princeton: Princeton University Press.Google Scholar
[14]Merz, M. and Wüthrich, M.V. (2008) Modelling the claims development result for solvency purposes. Casualty Actuarial Society E-Forum, Fall 2008, 542–568.Google Scholar
[15]Merz, M., Wüthrich, M.V. and Hashorva, E. (2013) Dependence modeling in multivariate claims run-off triangles. Annals of Actuarial Science, 7 (1), 3–25.CrossRefGoogle Scholar
[16]Möhr, C. (2011) Market-consistent valuation of insurance liabilities by cost of capital. ASTIN Bulletin, 41 (2), 315–341.Google Scholar
[17]Møller, T. (1998) Risk-minimizing hedging strategies for unit-linked life insurance contracts. ASTIN Bulletin, 28 (1), 17–47.CrossRefGoogle Scholar
[18]Møller, T. (2001) Risk-minimizing hedging strategies for insurance payment processes. Finance and Stochastics, 5 (4), 419–446.Google Scholar
[19]Papachristou, D. (2011) Statistical analysis of the spreads of catastrophe bonds at the time of issue. ASTIN Bulletin, 41 (1), 251–277.Google Scholar
[20]Salzmann, R. and Wüthrich, M.V. (2010) Cost-of-capital margin for a general insurance liability runoff. ASTIN Bulletin, 40 (2), 415–451.Google Scholar
[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. 538–574. Cambridge, UK: Cambridge University Press.CrossRefGoogle Scholar
[22]Schweizer, M. (2001) From actuarial to financial valuation principles. Insurance: Mathematics and Economics, 28 (1), 31–47.Google Scholar
[23]Swiss Solvency Test (2006) FINMA SST Technisches Dokument, Version 2. October 2006.Google Scholar
[24]Thomson, R.J. (2005) The pricing of liabilities in an incomplete market using dynamic mean-variance hedging. Insurance: Mathematics and Economics, 36 (3), 441–455.Google Scholar
[25]Venter, G.G. (2004) Capital allocation survey with commentary. North American Actuarial Journal, 8 (2), 96–107.CrossRefGoogle Scholar
[26]Wüthrich, M.V., Merz, M. (2013) Financial Modeling, Actuarial Valuation and Solvency in Insurance. Berlin: Springer.CrossRefGoogle Scholar
[27]Zanjani, G. (2002) Pricing and capital allocation in catastrophe insurance. Journal of Financial Economics, 65, 283–305.CrossRefGoogle Scholar