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Valuation of pension liabilities in incomplete markets*

Published online by Cambridge University Press:  23 May 2008

FRANK DE JONG
FRANK DE JONG*
Affiliation:
Tilburg University and Netspar
*
Correspondence address: Department of Finance, Tilburg University, P.O. Box 90153, 5000 LE Tilburg, the Netherlands. E-mail: [email protected].
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Abstract

This paper discusses the valuation of wage-indexed pension liabilities. Valuation of these contingent claims by replication is typically not possible as the wage index cannot be hedged perfectly with financial market instruments. This paper discusses several methods to find a value in such incomplete markets and advocates utility-based valuation. This approach implies a simple adjustment on the discount factor.

Type
Articles
Information
Journal of Pension Economics & Finance , Volume 7 , Issue 3 , November 2008 , pp. 277 - 294
Copyright
Copyright © 2008 Cambridge University Press

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Footnotes

*

Thanks to Lans Bovenberg, Ralph Koijen, Vicky Henderson, Roger Laeven, Antoon Pelsser, Peter Schotman and participants at the University of Warwick Pensions and Long Term Investment conference (March 2007) and the Integrated Risk Management conference at Tilburg University (April 2007) for useful discussions and comments on earlier versions.

References

Benzoni, Luca, Collin-Dufresne, Pierre, and Goldstein, S. Robert (2007) Portfolio choice over the life-cycle when the stock and labor markets are cointegrated. Journal of Finance, 62: 2123–67.CrossRefGoogle Scholar
Black, Fisher and Scholes, Myron (1973) The pricing of options and corporate liabilities. Journal of Political Economy, 81: 637–59.CrossRefGoogle Scholar
Bodie, Zvi, Merton, C. Robert, and Samuelson, F. William (1992) Labor supply flexibility and portfolio choice in a life cycle model. Journal of Economic Dynamics and Control, 16: 427–49.CrossRefGoogle Scholar
Brennan, Michael J. and Xia, Yihong (2002) Dynamic asset allocation under inflation. Journal of Finance, 57: 1201–38.CrossRefGoogle Scholar
Campbell, John Y., Lo, Andrew, and Craig MacKinlay, A. (1997) The Econometrics of Financial Markets. Princeton, NJ: Princeton University Press.CrossRefGoogle Scholar
Campbell, John Y. and Viceira, Luis (2005) The term structure of the risk-return tradeoff. Financial Analysts Journal, 61(1).CrossRefGoogle Scholar
Chen, An, Pelsser, Antoon, and Vellekoop, Michel (2007) Approximate solutions for indifference pricing with general utility functions. Working paper, University of Amsterdam.Google Scholar
Cochrane, John H. (2001) Asset Pricing. Princeton, NJ: Princeton University Press.Google Scholar
Cochrane, John H. and Saá-Requejo, Jesus (2000) Beyond arbitrage. Journal of Political Economy, 108: 79–119.CrossRefGoogle Scholar
Cox, John C., and Huang, Chi-fu (1989) Optimal consumption and portfolio policies when asset prices follow a diffusion process. Journal of Economic Theory, XXXIX: 33–83.CrossRefGoogle Scholar
Cvitanic, Jasak, Pham, Huyen, and Touzi, Nizar (1998) A closed form solution to the problem of super-replication under transaction costs. Finance and Stochastics, 3: 35–54.Google Scholar
Cvitanic, Jasak, Pham, Huyen, and Touzi, Nizar (1999) Super-replication in stochastic volatility models under portfolio constraints. Journal of Applied Probability, 36: 523–45.CrossRefGoogle Scholar
De Jong, Frank (2008). Pension fund investments and the valuation of liabilities under conditional indexation. Insurance: Mathematics and Economics, 42: 1–13.Google Scholar
De Jong, Frank, Driessen, Joost, and Van Hemert, Otto (2007) Hedging house price risk: portfolio choice with housing futures. Working paper, University of Amsterdam.CrossRefGoogle Scholar
Duffie, Darrel (1996) Dynamic Asset Pricing Theory. Second edition, Princeton, NJ: Princeton University Press.Google Scholar
Fama, Eugene F. and French, R. Kenneth (2002) The equity premium. Journal of Finance, 57(2): 637–59.CrossRefGoogle Scholar
He, Hua and Pearson, D. Neil (1991) Consumption and portfolio choices with incomplete markets and short-sale constraints: the infinite dimensional case. Journal of Economic Theory, 54: 259–304.CrossRefGoogle Scholar
Heaton, John and Lucas, Deborah (2000) Portfolio choice in the presence of background risk. Economic Journal, 110: 1–26.CrossRefGoogle Scholar
Henderson, Vicky (2002) Valuation of claims on nontraded assets using utility maximization. Mathematical Finance, 12: 351–73.CrossRefGoogle Scholar
Henderson, Vicky (2005) Explicit solutions to an optimal portfolio choice problem with stochastic income. Journal of Economic Dynamics and Control, 29: 1237–66.CrossRefGoogle Scholar
Henderson, Vicky, and Hobson, David (2004) Utility indifference pricing – an overview. In Carmond, R. (ed.), Volume on Indifference Pricing. Princeton University Press.Google Scholar
Hodges, Stewart and Neuberger, Anthony (1989) Optimal replication of contingent claims under transaction costs. Review of Futures Markets, 8: 222–39.Google Scholar
Hoevenaars, Roy, Molenaar, Roderick, Schotman, Peter, and Steenkamp, Tom (2007) Strategic asset allocation with liabilities: beyond stocks and bonds. Working paper ABP Investments.CrossRefGoogle Scholar
Koijen, Ralph, Nijman, Theo, and Werker, Bas (2005) Labor income and the demand for long-term bonds. Netspar Discussion paper 2005-D020.Google Scholar
Munk, Claus and Sørensen, Carsten (2007) Dynamic asset allocation with stochastic income and interest rates. Working paper Copenhagen Business School.Google Scholar
Pliska, Stanley R. (1997) Introduction to Mathematical Finance: Discrete Time Models. Oxford: Blackwell Publishers.Google Scholar
Roorda, Berend, Schumacher, Hans, and Engwerda, Jacob (2005) Coherent applicability measures in multiperiod models. Mathematical Finance, 15: 589–612.CrossRefGoogle Scholar
Sangvinatsos, A. and Wachter, Jessica (2005) Does the failure of the expectations hypothesis matter for long-term investors? Journal of Finance, 60: 179–230.CrossRefGoogle Scholar
Svensson, Lars E. O. and Werner, Ingrid (1993) Nontraded assets in incomplete markets. European Economic Review, 37: 1149–61.CrossRefGoogle Scholar
Vasicek, Oldrich (1977) An equilibrium characterization of the term structure. Journal of Financial Economics, 5: 177–88.CrossRefGoogle Scholar