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GUARANTEE VALUATION IN NOTIONAL DEFINED CONTRIBUTION PENSION SYSTEMS

Published online by Cambridge University Press:  05 August 2016

Jennifer Alonso-García  and
Pierre Devolder
Jennifer Alonso-García*
Affiliation:
ARC Centre of Excellence in Population Ageing Research (CEPAR), School of Risk and Actuarial Studies, UNSW Business School, Level 3, East Wing, 223 Anzac Parade, Kensington NSW 2033, Australia
Pierre Devolder
Affiliation:
Faculty of Sciences, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA), Université Catholique de Louvain, Belgium E-Mail: pierre.devolder@uclouvain.be
*
E-Mail: j.alonsogarcia@unsw.edu.au
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Abstract

The notional defined contribution pension scheme combines pay-as-you-go financing and a defined contribution pension formula. The return on contributions is based on an index set by law, such as the growth rate of GDP, average wages or contribution payments. The volatility of this return compromises the system's pension adequacy and therefore guarantees may be needed. Here, we provide a minimum return guarantee to the pension contributions. The price is calculated in a utility indifference framework. We obtain a closed-form solution for a general dependence structure with exponential preferences and in presence of stochastic short interest rates.

Keywords

Public pensionpay-as-you-gooption pricingincomplete marketsexponential utility

Information

Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 46 , Issue 3 , September 2016 , pp. 677 - 707
Copyright
Copyright © Astin Bulletin 2016 

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References

Amin, K.I. and Jarrow, R.A. (1992) Pricing options on risky assets in a stochastic interest rate economy1. Mathematical Finance, 2, 217–237.CrossRefGoogle Scholar
Artzner, P., Delbaen, F., Eber, J.-M. and Heath, D. (1999) Coherent measures of risk. Mathematical Finance, 9, 203–228.CrossRefGoogle Scholar
Björk, T. (2004) Arbitrage Theory in Continuous Time. Oxford University Press.CrossRefGoogle Scholar
Black, F. and Scholes, M. (1973) The pricing of options and corporate liabilities. Journal of Political Economy, 81, 637–654.CrossRefGoogle Scholar
Börsch-Supan, A. (2006) What are NDC systems? What do they bring to reform strategies? In Pension Reform: Issues and Prospects for Notional Defined Contribution (NDC) Schemes (eds. Holzmann, R. and Palmer, E.), pp. 35–57. Washington, D.C.: The World Bank, chap. 3.Google Scholar
Boulier, J.-F., Huang, S. and Taillard, G. (2001) Optimal management under stochastic interest rates: The case of a protected defined contribution pension fund. Insurance: Mathematics and Economics, 28, 173–189.Google Scholar
Boyle, P.P. and Schwartz, E.S. (1977) Equilibrium prices of guarantees under equity-linked contracts. Journal of Risk and Insurance, 639–660.CrossRefGoogle Scholar
Brennan, M.J. and Schwartz, E.S. (1976) The pricing of equity-linked life insurance policies with an asset value guarantee. Journal of Financial Economics, 3, 195–213.CrossRefGoogle Scholar
Brigo, D. and Mercurio, F. (2007) Interest Rate Models - Theory and Practice: With Smile, Inflation and Credit 2nd ed. Berlin Heidelberg: Springer-Verlag.Google Scholar
Brunello, G. (2009) The effects of cohort size on European earnings. Journal of Population Economics, 23, 273–290.CrossRefGoogle Scholar
Campbell, J.Y. and Viceira, L.M. (2002) Strategic Asset Allocation: Portfolio Choice for Long-Term Investors. Oxford University Press.CrossRefGoogle Scholar
Cochrane, J.H. and Saá-Requejo, J. (2000) Beyond arbitrage: Good-deal asset price bounds in incomplete markets. The Journal of Political Economy, 108, 79–119.CrossRefGoogle Scholar
Cvitanic, J., Pham, H. and Touzi, N. (1999) A closed-form solution to the problem of super-replication under transaction costs. Finance and Stochastics, 3, 35–54.Google Scholar
De Menil, G., Murtin, F. and Sheshinski, E. (2006) Planning for the optimal mix of paygo tax and funded savings. Journal of Pension Economics and Finance, 5, 1–25.CrossRefGoogle Scholar
Denuit, M. (1999) The exponential premium calculation principle revisited. ASTIN Bulletin, 29, 215–226.CrossRefGoogle Scholar
Devolder, P. and Melis, R. (2015) Optimal mix between pay as you go and funding for pension liabilities in a stochastic framework. ASTIN Bulletin, 45, 551–575.CrossRefGoogle Scholar
Estrella, A. and Mishkin, F.S. (1998) Predicting US recessions: Financial variables as leading indicators. Review of Economics and Statistics, 80, 45–61.CrossRefGoogle Scholar
Floroiu, O. and Pelsser, A. (2013) Closed-form solutions for options in incomplete markets. Netspar Discussion Paper, no. 02/2013-004.CrossRefGoogle Scholar
Follmer, H. and Schweizer, M. (1991) Hedging of contingent claims under incomplete information. In Applied Stochastic Analysis (eds. Davis, M.H.A. and Elliott, R.J.), pp. 389–414. Amsterdam: Gordon and Breach Science Publishers.Google Scholar
Frittelli, M. (2000) The minimal entropy martingale measure and the valuation problem in incomplete markets. Mathematical Finance, 10, 39–52.CrossRefGoogle Scholar
Heath, D., Jarrow, R., Morton, A., (1992) Bond pricing and the term structure of interest rates: A new methodology for contingent claims valuation. Econometrica, 60, 77–105.CrossRefGoogle Scholar
Henderson, V. (2002) Valuation of claims on nontraded assets using utility maximization. Mathematical Finance, 12, 351–373.CrossRefGoogle Scholar
Hodges, S. and Neuberger, A. (1989) Optimal replication of contingent claims under transaction costs. Review of Futures Markets, 8, 222–239.Google Scholar
Holzmann, R. and Palmer, E. (2006) The status of NDC discussion: Introduction and overview. In Pension Reform: Issues and Prospects for Non-Financial Defined Contribution (NDC) Schemes (eds. Holzmann, R. and Palmer, E.), pp. 1–16. Washington, D.C.: The World Bank, chap. 1.CrossRefGoogle Scholar
Knell, M. (2010) The optimal mix between funded and unfunded pension systems when people care about relative consumption. Economica, 77, 710–733.CrossRefGoogle Scholar
Korn, R. and Kraft, H. (2002) A stochastic control approach to portfolio problems with stochastic interest rates. SIAM Journal on Control and Optimization, 40, 1250–1269.CrossRefGoogle Scholar
Matsen, E. and Thøgersen, Ø. (2004) Designing social security - A portfolio choice approach. European Economic Review, 48, 883–904.CrossRefGoogle Scholar
Merton, R.C. (1973) Theory of rational option pricing. The Bell Journal of Economics and Management Science, 4, 141–183.CrossRefGoogle Scholar
Miao, J. and Wang, N. (2007) Investment, consumption, and hedging under incomplete markets. Journal of Financial Economics, 86, 608–642.CrossRefGoogle Scholar
Miyahara, Y. (1996) Canonical martingale measures of incomplete assets markets. In Probability Theory and Mathematical Statistics (Tokyo, 1995), pp. 343–352.Google Scholar
Musiela, M. and Zariphopoulou, T. (2004) An example of indifference prices under exponential preferences. Finance and Stochastics, 8, 229–239.CrossRefGoogle Scholar
Næs, R., Skjeltorp, J.A. and Ødegaard, B.A. (2011) Stock market liquidity and the business cycle. The Journal of Finance, 66, 139–176.CrossRefGoogle Scholar
OECD (2013) Private pensions and public pension reserves. In Pensions at a Glance 2013: OECD and G20 Indicators (ed. OECD), pp. 187–204. OECD Publishing, chap. 8.Google Scholar
Palmer, E. (2006) What's NDC? In Pension Reform: Issues and Prospects for Non-Financial Defined Contribution (NDC) Schemes (eds. Holzmann, R. and Palmer, E.), pp. 17–35. Washington, D.C.: The World Bank, chap. 2.Google Scholar
Pennacchi, G.G. (1999) The value of guarantees on pension fund returns. Journal of Risk and Insurance, 66, 219–237.CrossRefGoogle Scholar
Persson, M. (2002) Five fallacies in the social security debate. In Social Security Reform in Advanced Countries: Evaluating Pension Finance (eds. Ihori, T. and Tachibanaki, T.), pp. 39–51. London: Routledge Press.Google Scholar
Poterba, J.M. (2001) Demographic structure and asset returns. Review of Economics and Statistics, 83, 565–584.CrossRefGoogle Scholar
Pratt, J.W. (1964) Risk aversion in the small and in the large. Econometrica: Journal of the Econometric Society, 122–136.CrossRefGoogle Scholar
Queisser, M. (1995) Chile and beyond: The second-generation pension reforms in Latin America. International Social Security Review, 48, 23–39.CrossRefGoogle Scholar
Rouge, R. and El Karoui, N. (2000) Pricing via utility maximization and entropy. Mathematical Finance, 10, 259–276.CrossRefGoogle Scholar
Samuelson, P. (1958) An exact consumption loan model of interest with or without the social contrivance of money. Journal of Political Economy, 66, 467–482.CrossRefGoogle Scholar
Severinson, C. and Stewart, F. (2012) Review of the swedish national pension funds. OECD Working Papers on Finance, Insurance and Private Pensions, no. 17.Google Scholar
Valdés-Prieto, S. (2000) The financial stability of notional account pensions. Scandinavian Journal of Economics, 102, 395–417.CrossRefGoogle Scholar
Vasicek, O. (1977) An equilibrium characterization of the term structure. Journal of Financial Economics, 5, 177–188.CrossRefGoogle Scholar
Young, V.R. (2004) Pricing in an incomplete market with an affine term structure. Mathematical Finance, 14, 359–381.CrossRefGoogle Scholar
Zariphopoulou, T. (2001) A solution approach to valuation with unhedgeable risks. Finance and Stochastics, 5, 61–82.CrossRefGoogle Scholar