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The numeraire portfolio: a new perspective on financial theory

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  • I. Bajeux-Besnainou
  • R. Portait

Abstract

The numeraire portfolio, also called the optimal growth portfolio, allows simple derivations of the main results of financial theory. The prices of self financing portfolios, when the optimal growth portfolio is the numeraire, are martingales in the 'true' (historical) probability. Given the dynamics of the traded securities, the composition of the numeraire portfolio as well as its value are easily computable. Among its numerous properties, the numeraire portfolio is instantaneously mean variance efficient. This key feature allows a simple derivation of standard continuous time CAPM, CCAPM, APT and contingent claim pricing. Moreover, since the Radon-Nikodym derivatives of the usual martingale measures are very simple functions of the numeraire portfolio, the latter provides a convenient link between the standard Capital Market Theory a la Merton and the probabilistic approach a la Harrison-Kreps-Pliska.

Suggested Citation

  • I. Bajeux-Besnainou & R. Portait, 1997. "The numeraire portfolio: a new perspective on financial theory," The European Journal of Finance, Taylor & Francis Journals, vol. 3(4), pages 291-309.
    • Handle: RePEc:taf:eurjfi:v:3:y:1997:i:4:p:291-309
    DOI: 10.1080/135184797337381
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    Cited by:

    1. Nicola Bruti-Liberati & Christina Nikitopoulos-Sklibosios & Eckhard Platen, 2010. "Real-world jump-diffusion term structure models," Quantitative Finance, Taylor & Francis Journals, vol. 10(1), pages 23-37.
    2. Morten Christensen & Eckhard Platen, 2004. "A General Benchmark Model for Stochastic Jump Sizes," Research Paper Series 139, Quantitative Finance Research Centre, University of Technology, Sydney.
    3. Lioui, Abraham & Poncet, Patrice, 2003. "Dynamic asset pricing with non-redundant forwards," Journal of Economic Dynamics and Control, Elsevier, vol. 27(7), pages 1163-1180, May.
    4. Dean Buckner & Kevin Dowd & Hardy Hulley, 2022. "Arbitrage Problems with Reflected Geometric Brownian Motion," Papers 2201.05312, arXiv.org, revised Sep 2022.
    5. Eckhard Platen & Jason West, 2004. "A Fair Pricing Approach to Weather Derivatives," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 11(1), pages 23-53, March.
    6. Hardy Hulley & Shane Miller & Eckhard Platen, 2005. "Benchmarking and Fair Pricing Applied to Two Market Models," Research Paper Series 155, Quantitative Finance Research Centre, University of Technology, Sydney.
    7. Ralf Korn & Frank Oertel & Manfred Schäl, 2003. "Notes and Comments: The numeraire portfolio in financial markets modeled by a multi-dimensional jump diffusion process," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 26(2), pages 153-166, November.
    8. Eckhard Platen, 2003. "Pricing and Hedging for Incomplete Jump Diffusion Benchmark Models," Research Paper Series 110, Quantitative Finance Research Centre, University of Technology, Sydney.
    9. Eckhard Platen, 2006. "On the Pricing and Hedging of Long Dated Zero Coupon Bonds," Research Paper Series 185, Quantitative Finance Research Centre, University of Technology, Sydney.
    10. Eckhard Platen & Renata Rendek, 2012. "Approximating the numéraire portfolio by naive diversification," Journal of Asset Management, Palgrave Macmillan, vol. 13(1), pages 34-50, February.
    11. Shunlong Luo & Jia-an Yan & Qiang Zhang, 2001. "Arbitrage Pricing Systems in a Market Driven by an Itô Process," World Scientific Book Chapters, in: Jiongmin Yong (ed.), Recent Developments In Mathematical Finance, chapter 22, pages 263-271, World Scientific Publishing Co. Pte. Ltd..
    12. Eckhard Platen, 2004. "Diversified Portfolios with Jumps in a Benchmark Framework," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 11(1), pages 1-22, March.
    13. Eckhard Platen, 2011. "A Benchmark Approach to Investing and Pricing," World Scientific Book Chapters, in: Leonard C MacLean & Edward O Thorp & William T Ziemba (ed.), THE KELLY CAPITAL GROWTH INVESTMENT CRITERION THEORY and PRACTICE, chapter 28, pages 409-426, World Scientific Publishing Co. Pte. Ltd..
    14. Eckhard Platen, 2009. "Real World Pricing of Long Term Contracts," Research Paper Series 262, Quantitative Finance Research Centre, University of Technology, Sydney.
    15. Kevin Fergusson & Eckhard Platen, 2017. "Less-Expensive Valuation of Long Term Annuities Linked to Mortality, Cash and Equity," Papers 1711.02808, arXiv.org.
    16. Sami Attaoui & Vincent Lacoste, 2013. "A scenario-based description of optimal American capital guaranteed strategies," Finance, Presses universitaires de Grenoble, vol. 34(2), pages 65-119.
    17. Nguyen, Pascal & Portait, Roland, 2002. "Dynamic asset allocation with mean variance preferences and a solvency constraint," Journal of Economic Dynamics and Control, Elsevier, vol. 26(1), pages 11-32, January.
    18. Eckhard Platen & Wolfgang Runggaldier, 2004. "A Benchmark Approach to Filtering in Finance," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 11(1), pages 79-105, March.
    19. Araújo, Fabio & Issler, João Victor & Fernandes, Marcelo, 2006. "A stochastic discount factor approach to asset pricing using panel data," FGV EPGE Economics Working Papers (Ensaios Economicos da EPGE) 628, EPGE Brazilian School of Economics and Finance - FGV EPGE (Brazil).
    20. Eckhard Platen, 2006. "A Benchmark Approach To Finance," Mathematical Finance, Wiley Blackwell, vol. 16(1), pages 131-151, January.
    21. Eckhard Platen & Jason West & Wolfgang Breymann, 2004. "An Intraday Empirical Analysis of Electricity Price Behaviour," Research Paper Series 140, Quantitative Finance Research Centre, University of Technology, Sydney.
    22. Hans Buhlmann & Eckhard Platen, 2002. "A Discrete Time Benchmark Approach for Finance and Insurance," Research Paper Series 74, Quantitative Finance Research Centre, University of Technology, Sydney.
    23. Hardy Hulley, 2009. "Strict Local Martingales in Continuous Financial Market Models," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 19, July-Dece.
    24. Eckhard Platen, 2004. "Capital Asset Pricing for Markets with Intensity Based Jumps," Research Paper Series 143, Quantitative Finance Research Centre, University of Technology, Sydney.
    25. Hardy Hulley, 2009. "Strict Local Martingales in Continuous Financial Market Models," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 2-2009.

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