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A Unifying Approach to Asset Pricing



This paper introduces a general market modeling framework under which the Law of One Price no longer holds. A contingent claim can have in this setting several self-financing, replicating portfolios. The new Law of the Minimal Price identifies the lowest replicating price process for a given contingent claim. The proposed unifying asset pricing methodology is model independent and only requires the existence of a tradable numeraire portfolio, which turns out to be the growth optimal portfolio that maximizes expected logarithmic utility. By the Law of the Minimal Price the inverse of the numeraire portfolio becomes the stochastic discount factor. This allows pricing in extremely general settings and avoids the restrictive assumptions of risk neutral pricing. In several ways the numeraire portfolio is the “best” performing portfolio and cannot be outperformed by any other nonnegative portfolio. Several classical pricing rules are recovered under this unifying approach. The paper explains that pricing by classical no-arbitrage arguments is, in general, not unique and may lead to overpricing. In an example, a surprisingly low price of a zero coupon bond with extreme maturity illustrates one of the new effects that can be captured under the proposed benchmark approach, where the numeraire portfolio represents the benchmark.

Suggested Citation

  • Eckhard Platen, 2008. "A Unifying Approach to Asset Pricing," Research Paper Series 227, Quantitative Finance Research Centre, University of Technology, Sydney.
  • Handle: RePEc:uts:rpaper:227

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    References listed on IDEAS

    1. Eckhard Platen, 2004. "A Benchmark Framework for Risk Management," World Scientific Book Chapters,in: Stochastic Processes And Applications To Mathematical Finance, chapter 15, pages 305-335 World Scientific Publishing Co. Pte. Ltd..
    2. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters,in: Theory Of Valuation, chapter 8, pages 229-288 World Scientific Publishing Co. Pte. Ltd..
    3. Jun Liu, 2004. "Losing Money on Arbitrage: Optimal Dynamic Portfolio Choice in Markets with Arbitrage Opportunities," Review of Financial Studies, Society for Financial Studies, vol. 17(3), pages 611-641.
    4. Eckhard Platen, 2006. "A Benchmark Approach To Finance," Mathematical Finance, Wiley Blackwell, vol. 16(1), pages 131-151.
    5. Eckhard Platen, 2001. "Arbitrage in Continuous Complete Markets," Research Paper Series 72, Quantitative Finance Research Centre, University of Technology, Sydney.
    6. Truc Le & Eckhard Platen, 2006. "Approximating the Growth Optimal Portfolio with a Diversified World Stock Index," Research Paper Series 180, Quantitative Finance Research Centre, University of Technology, Sydney.
    7. Harry M. Markowitz, 2011. "Investment for the Long Run: New Evidence for an Old Rule," World Scientific Book Chapters,in: THE KELLY CAPITAL GROWTH INVESTMENT CRITERION THEORY and PRACTICE, chapter 35, pages 495-508 World Scientific Publishing Co. Pte. Ltd..
    8. Merton, Robert C, 1973. "An Intertemporal Capital Asset Pricing Model," Econometrica, Econometric Society, vol. 41(5), pages 867-887, September.
    9. Constantinos Kardaras & Eckhard Platen, 2008. "On Financial Markets where only Buy-And-Hold Trading is Possible," Research Paper Series 213, Quantitative Finance Research Centre, University of Technology, Sydney.
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    Cited by:

    1. Ceci, Claudia & Colaneri, Katia & Cretarola, Alessandra, 2014. "A benchmark approach to risk-minimization under partial information," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 129-146.

    More about this item


    law of one price; law of the minimal price; benchmark approach; derivative pricing; numeraire portfolio; asset pricing; arbitrage;

    JEL classification:

    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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