IDEAS home Printed from https://ideas.repec.org/p/uts/rpaper/215.html
   My bibliography  Save this paper

The Law of Minimal Price

Author

Abstract

This paper introduces a realistic, generalized market modeling framework for which the Law of One Price no longer holds. Instead the Law of the Minimal Price will be derived, which for contingent claims with long term to maturity may provide significantly lower prices than suggested under the currently prevailing approach. This new law only requires the existence of the numeraire portfolio, which turns out to be the portfolio that maximizes expected logarithmic utility. In several ways it will be shown that the numeraire portfolio cannot be outperformed by any nonnegative portfolio. The new Law of the Minimal Price leads directly to the real world pricing formula, which uses the numeraire portfolio as numeraire and the real world probability for calculating conditional expectations. The cost efficient pricing and hedging of extreme maturity zero coupon bonds illustrates the new law in the context of the US market.

Suggested Citation

  • Eckhard Platen, 2008. "The Law of Minimal Price," Research Paper Series 215, Quantitative Finance Research Centre, University of Technology, Sydney.
    • Handle: RePEc:uts:rpaper:215
    as

    Download full text from publisher

    File URL: https://www.uts.edu.au/sites/default/files/qfr-archive-02/QFR-rp215.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Mehra, Rajnish & Prescott, Edward C., 1985. "The equity premium: A puzzle," Journal of Monetary Economics, Elsevier, vol. 15(2), pages 145-161, March.
    2. Mark Loewenstein & Gregory A. Willard, 2000. "Local martingales, arbitrage, and viability," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 16(1), pages 135-161.
    3. Harry M. Markowitz, 2011. "Investment for the Long Run: New Evidence for an Old Rule," 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 35, pages 495-508, World Scientific Publishing Co. Pte. Ltd..
    4. Eckhard Platen, 2004. "A Benchmark Framework for Risk Management," World Scientific Book Chapters, in: Jiro Akahori & Shigeyoshi Ogawa & Shinzo Watanabe (ed.), Stochastic Processes And Applications To Mathematical Finance, chapter 15, pages 305-335, World Scientific Publishing Co. Pte. Ltd..
    5. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    6. Eckhard Platen, 2006. "A Benchmark Approach To Finance," Mathematical Finance, Wiley Blackwell, vol. 16(1), pages 131-151, January.
    7. Long, John Jr., 1990. "The numeraire portfolio," Journal of Financial Economics, Elsevier, vol. 26(1), pages 29-69, July.
    8. Eckhard Platen, 2001. "Arbitrage in Continuous Complete Markets," Research Paper Series 72, Quantitative Finance Research Centre, University of Technology, Sydney.
    9. Hakansson, Nils H., 1971. "Capital Growth and the Mean-Variance Approach to Portfolio Selection," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 6(1), pages 517-557, January.
    10. Robert Fernholz & Ioannis Karatzas, 2005. "Relative arbitrage in volatility-stabilized markets," Annals of Finance, Springer, vol. 1(2), pages 149-177, November.
    11. Merton, Robert C, 1973. "An Intertemporal Capital Asset Pricing Model," Econometrica, Econometric Society, vol. 41(5), pages 867-887, September.
    12. Harrison, J. Michael & Kreps, David M., 1979. "Martingales and arbitrage in multiperiod securities markets," Journal of Economic Theory, Elsevier, vol. 20(3), pages 381-408, June.
    13. Eckhard Platen & Hardy Hulley, 2008. "Hedging for the Long Run," Research Paper Series 214, Quantitative Finance Research Centre, University of Technology, Sydney.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Johannes Ruf, 2010. "Hedging under arbitrage," Papers 1003.4797, arXiv.org, revised May 2011.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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..
    2. Renata Rendek, 2013. "Modeling Diversified Equity Indices," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 23, July-Dece.
    3. Renata Rendek, 2013. "Modeling Diversified Equity Indices," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 4-2013.
    4. Eckhard Platen, 2008. "A Unifying Approach to Asset Pricing," Research Paper Series 227, Quantitative Finance Research Centre, University of Technology, Sydney.
    5. 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.
    6. Kevin John Fergusson, 2018. "Less-Expensive Pricing and Hedging of Extreme-Maturity Interest Rate Derivatives and Equity Index Options Under the Real-World Measure," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 3-2018.
    7. 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.
    8. Baldeaux Jan & Ignatieva Katja & Platen Eckhard, 2014. "A tractable model for indices approximating the growth optimal portfolio," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 18(1), pages 1-21, February.
    9. repec:uts:finphd:40 is not listed on IDEAS
    10. Eckhard Platen & Renata Rendek, 2012. "The Affine Nature of Aggregate Wealth Dynamics," Research Paper Series 322, Quantitative Finance Research Centre, University of Technology, Sydney.
    11. 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.
    12. Eckhard Platen, 2009. "Real World Pricing of Long Term Contracts," Research Paper Series 262, Quantitative Finance Research Centre, University of Technology, Sydney.
    13. Platen, Eckhard, 2006. "Portfolio selection and asset pricing under a benchmark approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 370(1), pages 23-29.
    14. 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.
    15. Fergusson, Kevin, 2020. "Less-Expensive Valuation And Reserving Of Long-Dated Variable Annuities When Interest Rates And Mortality Rates Are Stochastic," ASTIN Bulletin, Cambridge University Press, vol. 50(2), pages 381-417, May.
    16. Ashkan Nikeghbali & Eckhard Platen, 2008. "On Honest Times in Financial Modeling," Research Paper Series 229, Quantitative Finance Research Centre, University of Technology, Sydney.
    17. Kevin Fergusson & Eckhard Platen, 2013. "Real World Pricing of Long Term Cash-Linked Annuities and Equity-Linked Annuities with Cash-Linked Guarantees," Research Paper Series 338, Quantitative Finance Research Centre, University of Technology, Sydney.
    18. Eckhard Platen, 2005. "On The Role Of The Growth Optimal Portfolio In Finance," Australian Economic Papers, Wiley Blackwell, vol. 44(4), pages 365-388, December.
    19. 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.
    20. Jan Baldeaux & Eckhard Platen, 2013. "Liability Driven Investments under a Benchmark Based Approach," Research Paper Series 325, Quantitative Finance Research Centre, University of Technology, Sydney.
    21. 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.

    More about this item

    Keywords

    law of one price; law of the minimal price; derivative pricing; real world pricing; numeraire portfolio; growth optimal portfolio; strong arbitrage; extreme maturity bond;
    All these keywords.

    JEL classification:

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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:uts:rpaper:215. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Duncan Ford (email available below). General contact details of provider: https://edirc.repec.org/data/qfutsau.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.