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A Unifying Approach to Asset Pricing

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Abstract

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.

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File URL: http://www.business.uts.edu.au/qfrc/research/research_papers/rp-227.pdf
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Bibliographic Info

Paper provided by Quantitative Finance Research Centre, University of Technology, Sydney in its series Research Paper Series with number 227.

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Length: 26
Date of creation: 01 Jul 2008
Date of revision:
Handle: RePEc:uts:rpaper:227

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

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References

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  1. Eckhard Platen, 2003. "A Benchmark Framework for Risk Management," Research Paper Series 113, Quantitative Finance Research Centre, University of Technology, Sydney.
  2. 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.
  3. Eckhard Platen, 2001. "Arbitrage in Continuous Complete Markets," Research Paper Series 72, Quantitative Finance Research Centre, University of Technology, Sydney.
  4. Robert C. Merton, 1973. "Theory of Rational Option Pricing," Bell Journal of Economics, The RAND Corporation, vol. 4(1), pages 141-183, Spring.
  5. Eckhard Platen, 2004. "A Benchmark Approach to Finance," Research Paper Series 138, Quantitative Finance Research Centre, University of Technology, Sydney.
  6. Merton, Robert C, 1973. "An Intertemporal Capital Asset Pricing Model," Econometrica, Econometric Society, vol. 41(5), pages 867-87, September.
  7. Truc Le & Eckhard Platen, 2006. "Approximating the Growth Optimal Portfolio with a Diversified World Stock Index," Research Paper Series 184, Quantitative Finance Research Centre, University of Technology, Sydney.
  8. Markowitz, Harry M, 1976. "Investment for the Long Run: New Evidence for an Old Rule," Journal of Finance, American Finance Association, vol. 31(5), pages 1273-86, December.
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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.

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