The Law of Minimum Price
AbstractThis 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.
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Bibliographic InfoPaper provided by Quantitative Finance Research Centre, University of Technology, Sydney in its series Research Paper Series with number 215.
Date of creation: 01 Feb 2008
Date of revision:
law of one price; law of the minimal price; derivative pricing; real world pricing; numeraire portfolio; growth optimal portfolio; strong arbitrage; extreme maturity bond;
Find related papers by JEL classification:
- G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
- G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
This paper has been announced in the following NEP Reports:
- NEP-ALL-2008-03-08 (All new papers)
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