Pricing and Valuation under the Real-World Measure
Abstract
In general it is not clear which kind of information is supposed to be used for calculating the fair value of a contingent claim. Even if the information is specified, it is not guaranteed that the fair value is uniquely determined by the given information. A further problem is that asset prices are typically expressed in terms of a risk-neutral measure. This makes it difficult to transfer the fundamental results of financial mathematics to econometrics. I show that the aforementioned problems evaporate if the financial market is complete and sensitive. In this case, after an appropriate choice of the numeraire, the discounted price processes turn out to be uniformly integrable martingales under the real-world measure. This leads to a Law of One Price and a simple real-world valuation formula in a model-independent framework where the number of assets as well as the lifetime of the market can be finite or infinite.
Keywords
Cite
@article{arxiv.1304.3824,
title = {Pricing and Valuation under the Real-World Measure},
author = {Gabriel Frahm},
journal= {arXiv preprint arXiv:1304.3824},
year = {2016}
}
Comments
Previous versions of this paper have been distributed under the titles "Pricing in Complex and Efficient Financial Markets," "Absorbability of Financial Markets," "The Fundamental Theorem of Asset Pricing for Liquid Financial Markets," and "Asset Pricing and Valuation under the Real-World Probability Measure."