Pricing and Valuation under the Real-World Measure

TL;DR

This paper demonstrates that in complete and sensitive markets, the fair value of contingent claims can be derived directly under the real-world measure, simplifying valuation without relying on risk-neutral measures.

Contribution

It establishes a model-independent valuation framework under the real-world measure for complete and sensitive markets, extending fundamental financial results.

Findings

Discounted price processes are uniformly integrable martingales under the real-world measure.

A Law of One Price holds in complete and sensitive markets.

Provides a simple valuation formula applicable to finite or infinite markets.

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.