  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.
