Pricing and valuation under the real-world measure
Publication date
2016-02-11
Document type
Forschungsartikel
Author
Organisational unit
Scopus ID
Publisher
World Scientific
Series or journal
International Journal of Theoretical and Applied Finance
ISSN
Periodical volume
19
Periodical issue
1
Article ID
1650006
Is a version of
Is referenced by
Part of the university bibliography
✅
Language
English
Keyword
Arbitrage
complete market
complex market
efficient market
enlargement of filtrations
fundamental theorem of asset pricing
growth-optimal portfolio
immersion
numéraire portfolio
pricing
sensitive market
valuation
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 numéraire, 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.
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Published version
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