Abstract
There are several ways to derive the no-arbitrage price of a contingent claim, such as following a replicating portfolio strategy or solving a partial differential equation. Another prominent approach is martingale pricing, which is the method we deal with in this chapter. We briefly review well-known facts on equivalent measures, the Radon-Nikodym derivative, martingale measures, and the change of numeraires following Geman, El Karoui, and Rochet [27]. The only measures we consider within this thesis are the ones equivalent to the physical measure. The ultimate goal in deriving the pricing formula for a claim is to write it in terms of possibly different artificial probabilites. It is known that the choice of different numeraires allows for a convenient computation of the claim’s fair price. This can be seen when looking at the BS formula: The easiest method for the valuation of a standard call is to choose appropriate normalizing assets and corresponding martingale measures. This will be reviewed to motivate the concept of different numeraires.
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References
For an appropriate definition of no-arbitrage excluding pathological scenarios see Delbaen and Schachermayer [15].
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© 2004 Springer-Verlag Berlin Heidelberg
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Esser, A. (2004). Pricing by Change of Measure and Numeraire. In: Pricing in (In)Complete Markets. Lecture Notes in Economics and Mathematical Systems, vol 537. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17065-2_2
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DOI: https://doi.org/10.1007/978-3-642-17065-2_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-20817-4
Online ISBN: 978-3-642-17065-2
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