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Arbitrage Theory in Continuous Time$
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Tomas Björk

Print publication date: 2004

Print ISBN-13: 9780199271269

Published to Oxford Scholarship Online: October 2005

DOI: 10.1093/0199271267.001.0001

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Change of Numeraire

Change of Numeraire

Chapter:
(p.348) 24 Change of Numeraire
Source:
Arbitrage Theory in Continuous Time
Author(s):

Tomas Björk (Contributor Webpage)

Publisher:
Oxford University Press
DOI:10.1093/0199271267.003.0024

This chapter discusses numeraire changes. It considers a pricing problem for a contingent claim χ, in a model with a stochastic short rate r. In most concrete cases, r and χ are not independent under the risk neutral martingale measure Q. This is because under Q, the stock will have r as its local rate of return, thus introducing a Q-dependence. A general pricing formula with a forward neutral measure QT is presented. Practice exercises are included.

Keywords:   pricing, contingent claim, numeraire changes, short rate, martingale measure

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