Chapter

Change of Numeraire

Tomas Björk

in Arbitrage Theory in Continuous Time

Second edition

Published in print March 2004 | ISBN: 9780199271269
Published online October 2005 | e-ISBN: 9780191602849 | DOI: http://dx.doi.org/10.1093/0199271267.003.0024

Series: Oxford Finance Series

Change of Numeraire

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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

Chapter.  8613 words. 

Subjects: Financial Markets

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