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Series:   Elements in Quantitative Finance

Girsanov, Numeraires, and All That

Published online by Cambridge University Press:  20 October 2022

Patrick S. Hagan  and
Andrew Lesniewski
Patrick S. Hagan
Affiliation:
Gorilla Science
Andrew Lesniewski
Affiliation:
Bernard M. Baruch College, City University of New York

Summary

In this Element the authors review the technique of the change of numeraire in the martingale approach to option pricing. Their intention is to present a reader friendly explanation of the technique itself, and illustrate how it is applied in various fields of quantitative finance as the basis for building option valuation models. They start with an informal review of Girsanov's theorem, followed by a brief summary of the basic concepts of the arbitrage free pricing, and the technique of change of numeraire. This is followed by a number of applications of the change of numeraire technique including interest rate models, FX quanto adjustments, credit risk modeling, mortgage backed securities, and CMS rates.
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Keywords

Girsanov’s theoremchange of measurenumerairemartingale pricingfinancial derivatives
Type
Element
Information
Series: Elements in Quantitative Finance
Online ISBN: 9781009339278
Publisher: Cambridge University Press
Print publication: 17 November 2022

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