Girsanov, Numeraires, and All That

Abstract

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.