Change of numeraire

Quantitative Finance Glossary

Girsanov-based transformation between equivalent martingale measures induced by switching the unit-of-account asset. If N and M are two strictly positive numeraires, the Radon-Nikodým derivative is left.dfracdmathbbQ^NdmathbbQ^Mright|_mathcalF_T = dfracN_T / N_0M_T / M_0. Switching to the T-forward measure (numeraire P(t,T)) lets one pull the discount factor out of the expectation — the standard trick for pricing swaptions and FRAs. Switching to the annuity measure makes the swap rate a martingale (LMM/SABR habitat).

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