In a monetary economy, one of the functions of money is to act as the numéraire, i.e. to serve as a unit of account and therefore provide a common benchmark relative to which the value of various goods and services can be measured against.
Using a numeraire, whether monetary or some consumable good, facilitates value comparisons when only the relative prices are relevant, as in general equilibrium theory.
priced in terms of the numéraire (in this case, M), are martingales with respect to a risk-neutral measure, say
is another strictly positive traded asset (and hence a martingale when priced in terms of the money market).
Jamshidian (1989) first used it in the context of the Vasicek model for interest rates in order to calculate bond options prices.
Geman, El Karoui and Rochet (1995) introduced the general formal framework for the change of numéraire technique.
Determining an appropriate numéraire has foundation in several financial pricing models such as options and certain assets.