Numeraire
Quantitative Finance glossary · Stochastic Calculus & Continuous Time Finance
Definition
An asset chosen as the unit of account for pricing; price ratios become martingales under the corresponding equivalent martingale measure.
Numeraire in plain English
Prices only mean something relative to a yardstick — $100 means one thing measured in dollars and another measured in gold ounces. A numeraire is simply the yardstick you choose to measure all other prices against; often it's a dollar in a safe savings account, but you're free to pick something else. The clever payoff is that once you pick the right measuring stick and pair it with a matching "fair-odds" way of weighting the future, every price measured in those units becomes a "martingale" — meaning its best guess for tomorrow is just its value today, with no built-in drift. Switching to a well-chosen numeraire often turns an ugly pricing problem into an easy one, the way rephrasing a word problem in better units can make the arithmetic fall out cleanly.
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