Radon-Nikodým derivative
Quantitative Finance glossary · Stochastic Calculus & Continuous Time Finance
Definition
The likelihood-ratio random variable that converts one probability measure into an equivalent one.
Radon-Nikodým derivative in plain English
In finance we often need to look at the same random future through two different sets of odds — for example, the 'real world' chance of an event versus a special 'pricing world' chance that makes fair-value math work. The Radon-Nikodym derivative is the exact conversion factor between those two views: for each possible outcome it tells you how much more or less likely it is under the new odds than the old ones, so you can translate probabilities from one world to the other. It's like an exchange rate, but for probabilities instead of money — multiply by it and you've switched currencies. The one rule is that both views must agree on what's impossible (a zero-chance event stays zero), which is what 'equivalent' measures means.
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