Change of Measure
Reweight probabilities to move between pricing numeraires.
Name the object before manipulating it.
Reweight probabilities to move between pricing numeraires. Fix the information set, units and market convention before using the relationship in pricing or risk.
Reweight probabilities to move between pricing numeraires.
State the governing relationship.
Notation and units
Decimal rates and volatilities, year-fraction time and continuous compounding unless stated otherwise.
Draw the boundary of the claim.
Definitions, units and information sets are fixed before the mathematical relationship is applied.
Rates and volatilities use decimal units and time uses year fractions unless stated otherwise.
The relationship is local to its stated assumptions and should not be extrapolated mechanically.
“An unstated convention is a future reconciliation break.”— THEQUANTBATEMAN
Connect the definition to an observable.
Change of Measure connects an observable Foundations quantity to valuation, scenario analysis or hedge interpretation. The desk view depends on units, timestamp and quotation convention.
Translate the concept into a risk question.
State the convention, identify the observable and ask which Foundations risk remains after the proposed hedge.
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