Martingales
Processes whose conditional future value equals their current value.
Name the object before manipulating it.
Processes whose conditional future value equals their current value. Fix the information set, units and market convention before using the relationship in pricing or risk.
Processes whose conditional future value equals their current value.
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.
Martingales 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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