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FX Delta Conventions

Premium-adjusted, forward and spot delta quotation choices.

Reviewed 2026-08-10TheQuantBateman Research2 linked labs
01Intuition

Name the object before manipulating it.

The same option can carry different delta numbers under valid market conventions.

ONE-LINE DEFINITION

Premium-adjusted, forward and spot delta quotation choices.

02Mathematics

State the governing relationship.

Δspot=e−rfTN(d1),Δfwd=N(d1)\Delta_{spot}=e^{-r_fT}N(d_1), \quad \Delta_{fwd}=N(d_1)
Notation and units

Decimal rates and volatilities, year-fraction time and continuous compounding unless stated otherwise.

03Assumptions

Draw the boundary of the claim.

01

Definitions, units and information sets are fixed before the mathematical relationship is applied.

02

Rates and volatilities use decimal units and time uses year fractions unless stated otherwise.

03

The relationship is local to its stated assumptions and should not be extrapolated mechanically.

“An unstated convention is a future reconciliation break.”— THEQUANTBATEMAN
04Market use

Connect the definition to an observable.

Smile construction and strike inversion require the exact pair-specific convention.

Intuition→Mathematics→Implementation→Desk risk
05Desk view
FRONT OFFICE VIEW

Translate the concept into a risk question.

State the convention, identify the observable and ask which FX risk remains after the proposed hedge.

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06Related

Follow the nearest dependency.