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FXpractitionermodel

Garman-Kohlhagen

Black-Scholes adapted to domestic and foreign interest rates.

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

Build the mental model first.

Treat the foreign currency like a dividend-paying asset whose yield is the foreign rate.

ONE-LINE DEFINITION

Black-Scholes adapted to domestic and foreign interest rates.

02Mathematics

Now make it exact.

C=S0erfTN(d1)KerdTN(d2)C=S_0e^{-r_fT}N(d_1)-Ke^{-r_dT}N(d_2)
Notation and units

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

03Assumptions

Every model has a price.

01

Educational conventions are stated explicitly and may simplify market quotation or settlement details.

02

Rates are continuously compounded unless the section says otherwise.

03

Inputs are deterministic in the base model.

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

Why a quant cares.

Baseline European FX option valuation and Greeks.

IntuitionMathematicsImplementationDesk risk
05Desk view
FRONT OFFICE VIEW

The hedge has opinions.

Start with the quote convention, then ask which FX risk survives the hedge. A number without its convention is merely well-dressed ambiguity.

Ask Bateman about this model
06Related

Continue through the graph.