FXpractitionermodel
Garman-Kohlhagen
Black-Scholes adapted to domestic and foreign interest rates.
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.
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.
Intuition→Mathematics→Implementation→Desk 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.
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