Garman-Kohlhagen
Black-Scholes adapted to domestic and foreign interest rates.
Start from the observable dynamics.
Treat the foreign currency like a dividend-paying asset whose yield is the foreign rate.
Black-Scholes adapted to domestic and foreign interest rates.
Write the state process and pricing map.
Notation and units
Decimal rates and volatilities, year-fraction time and continuous compounding unless stated otherwise.
Identify what the model cannot represent.
The state dynamics and valuation measure are stated independently of the calibration instruments.
Parameters are treated as deterministic over the pricing run unless the model says otherwise.
A calibration fit does not validate out-of-sample dynamics or hedge performance.
“An unstated convention is a future reconciliation break.”— THEQUANTBATEMAN
Separate calibration fit from dynamics.
Baseline European FX option valuation and Greeks.
Challenge the hedge outside the fitted slice.
A good FX calibration explains today's instruments; the hedge reveals whether the assumed dynamics survive tomorrow's move.
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