Black-76
Option pricing on forwards under lognormal forward dynamics.
Start from the observable dynamics.
Price the option on the forward and discount the expected payoff back to today.
Option pricing on forwards under lognormal forward dynamics.
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.
Common baseline for commodity, caplet and swaption quotation contexts.
Challenge the hedge outside the fitted slice.
A good COMM calibration explains today's instruments; the hedge reveals whether the assumed dynamics survive tomorrow's move.
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