Heston
Model variance as a mean-reverting square-root diffusion.
Start from the observable dynamics.
Separate state variables, dynamics and valuation measure before looking at a calibration. Model variance as a mean-reverting square-root diffusion. A fitted surface is evidence about today's prices, not proof of tomorrow's dynamics.
Model variance as a mean-reverting square-root diffusion.
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.
Heston is used to translate liquid EQ calibration instruments into prices and sensitivities. Residuals, parameter stability and hedge behaviour must be reviewed together.
Challenge the hedge outside the fitted slice.
A good EQ calibration explains today's instruments; the hedge reveals whether the assumed dynamics survive tomorrow's move.
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