A Heston model is only as good as its calibration. Five parameters must simultaneously match the ATM level, term structure, skew, and curvature of the observed implied vol surface. This note turns the theoretical framework into a working calibration procedure: the ATM approximation provides fast initial guesses, a least-squares objective (in implied vol space) drives the optimiser, and stability constraints prevent the calibration from finding unrealistic solutions.
Calibration under Heston is a small-scale (5-dimensional) nonlinear least-squares problem that runs in under a second with modern libraries. The hard part is choosing the right loss function and imposing the right constraints.
Learning objectives. By the end of this note you should be able to:
- compute an initial Heston parameter guess from the ATM level and skew of the surface;
- set up and solve the Heston calibration as a bounded nonlinear least-squares problem;
- identify the identifiability issue between and and explain how to resolve it;
- assess whether a calibrated Heston fit is stable and well-identified.
In this lesson
- 4.1 ATM approximation for initial guess
- 4.2 Calibration objective
- 4.3 Identifiability
Before you start
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