The Dupire formula is exact but brittle: differentiating market prices introduces noise that can produce negative local variance or exploding surfaces. This note turns the theoretical formula into a production-grade calibration by first fitting a smooth, arbitrage-free surface to market quotes, and then differentiating analytically. The workhorse is the SVI parameterisation from Topic 1, which gives closed-form derivatives. A second approach — fitting the Heston model and extracting its implied local vol surface — is also covered, since it links local vol directly to the stochastic vol parameters.
The practical calibration of an equity exotic desk proceeds in two stages: fit the surface (this note), then use the surface as an input to local vol Monte Carlo (next note). Getting stage one right determines whether stage two produces prices that are risk-manageable.
Learning objectives. By the end of this note you should be able to:
- describe the full pipeline from raw market quotes to a local vol surface;
- implement the SVI-then-Dupire route with analytical derivatives;
- explain why the Andersen-Brotherton-Ratcliffe regularisation is used and what it changes;
- use the Heston ATM approximation to seed an initial guess for SVI or Heston calibration.
In this lesson
- 2.1 The calibration pipeline
- 2.2 SVI-based calibration
- 2.3 The Andersen-Brotherton-Ratcliffe regularisation
- 2.4 Heston ATM approximation as a calibration seed
- 2.5 From Heston calibration to local vol
Before you start
The full lesson, with worked examples and exercise solutions, is for members.
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