A pricing model becomes operational only after its parameters have been tied to market observables. That step—calibration—is an inverse problem: choose parameters so that model prices reproduce a selected set of liquid quotes. A tiny calibration error at a benchmark option can become a large hedge or exotic-pricing error elsewhere, while an apparently perfect fit can conceal unstable parameters, stale data, or a model being pushed beyond its design domain.
This lesson develops the reusable calibration workflow behind volatility, rates, and credit models. The implied-volatility surface is the running example because it exposes the central tensions cleanly: quotes are sparse and noisy, different contracts have different economic importance, parameters are not equally identifiable, and the best numerical fit is not automatically the safest production model.
By the end of this note you should be able to:
- distinguish calibration from statistical estimation;
- specify instruments, quote conventions, weights, constraints, and an objective before running an optimiser;
- diagnose non-identifiability and parameter instability;
- separate in-sample fit from out-of-sample pricing and hedge performance; and
- design a calibration report that supports a model-risk decision.
In this lesson
- The big picture
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- Define the calibration contract
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- Understand identification before optimisation
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- A production calibration algorithm
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- Worked example: two fits with the same headline error
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- Validation beyond the fitted instruments
Before you start
- Reading the Implied Vol Surface — Moneyness, Term Structure, and Quoting Conventions
- Least Squares as Orthogonal Projection
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