Option Model Calibration With and Without Characteristic Functions

Summary

The answer explains that a known characteristic function makes Fourier-based pricing and calibration efficient for many affine stochastic-volatility and Lévy models. It contrasts these with models that lack a known characteristic function, which can still be calibrated using methods designed for their structure rather than the same Fourier route.

Examples include local-volatility models calibrated with Dupire’s method, local-stochastic-volatility models with their own calibration procedures, and SABR pricing based on a singular perturbation approach. The response therefore reframes the question: absence of a characteristic function does not rule out calibration, but changes the applicable pricing and calibration algorithm. It gives no implementation details, numerical comparison, or guidance on choosing among the models, so it is an overview of method families rather than a calibration recipe.

Key ideas

• Affine stochastic-volatility and Lévy models often have characteristic functions that support efficient Fourier methods.
• Some pricing models do not have a known characteristic function but can use alternative calibration procedures.
• Dupire’s method is identified as an approach for calibrating local volatility.
• Local-stochastic-volatility models have dedicated calibration methods.
• The answer describes SABR pricing as using a singular perturbation approach rather than a characteristic-function method.

Tags

# Calibration when characteristic function is not known


# Calibration when characteristic function is not known












The prices of the call and put options can be quickly calculated using many methods using the form of the characteristic function. But how to calibrate a model when we don't know the characteristic function? Actually, what models do not provide us a characteristic function?

## Answer by d_797 (score 7, accepted)

https://quant.stackexchange.com/a/59815

You are likely thinking of affine stochastic volatility (SV) or Levy models which have characteristic functions that can be obtained via semi-analytic expression. For these types of models Fourier approaches are of the most efficient known approaches.

There are other types of non-affine models that are used for pricing that don't have known characteristic functions, but have their own pricing/calibration algorithms.

For instance local volatility models, where the volatility component is calibrated using approaches like Dupire's method. There are also local SV (LSV) models with their own calibration method. Another example would be in the SABR approach which prices options using a singular perturbation approach (not CF)

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.