Choosing a Calibration Method for the Heston Stochastic Volatility Model

Summary

The document considers how to calibrate the Heston stochastic-volatility model and narrows its response to calibration from time series. Because volatility is latent, that task can be framed as nonlinear filtering. The answer points to research methods and literature associated with filtering and Bayesian estimation, including MCMC, unscented Kalman filters, and particle filters, alongside several cited research lineages.

The response also cautions that time-series calibration can be complex and urges the modeler to clarify the purpose and requirements before choosing it. In particular, it asks whether Heston is needed for the intended application or whether a simpler GARCH variant would suffice. The document does not describe calibration to option prices, provide a step-by-step estimation procedure, compare methods empirically, or give parameter constraints and diagnostics. Its contribution is therefore a high-level orientation to latent-volatility estimation and a reminder to match model complexity to the use case.

Key ideas

• Time-series calibration of Heston involves estimating a model with latent volatility.
• Nonlinear filtering provides one framing for that estimation problem.
• The response names MCMC, unscented Kalman filtering, and particle filtering as relevant approaches.
• Model choice should reflect the application, since a simpler GARCH variant may be sufficient.

Tags

# Calibration of Heston model


# Calibration of Heston model












I would like to calibrate the Heston model and I am wondering which are the most common approaches used in the literature. Any suggestions (references from the main stream literature, notes or presentations) is greatly appreciated.

## Answer by Kiwiakos (score 3, accepted)

https://quant.stackexchange.com/a/25362

If you want to calibrate on time series, then you have a 'non linear filtering' problem, since volatility is latent. There have been papers from late 90s/ early 00s that do that: Google for Heston together with Ghysels, Gallant, Renault, Chernov, Tauchen, Pan, Bates, Shephard, MCMC, unscented Kalman filter/ particle filter.

Given the significant complexity though, you should understand your motivation and requirements. Ask yourself why calibrate Heston on time series? Why a more straightforward Garch variant is not sufficient?

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