Calibrating Heston–Nandi GARCH Parameters to Option Prices

Summary

The document raises a model-calibration question: whether parameters in the Heston–Nandi GARCH option-pricing model can be estimated by fitting model prices to observed option prices instead of using maximum likelihood. The proposed approach is to choose a loss function that measures the gap between model and market call prices, then optimize the parameters to reduce that gap.

The post compares this idea with calibration commonly used for the Heston stochastic-volatility model, but it supplies no implementation, objective-function specification, dataset, or fitted results. It therefore identifies a practical alternative to likelihood-based estimation without establishing which loss function or calibration setup is suitable. Any application would need to define the option sample and pricing errors carefully; the document offers no evidence on calibration quality or out-of-sample performance.

Key ideas

• Heston–Nandi GARCH parameters can be considered for estimation by fitting model prices to observed option prices.
• A calibration objective can minimize differences between model and market call prices.
• This approach differs from estimating parameters with maximum likelihood.
• The document provides no code, loss-function choice, data, or evidence comparing estimation methods.

Tags

# Heston & Nandi GARCH model, parameters estimation from option data


# Heston & Nandi GARCH model, parameters estimation from option data












I wonder if anybody has code for the HN-GARCH model where the parameters is NOT estimated with maximum likelihood and instead estimated by looking at the option data where an loss function is chosen and is minimized, so the parameters in the model deliver a call price that is close as possible to the market price? Similar approach is common to use to estimate the parameters in the Heston stochastic volatility model.

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