Estimating Heston Variance Mean Reversion from Historical Returns

Summary

The document asks how to calculate an estimator for the long-run variance level in a Heston model under the real-world measure. The displayed estimator averages squared historical log returns over the observation period, and the answer confirms that it is computed from historical data. In practice, this means the inputs are successive observed asset prices, converted into log returns and squared before aggregation.

The exchange gives a narrow clarification rather than a full parameter-estimation procedure. It does not specify sampling frequency, annualization conventions, data cleaning, or how the estimator relates to other Heston parameters. Those choices should be checked against the cited paper before applying the estimate, since the document alone does not establish robustness or suitability for a particular market or dataset.

Key ideas

• The estimator for the real-world long-run variance level is based on squared log returns.
• The answer confirms that historical observations provide the data for the calculation.
• The document does not explain sampling choices or how to estimate the model's other parameters.

Tags

# Estimate the mean reversion level of the variance process under the real world measure


# Estimate the mean reversion level of the variance process under the real world measure












This paper gives on equation 22 an estimator for the mean reversion level of the variance process under the real world measure. The context is the Heston model, where the variance is stochastic and the paper is trying to give a proxy for the determination of the Heston model parameters under the real word measure.

My question is: I perfectly understand equation 22, but it is not really clear to me if I should use the historical log-returns to do the computation. Could you please confirm that all I need to compute the estimator in equation 22 are the historical log-returns?

The equation 22, wich I refer to, is the following: $$\hat{\bar{\nu}}^{*} := \frac{1}{T}\sum_{k=1}^{K}\left[\ln\left( \frac{S(t_k)}{S(t_{k-1})}\right)\right]^2$$

Thank you

## Answer by Joanna (score 1)

https://quant.stackexchange.com/a/34373

Answering my own question: Yes, on page 27 of the article the author says that equation 22 should indeed be computed from historical data.

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