Our execution algorithms rely heavily on volatility as a key analytic for numerous decision-making processes, such as limit order placement and estimating market impact. For example, our IS Zero algorithm considers the intraday seasonality of volatility in addition to the intraday seasonality of volume throughout the trading day. In addition, our limit order model incorporates volatility as a key input–higher volatility increases the likelihood of a passive order receiving a fill, even when it’s placed at a greater distance from the midpoint price.

The Challenge of Estimating Volatility

One of the challenges we have faced in estimating volatility is deciding which method to use. Should we rely on the standard measure of volatility, calculated as the standard deviation of close-to-close returns (or the standard deviation of returns calculated from the last prices of consecutive bins for intraday volatility)? Or should we use a range-based estimate such as Parkinson volatility, which uses the high and low range of each trading period–whether a full day or shorter intraday bins–rather than just the closing prices?

Literature suggests that Parkinson volatility is a superior estimator, primarily because it incorporates more information by accounting for intraday price swings through the high and low prices. Our analysis, shared in the next section, supports this view.

The two methods are defined as follows:

• Standard volatility estimation:

• Parkinson volatility estimation:

Our Analysis: Standard vs. Parkinson Volatility

We evaluated the two estimates using daily high, low, and close prices for 75 of the futures instruments that BestEx Research currently supports. We calculated both the standard (close-to-close) volatility and Parkinson volatility for each instrument over the last three months (June to September 2024). Figure 1 below shares a comparison of the two measures. Figure 1 illustrates a high correlation (93%) between a standard deviation of close-to-close returns calculation of volatility and the Parkinson volatility calculation during the study period. 

When we exclude outliers from these calculations–those instruments with daily volatility higher than 250 basis points–the correlation was even stronger, reaching 98%, as illustrated in Figure 2 below. 

The regression coefficient between the two measures is 0.90, indicating that Parkinson’s estimate (y) is, on average, lower than the standard volatility measure (x), though a 4 basis point intercept incorporated. This is expected, as the Parkinson volatility calculation does not account for overnight returns, which can introduce additional variance. For trading algorithms, overnight returns are less relevant; if overnight returns are critical, the standard calculation can be used.

Impact of Sample Size on Volatility Estimation

One of the key takeaways of our analysis, shown above, was verifying that Parkinson’s measurement closely resembles the standard definition when ample data is available. However, there is often a trade-off between using more data for robustness of measurement and using less data to capture trends in real time.

For instance, if a geopolitical event occurs in the Middle East, energy products would likely experience a spike in volatility. Using three months of historical data to estimate volatility in such a scenario could lead to an underestimation. But real-time calculations often incorporate limited data by definition. To compare the effectiveness of longer-term versus shorter-term estimates, we calculated both volatility estimates using smaller samples (in this case, 5 days of data) and compared the results with calculations from larger samples.

For each of the 75 futures contracts evaluated in the illustrations above, we calculated both the standard volatility and Parkinson volatility over the most-recent 5-day and 90-day periods and plotted each to compare, as shown below in Figure 3AB.

As illustrated in Figure 3AB, our analysis shows that a 5-day Parkinson volatility estimate is substantially more robust than the standard deviation of returns using the same 5 days of data. The 5-day Parkinson calculation showed a correlation of 97% with the 90-day Parkinson calculation, indicating that far less data (only 5 days) can reasonably represent the information available in the 90-day estimate. The standard volatility calculation showed a substantially lower correlation between its 5-day and 90-day varieties, only 83%. Note that outliers have been removed as in Figure 2 above for this comparison. 

Assuming no recent trend of higher or lower volatility is present, the 5-day Parkinson volatility is better able to represent the conditions over the preceding 90-day period than the standard measure of volatility can. We conclude that Parkinson’s measure is more robust for estimation using a small sample. 

Conclusion

In summary, when sufficient data is available, both Parkinson and standard volatility estimates are highly correlated and provide similar estimates. If overnight volatility must be accounted for, then the standard volatility measure should be used. However, for intraday estimates and when dealing with limited data, Parkinson’s volatility is superior, offering a more robust estimate of volatility. 

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Reach out to your BestEx Research representative or info@bestexresearch.com to learn more about volatility estimation.