Volatility Cone [Loxx]

2022年10月27日

When it comes to forecasting volatility, it seems that the old axiom about weather is applicable: "Everyone talks about it, but no one can do much about it!" Volatility cones are a tool that may be useful in one’s attempt to do something about predicting the future volatility of an asset.

A "volatility cone" is a plot of the range of volatilities within a fixed probability band around the true parameter, as a function of sample length. Volatility cone is a visualization tool for the display of historical volatility term structure. It was introduced by Burghardt and Lane in early 1990 and is popular in the option trading community. This is mostly a static indicator due to processor load and is restricted to the daily time frame.

Why cones?
When we enter the options arena, in an effort to "trade volatility," we want to be able to compare current levels of implied volatility with recent historical volatility in an effort to assess the relative value of the option(s) under consideration Volatility cones can be an effective tool to help us with this assessment. A volatility cone is an analytical application designed to help determine if the current levels of historical or implied volatilities for a given underlying, its options, or any of the new volatility instruments, such as VolContractTM futures, VIX futures, or VXX and VXZ ETNs, are likely to persist in the future. As such, volatility cones are intended to help the user assess the likely volatility that an underlying will go on to display over a certain period. Those who employ volatility cones as a diagnostic tool are relying upon the principle of "reversion to the mean." This means that unusually high levels of volatility are expected to drift or move lower (revert) to their average (mean) levels, while relatively low volatility readings are expected to rise, eventually, to more "normal" values.

How to use
Suppose you want to analyze an options contract expiring in 3-months and this current option has an current implied volatility 25.5%. Suppose also that realized volatility (y-axis) at the 3-month mark (90 on the x-axis) is 45%, median in 35%, the 25th percentile is 30%, and the low is 25%. Comparing this range to the implied volatility you would maybe conclude that this is a relatively "cheap" option contract. To help you visualize implied volatility on the chart given an expiration date in bars, the indicator includes the ability to enter up to three expirations in bars and each expirations current implied volatility

By ascertaining the various historical levels of volatility corresponding to a given time horizon for the options futures under consideration, we’re better prepared to judge the relative "cheapness" or "expensiveness" of the instrument.

Volatility options
Close-to-Close
Close-to-Close volatility is a classic and most commonly used volatility measure, sometimes referred to as historical volatility .

Volatility is an indicator of the speed of a stock price change. A stock with high volatility is one where the price changes rapidly and with a bigger amplitude. The more volatile a stock is, the riskier it is.

Close-to-close historical volatility calculated using only stock's closing prices. It is the simplest volatility estimator. But in many cases, it is not precise enough. Stock prices could jump considerably during a trading session, and return to the open value at the end. That means that a big amount of price information is not taken into account by close-to-close volatility .

Despite its drawbacks, Close-to-Close volatility is still useful in cases where the instrument doesn't have intraday prices. For example, mutual funds calculate their net asset values daily or weekly, and thus their prices are not suitable for more sophisticated volatility estimators.

Parkinson
Parkinson volatility is a volatility measure that uses the stock’s high and low price of the day.

The main difference between regular volatility and Parkinson volatility is that the latter uses high and low prices for a day, rather than only the closing price. That is useful as close to close prices could show little difference while large price movements could have happened during the day. Thus Parkinson's volatility is considered to be more precise and requires less data for calculation than the close-close volatility. One drawback of this estimator is that it doesn't take into account price movements after market close. Hence it systematically undervalues volatility. That drawback is taken into account in the Garman-Klass's volatility estimator.

Garman-Klass
Garman Klass is a volatility estimator that incorporates open, low, high, and close prices of a security.

Garman-Klass volatility extends Parkinson's volatility by taking into account the opening and closing price. As markets are most active during the opening and closing of a trading session, it makes volatility estimation more accurate.

Garman and Klass also assumed that the process of price change is a process of continuous diffusion (geometric Brownian motion). However, this assumption has several drawbacks. The method is not robust for opening jumps in price and trend movements.

Despite its drawbacks, the Garman-Klass estimator is still more effective than the basic formula since it takes into account not only the price at the beginning and end of the time interval but also intraday price extremums.

Researchers Rogers and Satchel have proposed a more efficient method for assessing historical volatility that takes into account price trends. See Rogers-Satchell Volatility for more detail.

Rogers-Satchell
Rogers-Satchell is an estimator for measuring the volatility of securities with an average return not equal to zero.

Unlike Parkinson and Garman-Klass estimators, Rogers-Satchell incorporates drift term (mean return not equal to zero). As a result, it provides a better volatility estimation when the underlying is trending.

The main disadvantage of this method is that it does not take into account price movements between trading sessions. It means an underestimation of volatility since price jumps periodically occur in the market precisely at the moments between sessions.

A more comprehensive estimator that also considers the gaps between sessions was developed based on the Rogers-Satchel formula in the 2000s by Yang-Zhang. See Yang Zhang Volatility for more detail.

Yang-Zhang
Yang Zhang is a historical volatility estimator that handles both opening jumps and the drift and has a minimum estimation error.

We can think of the Yang-Zhang volatility as the combination of the overnight (close-to-open volatility ) and a weighted average of the Rogers-Satchell volatility and the day’s open-to-close volatility . It considered being 14 times more efficient than the close-to-close estimator.

Garman-Klass-Yang-Zhang
Garman Klass is a volatility estimator that incorporates open, low, high, and close prices of a security.

Garman-Klass volatility extends Parkinson's volatility by taking into account the opening and closing price. As markets are most active during the opening and closing of a trading session, it makes volatility estimation more accurate.

Garman and Klass also assumed that the process of price change is a process of continuous diffusion (geometric Brownian motion). However, this assumption has several drawbacks. The method is not robust for opening jumps in price and trend movements.

Despite its drawbacks, the Garman-Klass estimator is still more effective than the basic formula since it takes into account not only the price at the beginning and end of the time interval but also intraday price extremums.

Researchers Rogers and Satchel have proposed a more efficient method for assessing historical volatility that takes into account price trends. See Rogers-Satchell Volatility for more detail.

Exponential Weighted Moving Average
The Exponentially Weighted Moving Average (EWMA) is a quantitative or statistical measure used to model or describe a time series. The EWMA is widely used in finance, the main applications being technical analysis and volatility modeling.

The moving average is designed as such that older observations are given lower weights. The weights fall exponentially as the data point gets older – hence the name exponentially weighted.

The only decision a user of the EWMA must make is the parameter lambda. The parameter decides how important the current observation is in the calculation of the EWMA. The higher the value of lambda, the more closely the EWMA tracks the original time series.

Standard Deviation of Log Returns
This is the simplest calculation of volatility . It's the standard deviation of ln(close/close(1))

Sampling periods used
5, 10, 20, 30, 60, 90, 120, 150, 180, 210, 240, 270, 300, 330, and 360

Historical Volatility plot
Purple outer lines: High and low volatility values corresponding to x-axis time
Blue inner lines: 25th and 75th percentiles of volatility corresponding to x-axis time
Green line: Median volatility values corresponding to x-axis time
White dashed line: Realized volatility corresponding to x-axis time

Additional things to know
Due to UI constraints on TradingView it will be easier to visualize this indicator by double-clicking the bottom pane where it appears and then expanded the y- and x-axis to view the entire chart.
You can click on each point on the graph to see what the volatility of that point is.
Option expiration dates will show up as large dots on the graph. You can input your own values in the settings.