Click here to Login




Historical volatility estimators

Updated on 2010-01-20





Look at these charts.





Did you notice what they have in common?
They both have the same return. But do you know what is the difference between them?
It is the volatility.

The first stock moves up and down more frequently and with higher amplitude than the second stock. This translates into a higher volatility.

The volatility is a measure of the variability and the degree of fluctuation of a time-series or an asset. The higher the volatility is the more fluctuations and unexpected moves happen to a security compared to a security with low volatility.
Example: A stock that went up 3% yesterday and went down 10% today has more volatility than a stock that increased 1% yesterday and 2% today.

The estimation of the future realized volatility in trading is important, but very difficult. Stock traders can use this information to adjust their portfolios, reduce their risks, and options traders can use it to trade against the options implied volatility...
Before estimating this future volatility, a trader should first calculate the historical volatility. This volatility (Historical) is calculated by looking at the past bars of the security or stock. The more common and well-known method to calculate the historical volatility is called the close-to-close volatility estimator. This estimator consists of calculating the standard deviation of the logarithmic returns over a given period of observation.
The issue of the period of observation or lookback period can result into a proliferation of historical volatility values. In fact, even if the close-to-close volatility is an annualized value, using different period of observations can lead to different results.
As example, if we use a daily standard deviation and multiply the result by the annualization factor we will get a different result than if we had used a weekly standard deviation and its associated annualization factor. Note that, the annualization factor is the square root of the number of trading days in a year (252 in the United States) divided by the number of days used to calculate the raw standard deviation value.
There is no such best look-back period to use for the calculation of the historical volatility and each trader chooses the period that suits him best. A low period catch the most recent volatility trend in a stock but can result in a great amount of noise, while a long period catch the long-term volatility trend.

Another issue concerns the estimator to use to calculate the volatility, we just saw the close-to-close volatility estimator, but there are many other estimators, each one with its own benefits and drawbacks.
The Historical High-Low Volatility: Parkinson Estimator calculation uses the daily range and can then capture the intraday move, however it cannot handle trends and jumps and it systematically underestimates the volatility.
The Garman-Klass Volatility Estimator is up to eight times more efficient than the close-to-close estimator. It also uses almost all the available price information; however, this estimator is more biased than the Parkinson estimator.
The Rogers-Satchell Volatility Estimator allows for the presence of trends (non-zero drift), but it doesn't account for jumps.
The Yang Zhang extension of the Garman-Klass Volatility Estimator is the one that has the lowest estimation error, it handles both drift and jumps and it is 14 times more efficient than the close-to-close estimator. The bad news is that this estimator performance degrades to that of the close-to-close estimator when there are several opening jumps in the price series.

The conclusion regarding these estimators is that there is no such best estimator. As we have indicated, each one has its benefits and drawbacks and the best thing to do is to combine different estimators' value to take a decision.

Here is the close-to-close estimator formula in the QuantShare trading software:
a = Log(close / ref(close, 1));
volatility = Stddev(a,30) * Sqrt(255 / 30) * 100;

For the other estimators, you can click on each estimator link to download its function.











no comments (Log in)

QuantShare Blog
QuantShare
Search Posts




QuantShare
Recent Posts

Create Graphs using the Grid Tool
Posted 1405 days ago

Profile Graphs
Posted 1510 days ago

QuantShare
Previous Posts

Historical volatility estimators
Posted 5375 days ago

Short Selling Stocks
Posted 5383 days ago

Stock split & dividend
Posted 5389 days ago

Survivorship bias
Posted 5396 days ago

Transaction Costs
Posted 5404 days ago

How to simulate options strategies
Posted 5418 days ago

Organizing Trading Objects
Posted 5425 days ago

How to search for a download item
Posted 5439 days ago

Trading orders - Part 2
Posted 5446 days ago

Trading Orders - Part 1
Posted 5453 days ago


More Posts

Back







QuantShare
Product
QuantShare
Features
Create an account
Affiliate Program
Support
Contact Us
Trading Forum
How-to Lessons
Manual
Company
About Us
Privacy
Terms of Use

Copyright © 2024 QuantShare.com
Social Media
Follow us on Facebook
Twitter Follow us on Twitter
Google+
Follow us on Google+
RSS Trading Items



Trading financial instruments, including foreign exchange on margin, carries a high level of risk and is not suitable for all investors. The high degree of leverage can work against you as well as for you. Before deciding to invest in financial instruments or foreign exchange you should carefully consider your investment objectives, level of experience, and risk appetite. The possibility exists that you could sustain a loss of some or all of your initial investment and therefore you should not invest money that you cannot afford to lose. You should be aware of all the risks associated with trading and seek advice from an independent financial advisor if you have any doubts.