Close-to-Close Historical Volatility Calculation – Volatility Analysis in Python

Follow us on LinkedIn

In a previous post, we touched upon a stock’s volatility through its beta. In this post, we are going to discuss historical volatilities of a stock in more details. If you want to use the online version, go to Historical Volatility Online Calculator.

Also referred to as statistical volatility, historical volatility gauges the fluctuations of underlying securities by measuring price changes over predetermined periods of time. It is the less prevalent metric compared to implied volatility because it isn’t forward-looking.

When there is a rise in historical volatility, a security’s price will also move more than normal. At this time, there is an expectation that something will or has changed. If the historical volatility is dropping, on the other hand, it means any uncertainty has been eliminated, so things return to the way they were. Read more

There are various types of historical volatilities such as close-to-close, Parkinson, Garman-KIass, Yang-Zhang, etc. These volatility measures play an important role in trading and risk management. In this post, we will discuss the close-to-close historical volatility.

The close-to-close historical volatility (CCHV) is calculated as follows,

historical volatility in python

where xi are the logarithmic returns calculated based on the stock’s closing prices,  and N is the sample size.  In this example, N=22, the average number of trading days in a month.

We implemented the above equation in Python. We downloaded SPY data from Yahoo finance and calculated CCHV using the Python program. The picture below shows the close-to-close historical volatility of SPY from March 2015 to March 2020.

volatility trading in python

It’s observed that the volatility is a mean-reverting process. The CCHV has the following characteristics [1]

Advantages

  • It has well-understood sampling properties
  • It is easy to correct bias
  • It is easy to convert to a form involving typical daily moves

Disadvantages

  • It is a very inefficient use of data and converges very slowly

References

[1] E. Sinclair, Volatility Trading, John Wiley & Sons, 2008

Further questions

What's your question? Ask it in the discussion forum

Have an answer to the questions below? Post it here or in the forum

LATEST NEWSMountain Province Diamonds Announces First Quarter Financial Results for 2024
Mountain Province Diamonds Announces First Quarter Financial Results for 2024
Stay up-to-date with the latest news - click here
LATEST NEWSRobinhood CEO Vladimir Tenev sells $4.48 million in company stock
Robinhood CEO Vladimir Tenev sells $4.48 million in company stock
Stay up-to-date with the latest news - click here
LATEST NEWSWest Red Lake Gold Announces Revised Terms to Previously Announced Bought Deal Public Offering
West Red Lake Gold Announces Revised Terms to Previously Announced Bought Deal Public Offering

NOT FOR DISTRIBUTION TO UNITED STATES NEWS WIRE SERVICES OR FOR DISSEMINATION IN THE UNITED STATES TORONTO, May 08, 2024 (GLOBE NEWSWIRE) — West Red Lake Gold Mines Ltd. (“West Red Lake Gold” or “WRLG” or the “Company”) (TSXV: WRLG) (OTCQB: WRLGF) is pleased to…

Stay up-to-date with the latest news - click here
LATEST NEWSArm shares drop as revenue forecast falls short despite AI boom
Arm shares drop as revenue forecast falls short despite AI boom

Lacklustre outlook raises concerns that spending on artificial intelligence chips could slow

Stay up-to-date with the latest news - click here
LATEST NEWSIn rapidly ageing China, millions can't afford to retire
In rapidly ageing China, millions can't afford to retire
Stay up-to-date with the latest news - click here

Leave a Reply