Volatility Forecasting Using GARCH(1,1)

Continuing on the current series of post, I was at the point of forecasting volatility. There is several ways to just that; this very topic is the subject of a lot of research in finance. Different models to model volatility are available and they range from both ends of the complexity spectrum. I am going to be using what I think is one of the most popular: the GARCH(1,1). Just as a side note however, I don’t think it is the best model to use, but I do think that the simplicity of it makes it very attractive. For the more sophisticated quant crowd, in the GARCH family, the EGARCH seems to better forecast market volatility than its counterparts. I will not go into to much detail on the GARCH process (ie this is not meant to be an introduction post), if you would like to hear more about it, please let me know in the comment section.

For SPY since 2000, here is what a GARCH(1,1) model looks like, plotted vs the 21 day standard deviation with the residuals at the bottom. Results have been created using the tseries and quantmod libraries for R.

In terms of significance, the model significantly filtered the ARCH effect and the conditional normality assumption does not seem to be violated (using Jarque Bera and Box-Ljung tests). Regardless of the textbook testing, eyeballing the chart, we see that the model is fairly good at predicting SPY’s volatility. Now that we have the model in place, the next post should be on how to use a similar model on volatility of volatility once it has been stripped of its correlation with the actual volatility to see if we can improve our trading results and especially our regime switching strategies.


About these ads

14 responses to “Volatility Forecasting Using GARCH(1,1)

  1. I’m following your blog now as you are putting interesting stuff up. Hoping that at some point that you do show an EGARCH example for the SPY.

    The GARCH(1,1) chart is hard to read (I know, getting charts right on WordPress is a pain). When you get the time, I would be interested to see what you are going to do with this volatility forecast. How do mean reverting strategies versus momentum strategies fare in different volatiltiy environments? Thanks for the good posts.

    • Thank you for the comment Frank,

      In terms of volatility environment, it seems that high volatility favors MR strategies and that the opposite favors momentum. I plan to post a regime switching system using the GARCH forecast very soon. As for the EGARCH example, I can surely do one, do you think it would be better to have it in a quick post like this or more of an introduction format ?


  2. I would be interested in finding out the details of the GARCH calculation if you have any good introductary links to hand.



    • In the equation S(t+1)=S(t)*(1+mu+sig(t)*z(t)) where z~N(0,1). Even if we know S(t) and mu, we are still estimating sig(t) because of the random z, right? We cannot let z(t) happens lots of times and compute the sig(t). That’s why you are using the 21 day std? But I doubt it still pulls much information from the past sigma. What about using historical implied volatility(t)?

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s