Among the models proposed to forecast Realized Volatility, the HAR-RV from Corsi stands out in terms of performance and simplicity.

“HAR-RV” stands for Heterogenous Autoregressive model of Realized Volatility and is based on the so called “Heterogenous Market Hypothesis”. This states that financial markets are an interaction of people acting at different fequencies (eg firms operating on High-Frequency, dealers trading intraday and institutional investors looking at much lower frequencies). Each class of market agents will cause volatility at difference frequencies, which will affect each other class to a certain degree. From these considerations it comes the idea to model each volatility frequency independently but jointly. This brings us to the following, very simple in structure, model:

RV_d+1 = b_0 + b_1 * RV_d + b_2*RV_w + b_3*RV_m

where RV_d+1 is the next day RV, RV_d is the previous day RV, RV_w is the previous week average daily RV, and RV_m is the previous month average daily RV. RV in this case is the square root of the sum of squared intraday returns at a given frequency.

b_0,b_1,b_2 and b_3 are the regression parameters to be found.

As you can see, the model is basically a simple regression, however it compares in terms of performance with way more complicate model, such as ARFIMA. In fact, HAR-RV is able to model the main stylzed facts about RV, such as autocorrelations and long memory effects (although the model itself is not a long memory model, it takes advantage of the finding that simple sum of AR(1) processes can appear as a long memory process).

Here is a plot of forecasted Realized Volatility:

and here are the residuals over the actual RV:

Andrea

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## About mathtrading

My name is Andrea La Rosa and I am a quant trader based in the UK.
In the past I worked as a quant in the prop desk of an investment bank, before deciding to fully dedicate myself to quantitative trading.

Hi Andrea,

have you checked this paper?

http://jfec.oxfordjournals.org/content/7/2/174.abstract

I work as a Quant for a German investment bank. I’m starting to get my head around ARFIMA although it’s pretty easy to get trapped in overanalysing. Have you read the Saint Loras – Johnson approach to long memory effects? That’s crazy shit, either I’m stupid or they’re mad.

I think it’s great to start a blog about the topic, although I would put more effort into avoiding spelling mistakes such as “advatange” (it’s advantage actually). It’s a pity when such mathematical skills are not matched by an equivalent attention to language.

Hi Mike,

Do you know the full title of the Saint Loras – Johnson paper you mentioned? I am interested!

Hi Mike,

Indeed the article from Corsi you are referring to is what the post is about. Thanks for linking it.

I haven’t read about the Saint Loras – Johnson approach, maybe you can point me to a paper?

In general I agree with you, the risk when dealing with this kind of subject is to get lost in some theoretical discussion, which from a practitioner’s point of view is not always useful. But I guess it all depends on what you final aim is.

And thanks for pointing out the typo.

Andrea

The Saint Loras – Johnson is still unpublished, circulating in Swiss universities.

Basically it disrupts a few “dogmas” in the literature, for instance, Bollerslev, T., Mikkelsen, H.O., 1996, (Modeling and pricing long memory in stock market volatility), and promotes a much more ad hoc parameterization.

Thank you for this Mike, I will keep an eye open for when it gets published.

Andrea

A side, trivial question (feel free not to answer if you don’t want to): may I ask you what is your net salary? Thanks

I have been following this trading blog, what on earth has personal salary amounts got to do with this thread? This is supposed to be a discussion about trading strategies……

Well John, since I’m trading my time for money I guess it’s appropriate indeed!

You can find code for the model and some high frequency data here:

http://eranraviv.com/blog/a-simple-model-for-realized-volatility/

Both in R software.

Hi Eran,

Thanks for sharing it.

Andrea

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