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What makes GARCH(1,1) so prevalent in modeling especially in academia? What does this model has that is significantly better than the others?

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simple, easy to use and fast –  pyCthon Feb 13 '13 at 3:36
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Freddy is right .. and I think we have to change the wording of the question ... I don't dare to edit it, but would you Wang Weinan? GARCH does not predict prices but (if at all) volatility. –  Richard Feb 13 '13 at 12:54
    
Just did so! Thanks Richard –  Wang Weinan Mar 5 '13 at 7:15

2 Answers 2

up vote 17 down vote accepted

First, Garch models stochastic volatility. Thus its use should be limited to estimating the volatility component. The difference in some of the volatility models is the assumption made of the random variance process components.

I believe it has been popular because it is an extension of the ARCH family of models and it is relatively easy to setup and calibrate because it relies on past observations. Think of it this way: If you are to pinpoint your PhD dissertation topic would you take the risk to delve into deriving a new model, taking the risk you utterly fail and get nowhere over your x years of research or are you more likely to work on extensions or improvements of what currently exists? The same applies here GARCH is an extension of ARCH and there are numerous extensions of GARCH as well, such as GARCH-M, IGARCH, NGARCH...

I disagree with cdcaveman that it is the best model out there because it suffers from major deficiencies. Every model makes assumptions but there are better models out there for sure which is why I do not know of too many volatility traders that rely primarily on GARCH models in their quest to forecast volatility.

Deficiencies:

  • It depends heavily on past variances
  • The definition of "long-term variance" is at best arbitrary
  • making the assumption of the randomness originating from a normal distribution
  • The weights are just a result of optimization (MLE or other optimizers) of past data and make up the bulk of the calibration process. Volatility dynamics are changing in the same way as most other inputs to asset prices are dynamic thus making the assumption that an optimization of past variances, which results in the weights that make up the bulk of the current variance estimate, will yield anything that produces excess returns is a horrible assumption, imho.
  • Though most multivariate models can get quickly complex, multivariate GARCH can be tricky in regards to specifying the covariances (VECH or BEKK come to mind). (credit to Bob Jansen for pointing out this aspect of GARCH).

Volatility models that are originating from trading desks and that are rarely to be found in academic paper or the public domain often

  • do not make a normal distribution assumption of the variance dynamics
  • heavily incorporate regime shifts
  • rarely rely on functions of linear nature
  • incorporate correlation structures with other asset classes and even non-price return related inputs.

In summary, its a neat model to output something to show off within minutes. Whether the results are usable is an entirely different question and again I do not know of too many pure index vol traders who embrace GARCH.

Edit:

A look at the SABR model (or dynamic SABR) might be beneficial when searching for better models, though the "backbone" dynamics of the SABR model are more applicable for some derivatives than others.

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Thanks, Freddy! That's very helpful! –  Wang Weinan Feb 13 '13 at 4:54
    
Also, I would like to know why are people tend to use GARCH(1,1) but not other values for p,q? –  Wang Weinan Feb 13 '13 at 4:54
    
Erroneous simplicity assumptions? After all, we all think most recent events are more relevant than the ones longer time ago. –  Matt Wolf Feb 13 '13 at 6:02
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Another drawback of GARCH is that it is impractical to estimate multivariate GARCH so you can't really use it with more than a small number of assets. –  Bob Jansen Feb 13 '13 at 7:23
    
Thanks! great response..... i don't use Garch to trade... think about what garch will tell you if you looked at it right before earnings.. I like how you talk about relative pricing.. a trader or maket maker would look for relative pricing anomalies.. i think if foward vol in the back of the term structure is priced the best .. that is best to use as a basis.. buck vega or root vega.. –  cdcaveman Feb 13 '13 at 7:27

Volatility tends to cluster and mean revert... garch incorporated the behavior the best..... Ema doesn't do that.. its a step beyond exponential smoothing and weighting to replicate vol behavior

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Garch by far does not incorporate the behavior the best. Thats a pretty bold statement at best. –  Matt Wolf Feb 13 '13 at 4:09
    
Freddy is correct, there are better "general" models known to the academic communities and that is still far from what is state-of the art in the industry –  pyCthon Feb 13 '13 at 4:22
    
great.. so tell the guy about the other models.. i was just speculating as to why the guy got that impression.. just trying to contribute :) –  cdcaveman Feb 13 '13 at 7:32
    
Agree with @cdcaveman. unlike other models, GARCH is capable of catching persistency, which allows for prediction –  Anya Mar 6 '13 at 10:20

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