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dcthulu
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How is ARCH different from Implied Volatility?

March 8th, 2018, 2:33 pm

If I want to know the volatility of a stock tomorrow, I look at its implied volatility, given by the market (option demand). 
So why do I need ARCH/GARCH? 
What benefit does ARCH/GARCH provide that implied volatility does not?
And vise versa?
 
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outrun
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Re: How is ARCH different from Implied Volatility?

March 8th, 2018, 3:27 pm

ARCH/GARCH are *models*, they are calibrated to historical data/events (model parameters) and they have a state that summarized part events (the latent volatility estimate). Like any model ARCH/GARCH has flaws.

Implied volatility is forward looking and is driven by supply and demand. It is not always a prediction of the future. If I buy 250.000 at the money IBM options then the implied vol will go up instantly.
Implied volatility is loosely tied to expected future historical vol and it will typically include predictable future details like annual report dates, bank holidays. It will also have expectations about the future being different than the past: e.g. a company might had said "one of our factories broke, production will be unstable going forward". Implied vol is loosely tied to expected future actual vol because you can hedge implied with actual(ish). Lots of professional traders try to statistically arbitrage between those two -which drives them closer together-, but there is also other factor that go into implied volatility, like risk aversion. The fact that I can drive up implied by buying a lot is related to risk aversion. As some point people no longer want to sell, or can no longer sell at their expected future vol estimate. maybe they think "does this guy know something about the future that I don't?!" or maybe his boss is saying "we are running out of capital to protect our trading firm against the large implied vol exposure you have because you sold too many options. Buy them back. At any price."
 
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Alan
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Re: How is ARCH different from Implied Volatility?

March 8th, 2018, 3:42 pm

There are many implied volatilities. Even if you are talking about an at-the-money implied volatility (IV), there is a different one for each option expiration.
If the option expiration is not tomorrow, then the IV will reflect events occurring beyond tomorrow. In addition, the farther away the expiration is, the more the IV will incorporate risk-aversion effects and be "too large" vs. the realized vols. (There is a very strong term structure effect). The good thing about IV's, however, is that they are *forward looking*.

ARCH/GARCH volatility estimates, on the other hand, are more time-uniform and reflect the actual stock price process without the strong risk-aversion effects. But they only know about history.

The bottom line is that tomorrow's volatility is quite hard to predict. Your best predictor will likely incorporate a combination of a GARCH-type model and the IV. Even then, it will only be mildly accurate. 

================================================
edit: cross-posted with outrun, who already says a lot of what I say. But I will leave it with the following addition.
I make a point in a recent book that GARCH (alone) vol predictors are 'sub-optimal',  as they do not account for forward-looking events. 
Similarly, IV (alone) vol predictors will also be sub-optimal for the reasons given above + outrun's excellent reasons. 
Last edited by Alan on March 8th, 2018, 3:56 pm
 
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outrun
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Re: How is ARCH different from Implied Volatility?

March 8th, 2018, 3:56 pm

good point about the "many implied volatilities". The fact that it depends on strike -even if you just consider options that expire tomorrow- means that knowing "the volatility of a stock tomorrow" does not contain all the information you need to price derivatives that expire tomorrow.
 
dcthulu
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Re: How is ARCH different from Implied Volatility?

March 8th, 2018, 4:05 pm

Alan - I'm curious. How would one combine GARCH and IV into a single model to predict future volatility? Explaination (can be high-level or detailed).
 
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Alan
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Re: How is ARCH different from Implied Volatility?

March 8th, 2018, 4:29 pm

Sure. 

A simple scheme takes the final prediction to be a weighted linear combination of a GARCH-based prediction and an IV-based prediction. Then, determine the weight to minimize the historical prediction error.
 
dcthulu
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Re: How is ARCH different from Implied Volatility?

March 8th, 2018, 4:45 pm

Thank you. Can you refer me to any documentation that illustrates the details of constructing this hybrid  [GARCH / IV] model ?
 
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Alan
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Re: How is ARCH different from Implied Volatility?

March 8th, 2018, 4:53 pm

No, I used the general idea at a money manager some 20+ years ago. Just experiment. But I can add some closely related things to look at.

First, the general subject here is "combining predictors". If you google that, you will see lots of stuff in the context of machine learning. So I suggest that you look at that. (outrun knows a lot about that...)

Second, another way to proceed might be to include the IV's as exogenous variables in the GARCH model. (I haven't tried this, but the idea has crossed my mind). For that, just take a look at the documentation for the GARCH model(s) implementation (assuming you will not write your own). For example, I'm pretty sure there is an R GARCH package allowing this generality. Of course, this just tells you the mechanics -- there will still be a lot of "art" in choosing which type of GARCH and which type of IV to use. Again, your best bet is to experiment.

Finally, if you go to "Option Valuation under Stochastic Volatility II" at amazon, use the "Look inside" feature and search for "R-probabilities", you will see some general advice on pg. 257 about volatility prediction that you may find valuable.
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