How are volatility estimates used?

[miggety]

Hi All, I've asked a question or two on these boards about volatility and seen a couple of other threads on the subject posted as well. I'm still trying to wrap my head around the idea of how this information is used. For example, I know with a GARCH I can forecast volatility say 10 days in the future. My questions is once I have this estimate, what is it then used for? Can some one give an relatively simple example of a situation where they'd need to know future volatility? Is the estimate used as a parameter to some other model? I understand the calculations for GARCH but i'm not seeing the applications of the model, i'm hoping someone could provide some concrete examples.

Thanks in advance!

 

[miggety]

How is that information used to price assets? If i have an estimate of volatility 10 days out, how would i use it in that case? Regarding Cao's comment, the question isn't "what is the purpose of forecasting the market", it's more along the lines of how. I understand that GARCH is one piece in the puzzle, i'm trying to understand how that piece is used. Once i have the model, i'm looking for a concrete example of how i'd use it to, as you mentioned, price an asset.

 

[Yike Lu]

If you have a good vol predictor, and your vol predictor says there will be more vol than the IV of a given option, you buy the option and delta hedge, and make a profit (assuming your predictor was right).

The rest of the main use of vol estimates is just further generalization of that idea.

 

[miggety]

Thanks cao that's exactly what i was looking for. One other question, if i wanted to estimate the price of an option 10 days from now would I use the estimate from my GARCH model of volatility 10 days from today and plug that into the Black Scholes formula? And if that is the case would I then use Monte Carlo simulations to estimate the price of the stock 10 days from now as well to plug into BS also?

 

[Yike Lu]

"The rest of the main use of vol estimates is just further generalization of that idea."

I think there's a lot more than just this...

Well, in the domain of option pricing, that's really as far as it goes - making money, or keeping yourself from losing money.

Of course there are other domains, but options pricing is first and foremost.

 

[miggety]

Thanks Yike Lu, I somewhat understand what you're referring to. I've been reading Euan Sinclair's "Volatility Trading" to get a better understanding of how volatility is used in the market place. From what I gather, when vol trade you're comparing you're volatility estimates to IV and and using delta hedging to attempt to hedge out all other risk factors. From what i've read so far, GARCH isn't really applied in case because it just gives a point forecast of volatility which isn't all that useful. What is instead used are volatility distributions and this is done using volatility cones. Let me know if my understanding is off. Thanks guys.

 

[Yike Lu]

From what i've read so far, GARCH isn't really applied in case because it just gives a point forecast of volatility which isn't all that useful. What is instead used are volatility distributions and this is done using volatility cones. Let me know if my understanding is off. Thanks guys.

Certainly there must be better methods, although this is not my personal area of expertise. I'm just pointing out the basic idea of using a vol forecast, and GARCH falls into the category. The practical use of pricing is just a special case of vol trading.

Another (this time orthogonal) use would be e.g. portfolio optimization.

 

[miggety]

Thanks Yike, i'm trying to get an example of a situation where you would need to use GARCH to estimate volatility N days out and then once you have that estimate what could you do with it next? Would you plug into a BS equation to price an option? I've been at this a couple months I'm starting to understand some of the different pieces, Black Scholes, GARCH, monte carlo, etc.....i'm just not sure how they're used in conjunction.

 

[Yike Lu]

Very simplistically, say there is an option trading with 30 days from expiry, with IV of 18%/20% (bid/ask). Your 30 day GARCH says future vol should be 14%. You short the option and delta hedge, expecting to make 4 vol points.

You can plug in your GARCH vol into BS to see what the price should be and therefore see how much you expect to make.

You can also MC sample paths to get an idea of the distribution of your PnL over time by setting up some simulation where you make a path with your vol and delta hedge it.

 

[Ken Abbott]

GARCH is often used to proxy implied vol time series where they don't exist or are of poor quality.

 

[miggety]

Thanks for the responses. Everything doesn't make sense yet, I'm still having problems connecting all the dots but the information you all are providing is very helpful.