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# Forward volatility calculation.

Discussion in 'Options' started by jansen_ja, Nov 16, 2003.

1. ### jansen_ja

Does anybody know where to get something what could calculate forward volatility?

With forward volatility i mean what should become the implied volatility over a period of time in the future, knowing volatility from now to TIME1, and knowing volatility from now to TIME2.
Then what should be the volatility from TIME1 to TIME2?

or in other words:
Imagine jan04 trading at 60% and apr04 at 50%, what should apr04 be trading when reaching jan04, (imagining jan04 will stay on vol 60% until expiration)
Then what should now be the volatility of april04?
it should be lower then 50%, but how much?
This is an important instrument for evaluation optionprices, specially when there are differences in volatility over different periods.

2. ### jem

I hope someone answers this because I am pretty much just and observer of options. I could be dead wrong. But isn't your question pretty much the point of of professional options trading or market making?

3. ### Maverick74

What you are referring to is skew. The skew is what dictates what the vol is over different strikes and different months and it changes daily depending on the paper that comes into the pit. You can't use a formula for what vol should be in jan. That's like using a formula for what the underlying will be in jan. If you know that then you can predict the future. The vol will change constantly every day. Hell by jan the april vol could be 100% up from 50%.

By correctly estimating the skew you can graph what the vol should be NOW according to today's vol estimates. The only general things I can say about vol is that typically, the farther you go out, vol tends to be higher. This is due to the fact that there is more uncertainty further out. So again we come back to the vol smile. This smile gets wide over time and over OTM strikes. So all I can say is, all things constant, by jan the april vol would tend to come in a little. However, you cannot use that because come january, if everyone starts buying premium, vol could run up 50 ticks.

There are many great software programs out that there that will let you graph the skew and change the skew to whatever you want so you can price options in the future. Hope this helps.

4. ### jansen_ja

I am not talking about skew over different strikes, I am just referring to different months trading different volatility, over the same strikes. (if you call that skew as well... ok...didnt know that...)

I didnt formulate my question well, or you misunderstood what i meant.
I will try it again.
Imagine the jan04 50 call trading at IV 70% now.
At the same time, the IV for the apr04 50 call is trading at IV 50%.
Then looking at the situation at this moment, the market does make an estimate for what the SV is gonna be over the period Jan04-apr04. Because from now till jan04 costs IV 70%, and from now till apr04 costs IV50%. Then based on these assumptions what is the market estimate of jan04-apr04 volatility AT THIS MOMENT? I would guess something like 40%, but dont know exactly.
And yes, you can calculate this for sure.
But nevermind.

5. ### Maverick74

Yes, i think I understand what your asking and again it's skew. And the answer to your question is 50%. The market is telling you that it's predicting the stock to be less volatile over the long run then the short run and it's pricing that volatility at 50%. At least today it is. Tomorrow it could be 55%. You can't price the vol between jan 04 and april 04 because that option does not exist. Now if one were to create a flex option or exotic option that was structured to begin in jan 04 and expire in april 04 then that is a different story. That would be an OTC product.

Maybe the better question to ask is what are you trying to do with this information? Perhaps you are going about it the wrong way.

6. ### TheStudent

jansen_ja is right - skew traditionally refers to the difference in IV at one point in time over a variety of strike prices.

jansen_ja is trying to do something with the calender spread in vol. I'm not sure what it is, but it does sound interesting.

if 6 month vol is priced at 60 and 12 month vol is priced at 40, then the implied mkt prediction is that vol will decay 20pts btw T + 6mo and T + 12 mo, assuming you have used the right interest rates to take out the effect of the forward yield curve.

I suppose if you believe that that is ridiculous (why should vol decay 20pts over 6 months), you want to sell the 6 month and buy the 12 month and delta hedge accordingly.

7. ### NUTSNEAL

Assuming you just picked your time frame out of the air Jan 04 and April 04. If that is the case you can compare Jan 04 to March 04 June 04 or Jan 05 at least for some insturments.

8. ### Maverick74

Yes, you would put on a calendar spread for that trade but that is what you trade calendars on, the skew. This is why calendars are put on to begin with. Otherwise there is no edge in the trade. And the reason the jan's are higher could be for the simply reason that there is just a lot of paper being bought in that month. Perhaps someone knows something you don't know. And from being on the floor, I can tell you they most definitely do! LOL.

But back to his question about actually coming up with a forward volatility rate between jan and april, well I'm still going with it doesn't exist. I would use the 50% that the april options are trading at. Otherwise you need to create a structured term product for that period and price it in the marketplace.

9. ### quantpatterns

jansen_ja & Maverick,

maverick does have a point. But I think jansen_ja is trying to find something similar to the "forward curve" in fixed income securities.

The formula for the forward rates given certain assumptions of term structure of interest rates is trivial and can be calculated.

What you are talking is a term structure of implied volatility. Yes, there is such a thing. The subject is rather complex. It depends how you define the term structure of volatility and wheter it's stochastic, heteroskedastic etc. From this one can derive a volatility surface map.

Go read some more quant books. Requires some statistical techniques like bootstrapping and jacknife. And whether the underlying process is Ornstein Ullenbeck etc. Obviously, one has to do calibration with real market data to get accurate values.

have fun!

10. ### NUTSNEAL

Would you please recommend 2 or 3 quant books (intro or overview) that might be good to begin with.

When it comes to trading I can generally tell rather quickly if the book is worth my time or not. But with a quant book I would have no idea if I was in a gold mine or just a deep well.

Would appreciate your help, anyone else also.

Thanks

#10     Nov 17, 2003
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