Forward volatility calculation.

[TheStudent]

Quote from 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!

Interesting, I didn't think about bootstrapping vol. Learn something new everyday.

Could you perhaps sketch out the broad ideas behind a term structure of vol?

Thanks.

 

[MDCigan]

Here is an excerpt from an old newsletter of mine which I think addresses the issue/question here. FWIW, the newsletter was the old Saliba newsletter and this was written by one of his trading partners so I am pretty confident this is right. It confirms what Jan is trying to analyze.

****************************************************
Forward Volatility Analysis

Forward volatility analysis is the analysis of term structure and the volatilities implied by the differences in implied volatilities between months. Consider a 30-day option and a 90-day option:
Since the expiration dates overlap and both trade at a different implied volatility, there is a volatility implied for the period between the two dates. This is the implied forward volatility. This makes sense intuitively, since the volatility that takes place during the life of the 30-day option must also affect the 90-day option, then the difference in implied volatilities must be explained by the expected volatility between day 30 and day 90.
Computing Forward Implied Volatility


Where:
= Implied volatility of the longer dated option
= Implied volatility of the shorter dated option
= Days to expiration of the longer dated option
= Days to expiration of the shorter dated option

For example:
= .54
= .36
= 90
= 30

= .61 or 61%

This means that by pricing 90-day volatility at 54% and the 30-day volatility at 36%, the market is pricing 61% volatility for the period between 30 and 90 days.

How do we use this information to trade calendar spreads? We simply use this as a part of our decision making process. Common sense must be involved as well. There may be a perfectly good reason that forward volatility is at a substantial discount or premium to the long-term mean. What if the 30-day option includes a holiday weekend or a seasonal slow period (August, for example)? It makes sense that it would trade at a discount to the other longer dated options. What about the October (crash) options or options covering earnings periods? They usually trade at a premium, and for good reason.

Let’s take a look at a decision making process for a calendar trade:

Market View: I expect the market to continue to move sideways through the end of the year, however, with implied volatilities at these low levels, I am reluctant to sell volatility outright. I would like to put on a calendar spread instead.

Forward Volatility Analysis: ABC stock has a 2-year historical volatility of 40%. The options are priced as follows:

Month Implied Volatility Days to Expiry Fwd. Implied Vola.
Sept. 35% 38 NA
Oct. 41% 66 48%
Jan. 36% 157 32%

This analysis reveals that the volatility implied for the period between September expiration and October expiration is 48%, 20% higher than the long term mean. The Sept./ Oct. calendar might be considered a sell candidate. The volatility implied for the period between October expiration and January expiration is 32%, 20% lower than the long term mean. The Jan./Oct. calendar might be considered a buy candidate. Given the above market view, the logical choice would be to buy the Jan./Oct. calendar spread.

There are many other considerations that go in to the selection of a calendar spread, and buying cheap or selling expensive implied forward volatility is no guarantee that you will make money, but it can be of great help if one is “on the fence” regarding strategy selection.

 

[Maverick74]

Hey, do you have any other old Saliba newsletters lying around? Tony's insights are invaluable.

 

[MDCigan]

Quote from Maverick74:

Hey, do you have any other old Saliba newsletters lying around? Tony's insights are invaluable.

Yeah, I've got a couple of them saved in pdf format. I've also got Coulda Woulda Shoulda saved as pdf if you want that also. Send me a private message with your e-mail address and I will send them.

 

[jansen_ja]

mdcigan, thats exactly what i meant.
i already have the formula for calculating forward volatility.
it is a nice easy formula, you can put it into excel easily, and it gives a nice insight in the volatilty structure on a stock... specially when there are big differences in iv over different months.

Here comes the formula:

FV=Squareroot((T2*IV2-T1*IV1)/(T2-T1))

where T2=further away expiration(in days or years or whatever)
where IV2 is iv of furthest away optionseries
where T1=nearby expiration
where IV1=iv of nearby expiration

FV is supposed volatility between T1 and T2, estimated right now.

if you dont agree with the FV, you could buy or sell the FV by opening a gamma neutral position, with long or short FV vega!
isnt that great?!!!

 

[jansen_ja]

Here is the formula in a excel file for calculating the FV.
I am not positively sure it is correct, there i found it out myself with a math student friend of mine, but it should be correct.

 

[sle]

Quote from quantpatterns:
jansen_ja & Maverick,
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.

The reason you have such a thing as forward rates is that you can lock in the rates by selling a shorter bond and buying a longer bond. In a similar manner, you can lock in the forward vol by going long on a calendar and shorting butterflies - you get a lock on forward vols at zero net cost. So, then you can estimate forward vol using SQRT( variance(end) - variance(start) / period length ). Note that variance should be normalized by time (from regular vol => vol * vol * time to expiry). As simple as a shot of scotch.

NB. Forward vol lock applies only to options on the same underl. instrument - so do not try to do it on treasury bond options, for example.

NB2. It is not possible to lock in implied vols away from the money for reasons that are too murky to get into.

Quote from quantpatterns:
And whether the underlying process is Ornstein Ullenbeck etc.

It is amazing how easy it is to make a difficult concept from a simple one - if you would have said "mean-reverting", it would not have sounded as bad-ass.

Quote from quantpatterns:
Obviously, one has to do calibration with real market data to get accurate values.

He was NOT asking about DK surface or any other stoch. vol models - his question was simple.

 

[quantpatterns]

Quote from sle:



It is actually much simpler. The reason you have such a thing as forward rates is that you can lock in the rates by selling a shorter bond and buying a longer bond. In a similar manner, you can lock in the forward vol by going long on a calendar and shorting butterflies - you get a lock on forward vols at zero net cost. So, then you can estimate forward vol using SQRT( variance(end) - variance(start) / period length ). Note that variance should be normalized by time (from regular vol => vol * vol * time to expiry). As simple as a shot of scotch.

NB. Forward vol lock applies only to options on the same underl. instrument - so do not try to do it on treasury bond options, for example.

NB2. It is not possible to lock in implied vols away from the money for reasons that are too murky to get into.



It is amazing how easy it is to make a difficult concept from a simple one - if you would have said "mean-reverting", it would not have sounded as bad-ass.



He was NOT asking about DK surface or any other stoch. vol models - his question was simple.

sle,

Haha. I guess I shouldn't have given the full treatment. Things can be as simple as you like or as detailed and complex as one like.

But it seems like you like to come on this board strutting your supposedly all knowing exotics knowledge. Many people here on ET knows about derivatives and even exotics one as well.

But good to have you around for a debate.

cheers

 

[sle]

Quote from quantpatterns:

I guess I shouldn't have given the full treatment. Things can be as simple as you like or as detailed and complex as one like.

True. Very much true.

Quote from quantpatterns:

Many people here on ET knows about derivatives and even exotics one as well.

Well, you right - i am bored and like to come here to show off All I was trying to say was that for a true discussion of this sort you should go to wilmott.

 

[jansen_ja]

Quote from sle:



you can lock in the forward vol by going long on a calendar and shorting butterflies - you get a lock on forward vols at zero net cost. ]

Sle, could you explain this a bit more clear, how you mean to lock forward vol?

When disagreeing with forward vol, i would just think about setting up a gamma neutral trade, then keeping it gamma neutral with slowly selling of the nearest month, done the trade with positive/negative vega, depending on your outlooks on future IV, or is this more or less the outcome from what you said above?