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# Forward Volatility and Volatility Surface

Discussion in 'Options' started by Grant, Dec 2, 2006.

1. ### Grant

Two questions, if I may.

Does forward volatility provide additional information over (plain vanilla) implieds or is it relevant only to exotics?

Similarly, does a volatility surface provide any insight? On a very basic level I assume
it fills in any gaps but being theoretical can it be used as a basis for extrapolation or inference?

Thank you.

Grant.

2. ### rosy2

do you mean taking the implied vol of forwards/futures to get your forward vol curve? or is your forward vol something else?

vol surfaces are used all the time to see what's cheap and expensive.

3. ### panzerman

By comparing the current surface to the historic surface, you can get an idea if an option is being mispriced, or that an event in the underlying is possibly about to unfold. Of course to build a historic surface, one must properly normalize the data first.

There is some evidence that surface structures are stable over time. If there was no stability, then all comparisions to historic data would be meaningless.

4. ### Profitaker

Grant

That's probably a bit too "quanty" for ET. You'd probably get more respone on the Willmott Forums.

5. ### Grant

Rosy,

In the context of options, by forward volatility I mean the volatility between two points in time (dates or expiries) derived from the spot ivâs.

The reason I ask can best be illustrated by a couple of examples (the formula is as constructed in Excel):

T1 = 1(year)
T2 = 2(years)
IV1 = 12%
IV2 = 10%

Forward vol = SQRT(IV2^2*T2-IV1^2*T1)/(T2-T1) =

SQRT(0.10^2*2-0.12^2*1)/(2-1) = 7.48%.

Now compare the next example:

T1 = 0.082 (30 days)
T2 = 0.164 (60 days)
IV1 = 15%
IV2 = 12%

Forward vol = 27.69%

Assuming my figures are correct, why is the first figure less than the ivâs, and why is the second greater?

What does this tell us, and how can it be used?

Panzerman,

I totally misread the nature of a surface, hence my question is no longer relevant.

But to pick up on a couple of your points, if I may. You say historic data has to be normalised. Could you be a little more specific? For example, if I had a series of daily ivâs for a certain month, why would these be inadequate in themselves â is it because of a possible shift in moneyness?

Stability over time: do you mean ivâs revert to the mean which over time would give the appearance of stability but in the interim fluctuate. By way of an analogy, a series of prices (log of changes?) over time exhibit a normal distribution but at intervals are volatile?

Thank you for your help.

Grant.

6. ### panzerman

When you normalise historic data, you must generate a relative strike, a relative IV, and be consistent in the time until expiration. Have a look at the file I have attached.

When I say surfaces are stable over time, look at the current surface for the December contract of your choice, and then look at the surface for the November contract when it had the same number of days until expiration (properly normalised of course), then the normalised October contract, then September etc... back in time. You will notice that the surfaces all generally have the same structure. The surface may have some irregularities due to weather events or terrorist attcks or other black swan event, but basically they should look similar.

File size:
24.5 KB
Views:
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7. ### Grant

Profitaker,

âquantyâ? Come on, nothing ET canât handle. Willmott so-far-up-your-own-arse forum? No, thanks. Nuclear Phynance is good (ex-Willmot refugees) with FDAXhunter, late of ET â always worth reading (and Aaron).

Panzerman,

Excellent info. Thank you.

Grant.

8. ### rosy2

maybe someone else can tell you about your figures. From what you say then you could do some kind of vol arbitrage. buy the 1y atm and 2 y atm and sell 2 1y 1y from now atm forwards.

if you have access, you can get a better idea of what i am saying by looking at how interest rate swaptions are quoted

9. ### nonprophet

miscalc: forward vol = 7.94%

10. ### Grant

Nonprophet,

Please check the attached file containing both examples.

If there is an error, I reckon its down to the idiosyncracies of how Excel determines priority and order of calculation.

(Attaching Excel files has proved difficult. If it hasn't attached, I'll keep trying)

Hasn't worked. Will try again.

Grant.

#10     Dec 2, 2006
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