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# Term structure of implied volatility - SPX

Discussion in 'Options' started by ben111, Jun 9, 2010.

1. ### ben111

Hello,

can somebody explain how the implied volatilities of the different expirations of the SPX options are linked? Is there any algorithm or general rule how back month IVs react to changing IV of front month options?
Normally when market goes down the IV of front month options will gain more in percent points than longer dated options. But how high will be the increase of the back month options in that case?

(Example: atm front month option has IV of 25% and increases to 30% - increase of 5 percent points. How much will increase the IV of the same strike front month +1 ? Normally something less than 5 percent points but how much?)

What calculations use the market makers?

Ben

2. ### MTE

There is no direct relationship between the different expirations so there is no formula. Term structure changes just like the skew does and it depends on the demand/supply in various expirations and strikes.

3. ### ben111

@MTE

But how are the market makers calculating their IVs of longer dated options or how do they model the term structure of vols?

Also for VIX and SPX there is a almost linear relationship. On average VIX moves 5-6 times more than SPX; eg. SPX goes down 1% you can expect on normal days (no crashes) that VIX will rise 5% to 6%.

Regards

4. ### MTE

It's interesting that you ask how they model the long dated volatility, but not the front month. Why? What, in your mind, makes front month volatility different?

In simple terms, they model the volatility surface and then calibrate it based on the market prices.

5. ### ben111

@MTE

There is no special reason why I'm interested in the longer dated options. It's just interesting how the term structure of vols ist modelled. I thougt that they start the process with the front month options and use their vols to get the vols of the longer dated options. Therefore I thought there must be something like a formula how they are connected.

In simple terms, they model the volatility surface and then calibrate it based on the market prices.

Right! And how do they model the surface? What model do they use and how is it calibrated?

I know that are a lot of questions but want to understand it in order to get a better feeling for the behavior of the IV.

Thanks

6. ### ben111

Example:

Actually the implied volatilities of the SPX options with strike 1000 are:

June: 33.54%
July: 33.26%
Aug: 32.35%
Sept: 31.63
Dec.: 30.74%

Now market goes sharply down and all IVs rise. Can you somehow say to what level the term structure of these strike 1000 IV will adjust?

Let's say June goes up to 38.54% (+5%) what IVs will the back month SPX 1000 options have? Or is it impossible to model?

Thanks

7. ### MTE

I don't think there is a precise way of calculating what would happen to back month volatilities if the front month rises by x%.