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Calculating Volatility

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Scotttombaugh View Post
The Dax Index provided by Deutche Borse gives an expected volatility range that can be extrapolated to a daily expected volatility range.

The formula is: (VDAX Close/19.1)*(Dax Close/100)
High for the day = Dax Close of previous day + Dax volatility
Low for the day + Dax Close of previous day - Dax volatility

The previous days day close can be found on the Deutsche Borse web site.

Question; Do the S&P or Dow Jones or any other US Index have a similar way to calculate the expected range of the index for the following day from the previous days close or range or?

Thank you,

Scott

The hint in your post is the factor 19.1. This is in fact the square root from 365, which was used to convert the annual implied volatility into a daily volatility term. You have not disclosed the source for your formula, but I think that it is debatable. Usually the daily expected volatility is calculated by using the number of business days per year. Most of the time the number 256 is used, because it is easy to obtain the square root from this number.
Therefore the correct factor would be 16.

Both VDAX and VIX give an indication of the expected annualized change of the underlying stock indices. The implied volatility is calculated from a basket of options. The annual percentage value that is obtained refers
to a 68% likelihood that the move will be smaller or equal when compared to this value.

Now you can calculate the "expected daily range" for a price move of the FDAX or ES. Please be aware that the "expected daily range" is the range such that

- there is a probability of 68% that the actual range will be smaller
- there is a probability of 32% that the actual range will be larger

Let us take the VIX close of yesterday which is around 14. By dividing through 16 you will get the expected daily change, which is 0.875%. Starting from yesterday's settlement price for ES 06-13, which was 1650.00, based on options implied volatility there is a 68% probability that ES 06-13 will close within the range

range low = 1650.00 * (1 - 0.00875) = 1635.50
range high = 1650.00 *(1 + 0.00875) = 1664.50

The meaning is that there is a 68% probability that ES 06-13 will close within this range today.


Modified Formula (for both DAX and ES)

This means that you can use your formula with the VIX and ES

expected price change = (VIX_Close/16) * (ES_Close/100)
range high = ES_Close + expected price change
range low = ES_Close - expected price change

But please use the divisor 16 in any case.

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