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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?

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If the market opens in balance, or to a lesser degree of probability in range, measuring the range of the previous day +/- 10% works decently. But an opening out of range can go anywhere.

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I am performing my analysis on the Index and making the trades on the underlying futures market. I learned the formula for the Dax index from someone else and it does give a good indication of the range of prices for the following day.

I will keep looking at volatility index closings and index closings to see if there is a quantifiable relation ship to the price range over time and the volatility for that underlying index.

Have you considered the R1/R2 and S1/S2 pivot points? This is exactly what they are intended for. The pivot itself is a close-weighted median which serves as a proxy for value, and the R and S levels are based on the range for the day, and are used as a measure of potential range, thus volatility. @Fat Tails has done a lot of work with volatility bands, so perhaps he can comment on this for you.

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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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I generally use the expected volatility as calculated an additional confirmation for a trade (sim). I never use it as a single indicator of support or resistance.

That said I will use both formulas daily to compare against the markets actual price range. I have not yet used this formula for the VIX but will begin to do so.

Pivot points are based on the historical volatility. The historical volatility is not necessarily a good predictor for the implied volatility. Let us consider the following cases

(1) During the first days of January, the historical volatility based on the prior week is typically low, as prices do not move much during the X-mas holidays. However, the implied volatility may be a lot higher than the historical volatility.

(2) After an earnings release, the historical volatility is typically high, while the implied volatility is a lot lower, because the news is already out.

Floor pivots take into account the (historical) volatility of the prior day. However, this volatility is not measured as the close-to-close move, but it is measured via the daily range.

The floor pivot R2 is calculated by adding the range of the prior day to the typical price of the prior day. The typical price - also called main pivot PP - is calculated as (prior high + prior low + prior close)/3. In a similar way the floor pivot S2 is calculated by subtracting the range of the prior day from the typical price. Floor pivots are thus based on value (typical price) and historical volatility (prior day's range).

If you use N-day rolling pivots, the volatility is based on the range of the prior N days, which in average should be sqrt(N) times larger than the range of a single day.

The following sources contain more information on floor pivots:

Welles Wilder - New Concepts in Technical Trading Systems (1978) - Section VII, The Reaction Trend System

This is a pretty dated book, but one of my favourites. Welles Wilder does not mention floor pivots, but he mentions

buy point B1 = PP - (H - PP) -> identical with floor pivot S1
sell point S1 = PP + (PP - L) -> identical with floor pivot R1
high breakout point HBOP = 2*PP - 2*L + H -> identical with floor pivot R3 = R1 + range
low breakout point LBOP = 2*PP - 2*H + L -> identical with floor pivot S3 = S1 - range

He used buy and sell points when the market was in reaction mode, and breakout point when the market was in trend mode.

Mark Fisher: The Logical Trader

Other than floor pivots, Mark Fisher introduces the notion of the pivot range.

John F. Carter - Mastering the Trade - Chapter 7, Pivot Points

A pretty standard approach based on trading pivot points.

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