ASX Charting Course

Chapter 17

Historical Price Volatility

Volatility is a measure of how wild or quiet the market is relative to its history. It can be more accurately defined as the standard deviation of a series of price changes measured at regular intervals. To the pure chartist, this indicator can be employed as an initial filter, which can applied over a selection of markets to arrive at the most suitable individual markets that will fit a particular style or method.

Volatility is generally measured using price changes expressed in logarithmic form, but can also be assessed using percentage changes in price. Price percentage changes would appear to reflect a more accurate picture of the market, despite the assumption that prices change at fixed intervals, which isn’t necessarily how it is. On the other hand, logarithmic price changes assume prices are changing continuously, but that doesn’t necessarily depict the market as it really is either.

A different approach at calculating historical volatility is to use the range between the high and the low and measure how it changes, rather than using standard deviation.

There are several steps to calculating historical volatility:
Percent Price Changes –

Xi = P(i+1) – Pi / Pi

Logarithmic Price Changes

Xi = log [Pi+1 / Pi]

where P is the price at the end of each interval i

High/Low Range Price Changes -

σ = √ 1/n Σ {0.5 [log (Hi/Li)] ^2 + 0.39 [log (Pi/Pi-1)] ^2}

where:
n = period
H = high price
L = low price
P = the price at the end of each interval i

n

m = 1/n Σ Xi

i=1

where m is the mean of n occurrences ( X )

Standard Deviation – can be simply described as the first standard deviation, which is about 68% of the scores closest to the mean.

Most software packages annualise historical volatility by multiplying the resulting standard deviation by the square root of the number of bars in a year. Depending on the time frame selected the number of bars will be determined by multiplying a daily indicator by 252, weekly by 52, monthly by 12 and intraday by (252 X Number of possible bars in a day.)

How to use it

This indicator is most often used by options traders, but can sometimes be employed in the selection of suitable markets for particular trading methods and styles. It can be used in conjunction with implied volatility to see how the current markets expectations differ from history and finally it is a crude indicator to a change in trend.

We can see from the above example that the volatility during September was fairly static apart from the beginning of the month which saw a pick up in volatility as a result of a change in trend and a subsequent retracement in price. The red line is a median line of price and we can see when price is at its farthest from this line, volatility appears to be at its lowest. The fact that volatility has picked up again as the market approaches the old highs indicates a high probability for the market to continue.