Charting and Studies User Guide - CQG.com

Page 268
Historical Volatility (HVol)
Historical Volatility measures the market’s past volatility. It is defined as the standard deviation
of a series of price changes measured at regular intervals. It can be used in conjunction with
Implied Volatility to gauge how the market’s current expectations differ from history.
The Historical Volatility display appears in a window below its corresponding chart. CQG allows
the user to define the Historical Volatility using either Percent or Logarithmic price changes.
Percent changes assume that prices change at fixed intervals. Logarithmic changes assume that
prices are continuously changing. Although the logarithmic method may seem more
appropriate, because it more accurately reflects an assumption of continuous trading, real world
trading is not always continuous, so the Percent method may be more realistic.
High/Low Range changes use a different approach to the standard deviation way of calculating
historical volatility. This approach uses high/low ranges that convey much more information
than a simple chart of closing prices.
The following formulas are used to calculate Historical Volatility:
Percent:
Price Changes
Logarithmic:
Price Changes
High/Low Range:
Price Changes
Mean:
Basic Studies
X
X
i
i
Pi +1 − Pi
=
P
⎛ Pi
+ 1 ⎞
= ln⎜
⎟
⎝ P ⎠
where P is the price at the end of each interval i
σ =
where:
1
n
i
∑
n
i
⎛ ⎞
⎜
⎝ ⎠ ⎟
⎡ ⎤ ⎛
⎢ ⎥ +
⎣ ⎦ ⎝ ⎜
⎞
⎠ ⎟
⎡
⎣ ⎢
⎧
⎤
⎨ ⎥
⎦
⎪
⎩⎪
−
2
hi
Pi
0. 5 ln 0. 39 ln
li
Pi
1
n = period
h = high price
l = low price
P is the price at the end of each interval I
1
m =
n
n
∑ xi i=
1
where m is the mean of n occurrences ( X )
2
⎫
⎬ ⎪
⎭ ⎪