Volatility
Selected volatility estimators/indicators; various authors.
volatility(OHLC, n = 10, calc = "close", N = 260, mean0 = FALSE, ...)
OHLC |
Object that is coercible to xts or matrix and contains
Open-High-Low-Close prices (or only Close prices, if |
n |
Number of periods for the volatility estimate. |
calc |
The calculation (type) of estimator to use. |
N |
Number of periods per year. |
mean0 |
Use a mean of 0 rather than the sample mean. |
... |
Arguments to be passed to/from other methods. |
Close-to-Close Volatility (calc="close")
sqrt(N) * runSD(ROC(Cl), n-1)
OHLC Volatility: Garman and Klass (calc="garman.klass")
The
Garman and Klass estimator for estimating historical volatility assumes
Brownian motion with zero drift and no opening jumps (i.e. the opening =
close of the previous period). This estimator is 7.4 times more efficient
than the close-to-close estimator.
sqrt(N/n * runSum(0.5 * log(Hi/Lo)^2 - (2*log(2)-1) * log(Cl/Op)^2, n))
High-Low Volatility: Parkinson (calc="parkinson")
The Parkinson formula for estimating the historical volatility of
an underlying based on high and low prices.
sqrt(N/(4*n*log(2)) * runSum(log(Hi/Lo)^2, n))
OHLC Volatility: Rogers and Satchell (calc="rogers.satchell")
The Roger and Satchell historical volatility estimator allows for non-zero
drift, but assumed no opening jump.
sqrt(N/n * runSum(log(Hi/Cl) * log(Hi/Op) + log(Lo/Cl) * log(Lo/Op), n))
OHLC Volatility: Garman and Klass - Yang and Zhang
(calc="gk.yz")
This estimator is a modified version of the Garman
and Klass estimator that allows for opening gaps.
sqrt(N/n * runSum(log(Op/lag(Cl,1))^2 + 0.5 * log(Hi/Lo)^2 - (2*log(2)-1) * log(Cl/Op)^2 , n))
OHLC Volatility: Yang and Zhang (calc="yang.zhang")
The Yang
and Zhang historical volatility estimator has minimum estimation error, and
is independent of drift and opening gaps. It can be interpreted as a
weighted average of the Rogers and Satchell estimator, the close-open
volatility, and the open-close volatility.
Users may override the default values of α (1.34 by default) or
k used in the calculation by specifying alpha or k in
..., respectively. Specifying k will cause alpha to be
ignored, if both are provided.
s <- sqrt(s2o + k*s2c + (1-k)*(s2rs^2))
s2o <- N * runVar(log(Op/lag(Cl,1)), n=n)
s2c <- N * runVar(log(Cl/Op), n=n)
s2rs <- volatility(OHLC, n, "rogers.satchell", N, ...)
k <- (alpha-1) / (alpha + (n+1)/(n-1))
A object of the same class as OHLC or a vector (if
try.xts fails) containing the chosen volatility estimator values.
Joshua Ulrich
The following sites were used to code/document these
indicators. All were created by Thijs van den Berg under the GNU Free
Documentation License and were retrieved on 2008-04-20. The original
links are dead, but can be accessed via internet archives.
Close-to-Close Volatility (calc="close"):
https://web.archive.org/web/20100421083157/http://www.sitmo.com/eq/172
OHLC Volatility: Garman Klass (calc="garman.klass"):
https://web.archive.org/web/20100326172550/http://www.sitmo.com/eq/402
High-Low Volatility: Parkinson (calc="parkinson"):
https://web.archive.org/web/20100328195855/http://www.sitmo.com/eq/173
OHLC Volatility: Rogers Satchell (calc="rogers.satchell"):
https://web.archive.org/web/20091002233833/http://www.sitmo.com/eq/414
OHLC Volatility: Garman Klass - Yang Zhang (calc="gk.yz"):
https://web.archive.org/web/20100326215050/http://www.sitmo.com/eq/409
OHLC Volatility: Yang Zhang (calc="yang.zhang"):
https://web.archive.org/web/20100326215050/http://www.sitmo.com/eq/409
See TR and chaikinVolatility for other
volatility measures.
data(ttrc)
ohlc <- ttrc[,c("Open","High","Low","Close")]
vClose <- volatility(ohlc, calc="close")
vClose0 <- volatility(ohlc, calc="close", mean0=TRUE)
vGK <- volatility(ohlc, calc="garman")
vParkinson <- volatility(ohlc, calc="parkinson")
vRS <- volatility(ohlc, calc="rogers")Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.