1) Garman-Klass volatility as defined by Euan Sinclair in his book "volatility trading" on page 23:
http://oneryng.com/library/ViolatilityTrading.pdf Cl1 <- lag(OHLC[, 4])
s <- sqrt(N/n * runSum(0.5 * log(OHLC[, 2]/OHLC[, 3])^2 - (2 * log(2) - 1) * log(OHLC[, 4]/Cl1)^2, n))
In the volatility function in the TTR package has (defined by the sitmo website):
http://web.archive.org/web/20081224134053/http://www.sitmo.com/eq/402 s <- sqrt(N/n * runSum(0.5 * log(OHLC[, 2]/OHLC[, 3])^2 - (2 * log(2) - 1) * log(OHLC[, 4]/OHLC[, 1])^2, n))
The difference is with the last term i.e. OHLC[,1] - today's open is used in the denominator in the TTR package rather than yesterday's close (Cl1). I have read various documents that use the same definition as Dr. Sinclair. Which is correct and why?
2) Yang Zhang volatility as defined by Euan Sinclair in his book "volatility trading" on page 24-25 :
k <- 0.34/(1 + (n + 1)/(n - 1))
s2o <- N/(n - 1) * runSum(log(OHLC[, 1]/Cl1), n))^2
s2c <- N/(n - 1) * runSum(log(OHLC[, 4]/OHLC[, 1]), n))^2
s2rs <- volatility(OHLC = OHLC, n = n, calc = "rogers.satchell", N = N, ...)
s <- sqrt(s2o + k * s2c + (1 - k) * (s2rs)^2, n)
But the volatility function in the TTR package has:
http://web.archive.org/web/20081224134117/http://www.sitmo.com/eq/417 k <- 0.34/(1 + (n + 1)/(n - 1))
s2o <- N/(n - 1) * runSum(log(OHLC[, 1]/Cl1) - 1/n *
runSum(log(OHLC[, 1]/Cl1), n))^2
s2c <- N/(n - 1) * runSum(log(OHLC[, 4]/OHLC[, 1]) -
1/n * runSum(log(OHLC[, 4]/OHLC[, 1]), n))^2
s2rs <- volatility(OHLC = OHLC, n = n, calc = "rogers.satchell",
N = N, ...)
s <- s2o + k * s2c + (1 - k) * s2rs
There are multiple differences - firstly the mean of the uo and uc are not present in Dr. Sinclair's version and moreover the last term in the TTR package seems to add a standard deviation (s2rs) with 2 variance calculations (s2c and s2o).
I would greatly appreciate if someone can comment on which versions are correct. Thank you.
> sessionInfo()
R version 2.13.0 (2011-04-13)
Platform: x86_64-apple-darwin9.8.0/x86_64 (64-bit)
locale:
[1] C/en_US.UTF-8/C/C/C/C
attached base packages:
[1] stats graphics grDevices utils datasets methods base
other attached packages:
[1] TTR_0.21-0 xts_0.8-0 zoo_1.6-5
loaded via a namespace (and not attached):
[1] grid_2.13.0 lattice_0.19-26 tools_2.13
Locked
