calc_var_ohlc: Calculate the variance of returns from _OHLC_ prices using...

In algoquant/HighFreq: High Frequency Time Series Management

Calculate the variance of returns from OHLC prices using different price range estimators.

Description

Calculate the variance of returns from OHLC prices using different price range estimators.

Usage

calc_var_ohlc(
  ohlc,
  method = "yang_zhang",
  closel = 0L,
  scale = TRUE,
  index = 0L
)

Arguments

ohlc	A time series or a matrix of OHLC prices.
method	A character string representing the price range estimator for calculating the variance. The estimators include: "close" close-to-close estimator, "rogers_satchell" Rogers-Satchell estimator, "garman_klass" Garman-Klass estimator, "garman_klass_yz" Garman-Klass with account for close-to-open price jumps, "yang_zhang" Yang-Zhang estimator, (The default is the method = "yang_zhang".)
closel	A vector with the lagged close prices of the OHLC time series. This is an optional argument. (The default is closel = 0).
scale	Boolean argument: Should the returns be divided by the time index, the number of seconds in each period? (The default is scale = TRUE).
index	A vector with the time index of the time series. This is an optional argument (the default is index = 0).

Details

The function calc_var_ohlc() calculates the variance from all the different intra-day and day-over-day returns (defined as the differences of OHLC prices), using several different variance estimation methods.

The function calc_var_ohlc() does not calculate the logarithm of the prices. So if the argument ohlc contains dollar prices then calc_var_ohlc() calculates the dollar variance. If the argument ohlc contains the log prices then calc_var_ohlc() calculates the percentage variance.

The default method is "yang_zhang", which theoretically has the lowest standard error among unbiased estimators. The methods "close", "garman_klass_yz", and "yang_zhang" do account for close-to-open price jumps, while the methods "garman_klass" and "rogers_satchell" do not account for close-to-open price jumps.

If scale is TRUE (the default), then the returns are divided by the differences of the time index (which scales the variance to the units of variance per second squared). This is useful when calculating the variance from minutes bar data, because dividing returns by the number of seconds decreases the effect of overnight price jumps. If the time index is in days, then the variance is equal to the variance per day squared.

If the number of rows of ohlc is less than 3 then it returns zero.

The optional argument index is the time index of the time series ohlc. If the time index is in seconds, then the differences of the index are equal to the number of seconds in each time period. If the time index is in days, then the differences are equal to the number of days in each time period.

The optional argument closel are the lagged close prices of the OHLC time series. Passing in the lagged close prices speeds up the calculation, so it's useful for rolling calculations.

The function calc_var_ohlc() is implemented in RcppArmadillo C++ code, and it's over 10 times faster than calc_var_ohlc_r(), which is implemented in R code.

Value

A single numeric value equal to the variance of the OHLC time series.

Examples

## Not run: 
# Extract the log OHLC prices of SPY
ohlc <- log(HighFreq::SPY)
# Extract the time index of SPY prices
indeks <- c(1, diff(xts::.index(ohlc)))
# Calculate the variance of SPY returns, with scaling of the returns
HighFreq::calc_var_ohlc(ohlc, 
 method="yang_zhang", scale=TRUE, index=indeks)
# Calculate variance without accounting for overnight jumps
HighFreq::calc_var_ohlc(ohlc, 
 method="rogers_satchell", scale=TRUE, index=indeks)
# Calculate the variance without scaling the returns
HighFreq::calc_var_ohlc(ohlc, scale=FALSE)
# Calculate the variance by passing in the lagged close prices
closel <- HighFreq::lagit(ohlc[, 4])
all.equal(HighFreq::calc_var_ohlc(ohlc), 
  HighFreq::calc_var_ohlc(ohlc, closel=closel))
# Compare with HighFreq::calc_var_ohlc_r()
all.equal(HighFreq::calc_var_ohlc(ohlc, index=indeks), 
  HighFreq::calc_var_ohlc_r(ohlc))
# Compare the speed of Rcpp with R code
library(microbenchmark)
summary(microbenchmark(
  Rcpp=HighFreq::calc_var_ohlc(ohlc),
  Rcode=HighFreq::calc_var_ohlc_r(ohlc),
  times=10))[, c(1, 4, 5)]  # end microbenchmark summary

## End(Not run)

algoquant/HighFreq documentation built on Oct. 26, 2024, 9:20 p.m.