如何从 R 中的每日收益计算历史月波动率？

Question

First I created an xts object, which contains 36 time series showing daily prices from 1980-01-02 to 2020-10-06.

ENERGY_data$time <- as.Date(ENERGY_data$time, format("%Y/%m/%d"))
ENERGY_xts <- ENERGY_data[order(ENERGY_data$time), ]
ENERGY_xts <- as.xts(ENERGY_xts[, 2:37], order.by=ENERGY_xts$time)

Then I calculated the continuously compounded daily returns by using the PerformanceAnalytics function CalculateReturns()

ENERGY_returns.cc <- CalculateReturns(ENERGY_xts, method="compound")

Now I would like to calculate the volatility for each month going from 1980-01-02 to 2020-10-06 on the basis of this formula: MONTHLY VOLATILITY FORMULA

Could you please give me some hints (in terms of coding)?

Answer 1

Take a look at this function and please note that I simulated returns, since you didn't provide yours.

library(xts)

set.seed(123)
returns <- matrix(rnorm(30*365*5, 0.0001, 0.0002), ncol = 30)
timeindex <- seq.Date(from = as.Date('2000-01-01'), length.out = 365*5, by = 'days')

test_xts <- xts(returns, order.by = timeindex)

calcFrenchVolOneAsset <- function(x){
  ndays <- nrow(x)
  first_part_of_formula <- sum(x^2)
  second_part_of_formula <- 2*sum(x[-1]*x[-nrow(x)])
  res <- sqrt(first_part_of_formula + second_part_of_formula)
  return(res)
}

calcFrenchVolMultipleAssets <- function(x){
  ndays <- nrow(x)
  first_part_of_formula <- colSums(x^2)
  second_part_of_formula <- 2*colSums(x[-1, ]*x[-nrow(x), ])
  res <- sqrt(first_part_of_formula + second_part_of_formula)
  return(res)
}

# test for the first month and the first asset
calcFrenchVolOneAsset(test_xts['2000-01', 1])
calcFrenchVolMultipleAssets(test_xts['2000-01', 1])

# apply monthly and on columns
monthly_vols <- apply.monthly(test_xts, calcFrenchVolMultipleAssets)
head(monthly_vols[, c(1:5)])
                    e1        e1.1        e1.2        e1.3        e1.4
2000-01-31 0.002030192 0.002402946 0.001717494 0.001888513 0.002322648
2000-02-29 0.001983995 0.002343783 0.001789346 0.001671332 0.001824278
2000-03-31 0.001910535 0.002429689 0.001709092 0.002492223 0.002068032
2000-04-30 0.001765052 0.002114554 0.001946232 0.002160436 0.002139949
2000-05-31 0.002269842 0.002476424 0.001626455 0.002030027 0.002400690
2000-06-30 0.002082933 0.001905620 0.001681579 0.001992082 0.002010535