问题描述
首先,我创建了一个xts对象,其中包含36个时间序列,显示1980年1月2日至2020年10月6日的每日价格。
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)
然后我使用PerformanceAnalytics函数CalculateReturns()计算了连续复利的每日收益
ENERGY_returns.cc <- CalculateReturns(ENERGY_xts,method="compound")
现在,我想根据此公式计算从1980-01-02到2020-10-06的每个月的波动率: MONTHLY VOLATILITY FORMULA
能不能给我一些提示(在编码方面)?
解决方法
看看这个函数,请注意,我模拟了收益,因为您没有提供收益。
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