# R 3.4.1
# Daily Volatilities Ex3_DailyVola_R.txt

library("tseries")
library("zoo")

# Read data
require(quantmod) # Finanzdaten download

spc <- new.env()
dax <- new.env()

setDefaults(getSymbols,src="yahoo")
getSymbols("^GSPC", env = spc, from = "1998-10-01", to = "2004-10-01")
getSymbols("^GDAXI", env = dax, from = "1998-10-01", to = "2004-10-01")
# read in series are of xts type,  plot is different for xts and ts

x.o <-as.zoo( spc$GSPC[,1]);       y.o <- as.zoo(dax$GDAXI[,1]); 
x.h <-as.zoo( spc$GSPC[,2]);       y.h <- as.zoo(dax$GDAXI[,2]); 
x.l <-as.zoo( spc$GSPC[,3]);       y.l <- as.zoo(dax$GDAXI[,3]); 
x.c <-as.zoo( spc$GSPC[,4]);       y.c <- as.zoo(dax$GDAXI[,4]); 

### Plot the data
plot(merge(x.c,y.c), main = "^GSPC , ^GDAXI")  # plot price series     
 
r.x  <- diff(log(x.c));         # return US stock index
r.y  <- diff(log(y.c));         # return other index

r.x <- r.x[is.na(r.x)==FALSE]
r.y <- r.y[is.na(r.y)==FALSE]

x.o <- x.o[is.na(x.o)==FALSE]
x.h <- x.h[is.na(x.h)==FALSE]
x.l <- x.l[is.na(x.l)==FALSE]
x.c <- x.c[is.na(x.c)==FALSE]

y.o <- y.o[is.na(y.o)==FALSE]
y.h <- y.h[is.na(y.h)==FALSE]
y.l <- y.l[is.na(y.l)==FALSE]
y.c <- y.c[is.na(y.c)==FALSE]

###########################
### volatility measures ###     #as in the slides
###########################
s2_0_x <- diff(x.c)^2
s2_0_y <- diff(y.c)^2

s2_2_x <- 0.3697*(x.h - x.l)^2
s2_2_y <- 0.3697*(y.h - y.l)^2

s2_5_x <- 0.5*(x.h - x.l)^2 - 0.386*(x.c - x.o)^2 
s2_5_y <- 0.5*(y.h - y.l)^2 - 0.386*(y.c - y.o)^2 
#
s_0_x <- sqrt(s2_0_x)
s_0_y <- sqrt(s2_0_y)

s_2_x <- sqrt(s2_2_x)
s_2_y <- sqrt(s2_2_y)

s_5_x <- sqrt(s2_5_x)
s_5_y <- sqrt(s2_5_y)

### x
nx <- length(s_5_x)
plot(s_0_x, main="x: daily volatility measures: 0 black, 2 blue, 5 green")
lines(s_2_x[2:nx], col="blue")
lines(s_5_x[2:nx], col="green")

plot(density(s_0_x), ylim=c(0,0.09), main="x: daily volatility measures: 0 black, 2 blue, 5 green")
lines(density(s_2_x[2:nx]), col="blue")
lines(density(s_5_x[2:nx]), col="green")

# correlation between 3 volatility measures 
cor(cbind ( as.vector(s_0_x), as.vector(s_2_x[2:nx]) , as.vector(s_5_x[2:nx]) ))

### y
ny <- length(s_5_y)
plot(s_0_y, main="y: daily volatility measures: 0 black, 2 blue, 5 green")
lines(s_2_y[2:ny], col="blue")
lines(s_5_y[2:ny], col="green")

plot(density(s_5_y[2:ny]), col="green", main="y: daily volatility measures: 0 black, 2 blue, 5 green")
lines(density(s_2_y[2:ny]), col="blue")
lines(density(s_0_y))

# correlation between 3 volatility measures 
cor(cbind ( as.vector(s_0_y), as.vector(s_2_y[2:ny]) , as.vector(s_5_y[2:ny]) ))

## EXERCISE:
# (1) Which vola measure would you prefer and why.