R and Matlab Chapter 3. Multivariate Volatility Models

# Chapter 3. Multivariate Volatility Models

### R and Matlab

Copyright 2011 - 2023 Jon Danielsson. This code is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version. This code is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. The GNU General Public License is available at: www.gnu.org/licenses.

##### Listing 3.1/3.2
p = read.csv('stocks.csv')
y=apply(log(p),2,diff)     # calculate returns
y = y[,1:2]                # consider first two stocks
y[,1] = y[,1]-mean(y[,1])  # subtract mean
y[,2] = y[,2]-mean(y[,2])
TT = dim(y)

##### Listing 3.1/3.2
p = csvread('stocks.csv',1,0);
p = p(:,[1,2]); % consider first two stocks
y = diff(log(p))*100; % convert prices to returns
y(:,1)=y(:,1)-mean(y(:,1)); % subtract mean
y(:,2)=y(:,2)-mean(y(:,2));
T = length(y);


##### EWMA in R
EWMA = matrix(nrow=TT,ncol=3)
lambda = 0.94
S = cov(y)                      # initial (t=1) covar matrix
EWMA[1,] = c(S)[c(1,4,2)]       # extract var and covar
for (i in 2:dim(y)){
S = lambda*S+(1-lambda)*  y[i-1,] %*% t(y[i-1,])
EWMA[i,] = c(S)[c(1,4,2)]
}
EWMArho = EWMA[,3]/sqrt(EWMA[,1]*EWMA[,2]) # calculate correlations
print(tail(EWMArho))

##### % EWMA in MATLAB
EWMA = nan(T,3);
lambda = 0.94;
S = cov(y);                 % initial (t=1) covar matrix
EWMA(1,:) = S([1,4,2]);     % extract var and covar
for i = 2:T                 % loop though the sample
S = lambda*S+(1-lambda)* y(i-1,:)'*y(i-1,:);
EWMA(i,:) = S([1,4,2]); % convert matrix to vector
end
EWMArho = EWMA(:,3)./sqrt(EWMA(:,1).*EWMA(:,2)); % calculate correlations


##### GOGARCH in R
library(rmgarch)
spec = gogarchspec(mean.model = list(armaOrder = c(0, 0),
include.mean =FALSE),
variance.model = list(model = "sGARCH",
garchOrder = c(1,1)) ,
distribution.model =  "mvnorm"
)
fit = gogarchfit(spec = spec, data = y)
show(fit)

##### % OGARCH in MATLAB
[par, Ht] = o_mvgarch(y,2, 1,1,1);
Ht = reshape(Ht,4,T)';
OOrho = Ht(:,3) ./ sqrt(Ht(:,1) .* Ht(:,4));


##### DCC in R
xspec = ugarchspec(mean.model = list(armaOrder = c(0, 0), include.mean = FALSE))
uspec = multispec(replicate(2, xspec))
spec = dccspec(uspec = uspec, dccOrder = c(1, 1), distribution = 'mvnorm')
res = dccfit(spec, data = y)
H=res@mfit\$H
DCCrho=vector(length=dim(y))
for(i in 1:dim(y)){
DCCrho[i] =  H[1,2,i]/sqrt(H[1,1,i]*H[2,2,i])
}

##### % DCC in MATLAB
[p, lik, Ht] = dcc(y,1,1,1,1);
Ht = reshape(Ht,4,T)';
DCCrho = Ht(:,3) ./ sqrt(Ht(:,1) .* Ht(:,4));


##### Sample statistics in R
matplot(cbind(EWMArho,DCCrho),type='l',las=1,lty=1,col=2:3,ylab="")
mtext("Correlations",side=2,line=0.3,at=1,las=1,cex=0.8)
legend("bottomright",c("EWMA","DCC"),lty=1,col=2:3,bty="n",cex=0.7)

##### % Correlation comparison in MATLAB
plot([EWMArho,OOrho,DCCrho])
legend('EWMA','DCC','OGARCH','Location','SouthWest')


##### Financial Risk Forecasting
Market risk forecasting with R, Julia, Python and Matlab. Code, lecture slides, implementation notes, seminar assignments and questions.