 # Chapter 3. Multivariate Volatility Models (in MATLAB/Python)

Copyright 2011 - 2022 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: https://www.gnu.org/licenses/.

##### Listing 3.1/3.2: Download stock prices in MATLAB Last updated August 2016

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);

##### Listing 3.1/3.2: Download stock prices in Python Last updated June 2018

import numpy as np
p = p[:,[0,1]]       # consider first two stocks
y = np.diff(np.log(p), n=1, axis=0)*100 # calculate returns
y[:,0] = y[:,0]-np.mean(y[:,0])          # subtract mean
y[:,1] = y[:,1]-np.mean(y[:,1])
T = len(y[:,0])


##### Listing 3.3/3.4: EWMA in MATLAB Last updated June 2018

%% create a matrix to hold covariance matrix for each t
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

##### Listing 3.3/3.4: EWMA in Python Last updated June 2018

EWMA = np.full([T,3], np.nan)
lmbda = 0.94
S = np.cov(y, rowvar = False)
EWMA[0,] = S.flatten()[[0,3,1]]
for i in range(1,T):
S = lmbda * S + (1-lmbda) * np.transpose(np.asmatrix(y[i-1]))* np.asmatrix(y[i-1])
EWMA[i,] = [S[0,0], S[1,1], S[0,1]]
EWMArho = np.divide(EWMA[:,2], np.sqrt(np.multiply(EWMA[:,0],EWMA[:,1])))
print(EWMArho)


##### Listing 3.5/3.6: OGARCH in MATLAB Last updated August 2016

[par, Ht] = o_mvgarch(y,2, 1,1,1);
Ht = reshape(Ht,4,T)';
%% Ht comes from o_mvgarch as a 3D matrix, this transforms it into a 2D matrix
OOrho = Ht(:,3) ./ sqrt(Ht(:,1) .* Ht(:,4));
%% OOrho is a vector of correlations

##### Listing 3.5/3.6: OGARCH in Python Last updated July 2020

## Python does not have a proper OGARCH package at present


##### Listing 3.7/3.8: DCC in MATLAB Last updated June 2022

%%The function 'dcc' in MFE toolbox currently cannot work in MATLAB R2022a.
%%The function 'dcc' use one MATLAB Optimization toolbox function 'fmincon'.
%%The changes of 'fmincon' cause this problem.
%%This block can work on Optimization 8.3
[p, lik, Ht] = dcc(y,1,1,1,1);
Ht = reshape(Ht,4,T)';
DCCrho = Ht(:,3) ./ sqrt(Ht(:,1) .* Ht(:,4));
%% DCCrho is a vector of correlations

##### Listing 3.7/3.8: DCC in Python Last updated July 2020

## Python does not have a proper DCC package at present


##### Listing 3.9/3.10: Correlation comparison in MATLAB Last updated June 2018

plot([EWMArho,OOrho,DCCrho])
legend('EWMA','DCC','OGARCH','Location','SouthWest')

##### Listing 3.9/3.10: Correlation comparison in Python Last updated July 2020

## Python does not have a proper OGARCH/DCC package at present