Code covered by the BSD License

# Risk and Asset Allocation

### Attilio Meucci (view profile)

16 Nov 2005 (Updated )

Software for quantitative portfolio and risk management

S_WishartCopulaSimul.m
```% this script simulates the copula of the diagonal elements of a 2x2 Wishart distribution
% see "Risk and Asset Allocation"-Springer (2005), by A. Meucci

clear;  close all;  clc;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
s=[1 2];
r=0.6;
nu=20;
NumSimul=10000;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Sigma=diag(s)*[1 r;r 1]*diag(s);

W_xx=[]; W_yy=[];
for j=1:NumSimul
X = mvnrnd(zeros(2,1),Sigma,nu);
W = X'*X;

W_xx=[W_xx
W(1,1)];
W_yy=[W_yy
W(2,2)];

end

a_xx=nu/2;
b_xx=2*Sigma(1,1);
a_yy=nu/2;
b_yy=2*Sigma(2,2);
Copula=[U_xx U_yy];			      % copula

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% plots
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
figure
% marginals
NumBins=round(10*log(NumSimul));

subplot('Position',[.05 .3 .2 .6])
[n,D]=hist(Copula(:,2),NumBins);
barh(D,n,1);
[y_lim]=get(gca,'ylim')
set(gca,'xtick',[])
grid on

subplot('Position',[.3 .05 .6 .2])
[n,D]=hist(Copula(:,1),NumBins);
bar(D,n,1);
[x_lim]=get(gca,'xlim')
set(gca,'ytick',[])
grid on

% scatter plot
subplot('Position',[.3 .3 .6 .6])
h=plot(Copula(:,1),Copula(:,2),'.');
set(gca,'xlim',x_lim,'ylim',y_lim)
grid on