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_TCopulaSimul.m
```% this script simulates the copula of a bi-variate t distribution
% see "Risk and Asset Allocation"-Springer (2005), by A. Meucci

clc; clear; close all
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% input parameters
Mu=[10  -1]';
r=-.3;
sigma=[20 10]';
nu=1;

NumSimul=20000;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
C=[1 r;r 1];
Std_X=mvtrnd(C,nu,NumSimul);  % standardized bi-variate t simulation
X_1=Mu(1)+sigma(1)*Std_X(:,1);
X_2=Mu(2)+sigma(2)*Std_X(:,2);
X=[X_1 X_2];                  % bi-variate t simulation

Copula = [U_1 U_2];			      % 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

% 3-d histogram (~rescaled pdf)
NumBins3d=round(sqrt(NumSimul)/5);
figure
hist3(Copula(:,[1 2]),[NumBins3d NumBins3d]);title('pdf copula')```