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

clc; clear;close all
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% input parameters
Mu=[1  -1]';
r=-.9;
sigma=[2 10]';

NumSimul=100000;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Sigma=diag(sigma)*[1 r;r 1]*diag(sigma);
Y=mvnrnd(Mu,Sigma,NumSimul); % bi-variate normal simulation
X=exp(Y);                    % bi-variate lognormal 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