montevar.m

统计工具软件

function [mvar] = montevar(delta,C,legame,valuta,cambi,fattori,prezzi,vm,t,p,modello,l,rendimento)

%MONTEVAR	Monte Carlo VaR.
%
%	[mvar] = montevar(delta,C,legame,valuta,cambi,fattori,prezzi,vm,t,p,modello,l,rendimento) 
%   calculates the monte Carlo VaR of a portfolio, given the vector vm of
%   portfolio value, the holding period t, and the probability p. Delta is
%   the sensibility vector, C the variance-covariance matrix of risk
%   factors yields. Cambi is the vector of current exchange rates, fattori
%   of the risk factors, and prezzi are the asset prices.
%   The vector legame set the relations between assets and risk factors.
%   Given 2 risk factors and 4 assets the vector (1 1 1 2) means that the
%   first three assets are related with the first risk factors, the fourth
%   asset with the second risk factor. The vector valuta set the relation
%   between tha asset and the exchange rate in the same manner of the
%   vector legame, with the convention that 0 is for the referred exchange
%   rate. Modello = 0 implies a linear simulation model, =1 a log-normal
%   simulation model, l is the number of simulations. Rendimento = 0 if the
%   yields are calculated with aritmetical method, 1 if yields are
%   logarithmic.
%
%	All data must be in colums.
%
%	See DELTAVAR, SIMULVAR
%

%	Copyright (c) 2004 by Flavio Bazzana
%   Department of Computer and Management Sciences
%   University of Trento
%   38100 - Trento ITALY
%   [e-mail]

n=size(C,1);
m=length(valuta);
r=length(fattori);
A=chol(C);

% calculation of the actual portfolio value

cp = vm./prezzi;
for j=1:m
	if valuta(j)==0
		x1(j)=1;
		else x1(j)=cambi(valuta(j));
	end
end
x2 = prezzi.*x1';
vp0 = x2'*cp;

if modello==0
	
% returns simulation of exchange rates and risk factors with normal method ...

	for i=1:l
		z=0;
		for j=1:t
			y=randn(n,1);
			z=z+y;
		end
		fc=A*z;
		
% ... calculation of final price of exchange rates and assets ...
		
		if rendimento==0
			cam=cambi.*fc(r+1:n)+cambi;
			for k=1:m
				h=legame(k);
				pre(k)=prezzi(k)*(1+delta(k)*fc(h));
			end
		else
			cam=cambi.*exp(fc(r+1:n));
			for k=1:m
				h=legame(k);
				pre(k)=prezzi(k)*exp(delta(k)*fc(h));
			end
		end
	
% ... and of portfolio value
	
		for k=1:m
			if valuta(k)==0
				x(k)=1;
				else x(k)=cam(valuta(k));
			end
		end
		vp(i)=(pre.*x)*cp;
	end

% returns simulation of exchange rates and risk factors with log-normal method ...

	else 
	for i=1:l
		z=0;
		for j=1:t
			y=randn(n,1);
			z=z+y;
		end
		fc=sqrt(diag(C)).*z;
		
% ... calculation of final price of exchange rates and assets ...
		
		if rendimento==0
			cam=cambi.*fc(r+1:n)+cambi;
			for k=1:m
				h=legame(k);
				pre(k)=prezzi(k)*(1+delta(k)*fc(h));
			end
		else
			cam=cambi.*exp(fc(r+1:n));
			for k=1:m
				h=legame(k);
				pre(k)=prezzi(k)*exp(delta(k)*fc(h));
			end
		end
	
% ... and of portfolio value
	
		for k=1:m
			if valuta(k)==0
				x(k)=1;
				else x(k)=cam(valuta(k));
			end
		end	
		vp(i)=(pre.*x)*cp;
	end
end

dvp = vp-vp0;
sdvp = sort(dvp);
mvar = -sdvp(fix(l-l*p));