How to implement a Correlated Brownian Motion correctly
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I have trouble implementing a Correlated Brownian Motion. I need the simulation for 1000 paths and T=5. Only the values of the evolution for t=1 and T=5 are relevant. The following code is running, but does not return the expected values. Does anybody know what I did wrong? Thankful for any advice or hint!
X1=100;
X2=90;
r=0.03;
sigma1=0.25;
sigma2=0.25;
rho=0.5;
T=5;
sigma=[sigma1 0;0 sigma2];
corr=[1 rho;rho 1];
cov=sigma*corr*sigma;
R=chol(cov,'lower');
N=1000;
X1_t=zeros(N,T+1);
X1_t(:,1)=A_0;
X2_t=zeros(N,T+1);
X2_t(:,1)=L_0;
dt=1;
for i=1:N
X=randn(T,2);
W=X*R;
for j=2:T+1
X1_t(i,j)=X1_t(i,j-1)*exp(r*dt+sigma1.*W(j-1,1)-(sigma1.^2./2)*dt);
X2_t(i,j)=X2_t(i,j-1)*exp(r*dt+sigma2.*W(j-1,2)-(sigma2.^2./2)*dt);
end
end
2 commentaires
Walter Roberson
le 29 Avr 2018
Modifié(e) : Walter Roberson
le 29 Avr 2018
Do not close questions that have an answer. The answer may be of use to other people.
Réponses (1)
jean claude
le 12 Déc 2017
here is a clear demonstration http://www.goddardconsulting.ca/matlab-monte-carlo-assetpaths-corr.html
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