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How to implement a Correlated Brownian Motion correctly

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Nina
Nina on 12 Dec 2017
Edited: Walter Roberson on 29 Apr 2018
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 Comments

Walter Roberson
Walter Roberson on 29 Apr 2018
Do not close questions that have an answer. The answer may be of use to other people.

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