How to implement a Correlated Brownian Motion correctly

Question

Nina 2017-12-12

0
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https://ww2.mathworks.cn/matlabcentral/answers/372572-how-to-implement-a-correlated-brownian-motion-correctly

编辑： Walter Roberson 2018-4-29

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