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
댓글 수: 2
Walter Roberson
2018년 4월 29일
편집: Walter Roberson
2018년 4월 29일
Do not close questions that have an answer. The answer may be of use to other people.
답변 (1개)
jean claude
2017년 12월 12일
here is a clear demonstration http://www.goddardconsulting.ca/matlab-monte-carlo-assetpaths-corr.html
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