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 Kommentare
Walter Roberson
am 29 Apr. 2018
Bearbeitet: Walter Roberson
am 29 Apr. 2018
Do not close questions that have an answer. The answer may be of use to other people.
Antworten (1)
jean claude
am 12 Dez. 2017
here is a clear demonstration http://www.goddardconsulting.ca/matlab-monte-carlo-assetpaths-corr.html
Siehe auch
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