February 12th, 2007, 12:51 pm
I too am looking at basket options in monte carlo. I understand that I have to simulate the underlyings using the Cholesky decomposition for the correlation matrix between the Brownian motions, however I'm not sure how to implement this in practice. I have the vols for each or my 3 assets and also the correlation matrix which I can form the Cholesky matrix from this. However I'm unsure then what do to next, I know that I should start by creating my normally distributed numbers for each asset and then somehow apply the Cholesky matrix, but how to I apply the matrix to the 3 sets of data.Let cholesky matrix be:1 0 0a b cd e fIs it the case that the first asset's data is left alone (hence the top of the Cholesky matrix is 1, 0, 0?Then the next asset is multiplied so you use a*asset 1 + b* asset (with no c term because c is always 0)Then the last asset is multipled so d*asset1 + e*asset2 + f*asset3Do I then use these three new assets (wwell ok asset1 is unchanged, but call the others asset2' and asset3') to find my basket return and hence do the normal calculate payoff, discount to today and run numerous times for my simulations?THANKS