Basket Option and Monte Carlo

ojim · June 1st, 2005, 5:05 pm

Hi,If I want to price a basket option of 3 equity index, with correlation matrix available. How do I incorporate the correlation info into the Monto Carlo Simulation? Do I build one set of random variates for 1 equity index first, and then create 2 more equity index according to the correlation matrix? Any idea / VB code / sources would be highly appreciated.Thank you so much for your great help.....

Antonio · June 1st, 2005, 5:17 pm

What you have to do is to create one brownian motion for one equity, then you simulate the two other Brownian motions using the "square root" of the covariance matrix, using a Cholesky decomposition. I have some vba or c++ code for that if you want, but I can't provide it to you before tomorrow (it's at home).

ojim · June 1st, 2005, 5:36 pm

that will be very helpful if you could post the code file.Thank you so much again!

junbum · June 2nd, 2005, 2:39 pm

Hello Antony,Could you please send theVB code for cholesky decomposition to to gvmrb@yahoo.co.uk .Your help will be appreciated and acknowledged. jun

Antonio · June 3rd, 2005, 12:27 pm

Hi,Here is the vba and c code for the Cholesky decomposition. There is also a short explanation on how to use it to simulate your correlated assets.Have fun

rhmari · July 7th, 2005, 6:59 am

hi i'am also trying to price a basket optioni see that antonio has sent the VBA Code for Cholesky Decompositioni took it but unfortunatelly,i don't know how to use it in Excel,i mean how do i enter my matrix A on Excel and how to obtain the L matrix wich is the cholesky decomposition of A.Can you please send me the excel File where i can find the pricing of the basket option if you have already done itthank you very much for your helpyou can send me the files at the following address : mohamed.rhrmaritlemcani@epfl.ch

rhmari · July 7th, 2005, 6:59 am

hi i'am also trying to price a basket optioni see that antonio has sent the VBA Code for Cholesky Decompositioni took it but unfortunatelly,i don't know how to use it in Excel,i mean how do i enter my matrix A on Excel and how to obtain the L matrix wich is the cholesky decomposition of A.Can you please send me the excel File where i can find the pricing of the basket option if you have already done itthank you very much for your helpyou can send me the files at the following address : mohamed.rhrmaritlemcani@epfl.ch

rhmari · July 18th, 2005, 1:20 pm

Hi Antonioi saw that you have a VB Code to price a Basket Optioncan you please send it to me (with the excel spreadsheet if it's possible) to this adress : mohamed.rhmaritlemcani@epfl.chThank you very much for your help

BLOBY · July 19th, 2005, 11:02 am

Please make benefit from it everyone...

Antonio · July 19th, 2005, 1:11 pm

Hi,Here is how to use the Cholesky decomposition in Excel. I don't have the pricer for Basket options with me, I'll have to look for it at home. But it really is immediate : just simulate the underlyings using the Cholesky decomposition for the correlation matrix between the Brownian motions, then calculate your final payoff, you discount it, you run that n times and you get your Monte Carlo price.

jfuqua · March 4th, 2006, 4:46 pm

Papers not code. Still perhaps of value.Pellizari P. 'Efficient Monte Carlo Pricing of Basket Options' U. VeniceDahl Lars, Fred Benth 'Valuation of Asian Basket Options with Quasi-Monte Carlo Techniques & Singular Value Decomposition' 2/2001

BasketOptions · 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

Sonyah · February 12th, 2007, 1:24 pm

Cholesky matrix should be applied to your normally distributed random number samples to create correlated distributions. Then you can generate your paths using the same formula you would for a 1 factor but using the correlated randoms.

vietdung · February 14th, 2007, 12:58 pm

In java we have a very useful package for manipulate the matrix, named : JAMA (includes Cholesky , LU ... decomposition).My case particular , I tried a basket of 40 assets and around 1000000 simulations 360 time steps , it costs 9h of simulation Anyone has a good ref results for the basket option ?