Non-Recombining Tree

sushilp · June 17th, 2008, 10:16 am

Hi AllI am pricing simple vanilla option using non-recombining binomial tree. We get 2^i nodes at ith time step. Depending upon computational strength of computer, it becomes almost impossible to compute after certain step due to high number of nodes. Like we get 1024 nodes at 10th time step. Proceeding from these many nodes is computationally not viable.So to reduce the number of nodes I am picking some nodes randomly. Please suggest what other things can be tried?

Cuchulainn · June 17th, 2008, 10:19 am

What kind of data structure are you using to store node values?

sushilp · June 17th, 2008, 10:31 am

I am using arrays. Code is in Visual Basic. However the point is how to reduse the number of nodes?

mj · June 17th, 2008, 10:50 am

Well you don't need to store the tree at all so memory is not a constraint. However, speed is. You could try using a tree that matches the first three moments or is well adapted to the option. See eg my paper on accelerating binomial trees on www.markjoshi.com. People generally solve this problem by not using non-recombining trees...

Cuchulainn · June 17th, 2008, 1:18 pm

Quotesolve this problem by not using non-recombining trees... is this the same as saying 'solve it using a recombining tree'?

mj · June 17th, 2008, 7:35 pm

well there are plenty of other techniques... eg lattices and Monte Carlo.

Paul · June 17th, 2008, 7:46 pm

sushilp, is the task to find the most complicated way to price a simple contract? You're doing a great job!P

thomasBr · June 27th, 2008, 11:41 am

sushilp,is your tree not recombining because of bucket dividends? Did you solve it?Anyway if you run into computationally trouble below 2^16 nodes there is also something wrong with the data structures.