mj


Total Posts: 1049 
Joined: Jun 2004 


We have done a new paper on how to do nested Monte Carlo using small number of subsimulation paths. I'd be interested in any comments.
https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2983510
There are many applications including CVA, VIX, PFE, VAR, capital modelling. I think this paper will be important for practitioners. 
More mathematical finance has been published.



ronin


Total Posts: 216 
Joined: May 2006 


Well, we do recycle everything these days. So I guess it's time to start recycling Monte Carlo paths too...
Seriously, I love the idea. But I still haven't got my head around how your estimators can converge so fast.

"People say nothing's impossible, but I do nothing every day" Winnie The Pooh 

mj


Total Posts: 1049 
Joined: Jun 2004 


Well the crucial point is that it's about bias elimination rather than variance reduction. If there was no bias, one subpath would be enough. So if we can eliminate most of the bias, a few subpaths are enough. 
More mathematical finance has been published.



ronin


Total Posts: 216 
Joined: May 2006 


Yes, that's the bit i am struggling with.
If there is no bias but there is variance, how can one path be enough? In other words, you may be sampling the right mean, but how do you know where the right mean is until you got rid of the variance?
I am sure the sums work. But I am struggling to get it past "explain it to your grandmother" test  I don't understand why they work.

"People say nothing's impossible, but I do nothing every day" Winnie The Pooh 

mj


Total Posts: 1049 
Joined: Jun 2004 


There are are inner paths and outer paths. The inner subsim errors cancel when averaged across the outer paths so the fact they appear big doesn't matter as long the errors are unsystematic.

More mathematical finance has been published.


