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mj


Total Posts: 1049
Joined: Jun 2004
 
Posted: 2017-06-09 02:03
We have done a new paper on how to do nested Monte Carlo using small number of sub-simulation 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: 193
Joined: May 2006
 
Posted: 2017-06-13 16:55

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
 
Posted: 2017-06-14 03:38
Well the crucial point is that it's about bias elimination rather than variance reduction. If there was no bias, one sub-path would be enough. So if we can eliminate most of the bias, a few sub-paths are enough.

More mathematical finance has been published.

ronin


Total Posts: 193
Joined: May 2006
 
Posted: 2017-06-14 11:37
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
 
Posted: 2017-06-14 12:41
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.
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