Monte Carlo Risk contributions

factfinder · Post by **factfinder** » Mon Dec 08, 2008 2:27 pm

As a utility we have long holding periods for risk, currently I am looking at using Monte carlo methods to calculate the risk over these long holding periods but when it comes to calculating the VaR contributions for different desk they are very unstable (if I run the same simulation twice the number can be very different). I am thinking about using seeded random numbers (or qmc) or using contribution to expected shortfall to calculate contirbution to the VaR number.

Has anyone any experience of this or any criticisms of the approaches I have written here? (assume here that millions of simulations are not possible to achieve total convergence, just 10k or so).

Path Integral · Post by **Path Integral** » Mon Dec 08, 2008 3:21 pm

I am thinking about using seeded random number

as opposed to?

factfinder · Post by **factfinder** » Mon Dec 08, 2008 8:20 pm

I meant the same seed each time, so the number does not change on a rerun.

Graeme · Post by **Graeme** » Mon Dec 08, 2008 8:47 pm

Hmmm... so the number will be the same each time. And, according to you, if you chose a different seed, it would be the same each time, but a different same. Ergo, there is something fishy happening. There should not be dramatic variations in the output. I would suggest you have an error somewhere in your methodology.

adeuklon · Post by **adeuklon** » Tue Dec 09, 2008 10:41 am

How are you calculating the VaR contributions?

If you are just taking the contributions to the P/L on the path that is the correct quantile for the VaR simulation I would expect instability even with a large number of simulations since the result is always dependent on a single path and this I expect would give it poor convergence properties (I'm not surprised that you get very different results when you rerun the simulation with a decent number of paths). I don't think any messing around with the seed number will help here, IMO it would just obscure the problem rather than solve it.

I think your suggestion of working with contributions to the expected shortfall would be more promising. In that case you'll be averaging the contribution to P/L over several simulations. There's a reason to expect some kind of convergence in this case because of the averaging.

factfinder · Post by **factfinder** » Tue Dec 09, 2008 11:22 am

Adeuklon Graeme

Thank you.

I was calculating the VaR contribution based on conribution to the single path which is clearly very unstable, but I will be using contribution to ES.

diogenes · Post by **diogenes** » Tue Dec 09, 2008 11:52 am

Just to follow up with the other replies, how many runs are you doing etc?

factfinder · Post by **factfinder** » Tue Dec 09, 2008 2:11 pm

about 10,000

diogenes · Post by **diogenes** » Tue Dec 09, 2008 5:41 pm

Is this for generation unit(s) and are you seeing similiar bands appear?

factfinder · Post by **factfinder** » Tue Dec 09, 2008 7:10 pm

what do you mean by bands?