Picking representative scenarios

[TiderInsider]

I'll post this in APM because I know it's on the syllabus and I think this forum gets more traffic than the life forum.

I need to pick some representative scenarios from 10,000 scenarios that were generated by the AAA generator. I wanted to update our treasury curve scenarios to today's yield curve, but I don't want to use 10,000 scenarios in my model. A couple of questions:

1. Is 200 representative scenarios picked from 10,000 better than just generating 200? I'm thinking yes because you know that your subset is representative of a larger set of scenarios.

2. How do you adapt distance measures discussed on the APMV syllabus to a curve (like the yield curve) as opposed to a single equity scenario? I have no problem picking out representative scenarios from the 10yr part of the curve, or the 5 yr, but how about the 3m,6m,1yr,2yr,etc?

TIA.

[campbell]

I'll have to dig up the references later, but Steve Craighead has written about this recently in a few places in SOA publications. I think he had something in the Financial Reporter recently, but I'd have to look it up.

There are methods of making a metric on the entire yield curve, but given that the curve is being driven by the 1-year and 20-year rates (the AAA generator just generates that, and the other rates are solved for via interpolation/extrapolation), I would use a metric revolving around those two.

[campbell]

Here's the issue of Financial Reporter:
http://soa.org/library/newsletters/financial-reporter/2008/june/frn-2008-iss73.pdf

Steve's article begins on page 17. I highly recommend reading that to start out.

[TiderInsider]

Thanks campbell....would you agree that a set of 200 representative scenarios is better than just generation 200 scenarios?

[campbell]

Thanks campbell....would you agree that a set of 200 representative scenarios is better than just generation 200 scenarios?

Yes, I agree.

[The Smokin' Cracktuary]

Thanks campbell....would you agree that a set of 200 representative scenarios is better than just generation 200 scenarios?

Yes, I agree.

Campbell know far more than I, but for what it's worth, I also agree.

[campbell]

I throw in a bit of caution here -- you need to take a look as to how these selected scenarios behave, and it depends on what you're trying to use these scenarios for (in terms of product and whether it's just to get a feel for range of behavior or CTE 90 or pricing or whatever.) Always consider the qualitative behavior as well as quantitatively what your metric is telling you. If the metric is saying "far apart" on two interest rate scenarios, you should be able to see it if you animate the two yield curves through time against each other.

[Mary Hardy]

I disagree

[campbell]

Dangit, I knew you'd come by here to disagree.

I assume you're referring to taking a particular larger set of scenarios and then winnowing them down to 200 is not better than just taking the first 200 scenarios.

[TiderInsider]

I disagreeCan you elaborate?

[The Smokin' Cracktuary]

It seems to me that the larger the set you generate, the more likely it is to capture the "true" (target) distribution. Then using the adequate methods to select representative scenarios you should be able to approximate the target distrbution pretty well, while ensuring that you are forcing some scenarios into the tails to capture tail risk.

Whereas, if you only generate 200 scenarios it seems less likely that you will cover the full set of possible outcomes. So your distribution may be incomplete (i.e.- not representative of the target distribution)

I guess I am thinking of it as selecting a good representative subset of the complete target distrubution (or as close as you can get with a large number of scenarios), as opposed to generating too few scenarios to insure adequate convergence to the target distrubtion, so you end up with only a partial distribution, which may not contain enough scenarios in the tails understating the tail risk.

If you have a high severity type scenario with a probability of occurance of .5% or less, it is less likely you will generate that scenario with only 200 hundred tries. .5% doesn't seem like a small enough probability to be in the realm of "Okay to ignore" high severity events.

On the other hand, 10,000 scenarios is much more likely to be adequate to capture these bad scenarios. Representaive sampling should ensure that you capture some of these scenarios in your 200.

Of course I am not basing this on anything accept what seems intuitive to me, which is often wrong.

[TiderInsider]

Right, but I believe Mary Hardy was saying that 200 pulled from 10,000 is not better than just generating 200.

[Mary Hardy]

The scenarios which are 'representative' depends on your objective. Representative for a tail measure are different to representative for a mean. Any kind of variance reduction requires knowledge of the objective function.

If you don't know the relationship between your objective function and the representative scenario algorithm, you are better off not using the algorithm. Only simple Monte carlo is independent of the objective function. Some variance reduction (including so called representative scenarios) will actually make things worse.

[TiderInsider]

The scenarios which are 'representative' depends on your objective. Representative for a tail measure are different to representative for a mean. Any kind of variance reduction requires knowledge of the objective function.

If you don't know the relationship between your objective function and the representative scenario algorithm, you are better off not using the algorithm. Only simple Monte carlo is independent of the objective function. Some variance reduction (including so called representative scenarios) will actually make things worse.Thanks...that makes sense.

My objective would be that the sample be representative of the underlying distribution of an infinite number of treasury curves produced by my (the academy's) generator. As n approaches infinity, I accomplish this goal, but that doesn't do me any good in the real world. From what I understand of the Chuch algorithim, it would accomplish this goal.

10,000 sounds like a reasonable number of scenarios to use, but due to computing time, I'd like to use 200. Using a representative set of scenarios seemed like a logical way to pack the punch of 10,000 scenarios into 200.

I'm sure there's a good paper on the proper number of scenarios to use under different circumstances. I'll start digging (through study notes? ugh!), but if anyone knows something off the top of there head, let me know.

[campbell]

By the way, there were some talks related to this at the spring meeting.

One of the things that Mary Hardy pointed out to me a while back (quasi-monte carlo techniques) relates to how you sample your "uniform random variates" that you feed into your stochastic model. But you can't apply it to a given set of scenarios, alas. Trevor Howes' slides discuss this (http://soa.org/files/pdf/2008-qc-chueh-dardis-41.pdf) (note that Chueh also gave a talk in this grouping, and talks about using her methods for parametric fitting)

I also recommend looking at these slides (http://soa.org/files/pdf/2008-qc-craighead-dardis-51.pdf), which also talk about techniques. Steve Craighead's slides are there, which are the same as his article in the Financial Reporter, I believe. Take a look at John Manistre's slides there, which have some good, practical ideas as well as showing results from a particular model.

I agree that it is better to do something with the underlying model, and using techniques such as control variates or low discrepancy sequences. Of course, the Economic Scenario Working Group have released all the specs of their model, so there's enough information there to create your own program to produce the sequences...if you have the time.

If you want to use the "old" model, you can pull the C3 Phase II enhanced generator (that goes to a zipped Excel file) (http://actuary.org/life/zip/generator06.zip), and mess around with the VBA to do what you want (just keep in mind this is different from the new Academy model).