Validation of long term equity return model

[Caramel]

First, this paper is very long and complex to read... all these models and parameters and no exercises...

Second, JAM study schedule said to read page 1 to 16 of this study notes, but in the JAM manual itself, it only covers up to section 4.8 Summary, which is only page 10 and JAM stops there, as if there is no materials of importance pass page 10!

I continued the reading for a little, and the papers provide detail analysis of model fits and comparison using a 20 years GMAB and under some assumptions, by page 12, I became brain-drained :(

Is it really essential to go through the findings of Hardy? How will these materials be tested?

Just felt like as if I am reading someone's Ph.D. thesis paper! Complex, impressive but useful? Booooo~~~~

[beck]

I dont get much of it either, but here's what i got from it, anyone please correct me if i am wrong....
i think hardy basically used MLE estimation to obtain the parameters for all those models, then used residual test of fit to test how well those models fit the historical data... and (here's what I think is the key) she found that all (or most) models have poor fit on the LEFT TAIL....

[Caramel]

I dont get much of it either, but here's what i got from it, anyone please correct me if i am wrong....
i think hardy basically used MLE estimation to obtain the parameters for all those models, then used residual test of fit to test how well those models fit the historical data... and (here's what I think is the key) she found that all (or most) models have poor fit on the LEFT TAIL....

None of the left-tails are fat enough! So, why did Hardy even bother showing us models that don't really work? :O

Then, the book poked fun of AAA, because it recommended the SLV model, while Hardy demonstrated that, SLV failed to fit the left and right tails.

But how in the hell I am going to remember their formula?! For each model?

Anyway, I am moving on to Chapter 4., just finished Chapt. 3 on MLE, it's like a university Stats 101 revisit...

I really hope they won't ask me to solve for MLE estimators during exam, this is already tested in Course 1, n'est-ce pas?

[campbell]

This is not about the exam, but real life:

It is going to be difficult to fit a simple model to the stats we see for interest rates, equities, etc. However, the more complicated we make the model, the less we have a grasp on how changing a single parameter will affect the overall behavior. So you pick a model as simple as possible that will be useful for whatever purpose you're going to use it for -- it won't necessarily be useful for all applications.

I've used the regular old lognormal for rough projections, as it's easy and fast to run, and you can stress parameters simply - there's only two parameters for each item you're running, and it's simple to make correlated lognormals if you've got several different asset classes you're simulating. It was useful for proof-of-concept work.

AAA set its calibration criteria as matching certain percentiles - and it's not like you have to be spot-on, just that you need to have tails at least as fat as the calibration criteria. They went this route because they're not using these models to determine expected value or fair value of a block of business, but because these models will be used for solvency-related calculations. So you have conservatism built in to the models, both for the financial-type part (interest rates, equities) and the policyholder behavior part.

It is good to have some skepticism of any models of equities and interest rates. As Patsy said in Monty Python and the Holy Grail:
It's only a model.
So none of these models are perfect, and you've got to figure out which is most pertinent for what you want. Both RSLN-2 and SLV have their place...as well as good ole LN.