Solvency 2, what I don't understand

There has been much fanfare about Solvency II, and how it will be coming to the US now that it is pretty much fait accompli to be a requirement for UK and European insurance companies starting in 2013. Perhaps I am missing something basic, but blow are some of the issues that I have with Solvency II:

1. Isn't Solvency II based on the same principles as Basel II/III? Now how well has that worked for Europe. Greece, Iceland, Ireland anyone?
2. The first pillar of Solvency II (Article 75 (1)(b)) requires that "...liabilities shall be valued at the amount for which they could be transferred, or settled, between knowledgeable willing par­ties in an arm’s length transaction." I don't know about the rest of you, but there really is no liquid market for (re)insurer loss reserves. I've been involved in pricing a few loss portfolio attempts--none of which came to fruition mind you--and each one is really a bespoke transaction. Different counter-parties to the same transaction will arrive at different values for the reserves. So how is Solvency II going to handle this?
3. At its heart, the capital requirement is still a Value at Risk (VaR) measure, albeit at the 99.5%-ile. When will people learn that VaR is a rather non-robust statistic? It is a point on the cumulative frequency distribution, with no "knowledge" of what is above or below it. It is very susceptible to discontinuities (think step function), and its components are non-additive. At the very least, the measure should be based on TVaR, or the expected value above a given point. As an expectation, it is additive in its components (Co-TVaR measures exist and are meaningful) and it, as a first moment, reflects to some extent the entire distribution in the tail above the point, not just a point. As we all know, actually seeing any particular result from a continuous distribution almost never happens, which is why we talk intervals and not points.
4. While Operational Risk is certainly a significant factor in a company's risk profile, I have yet to see any good measure or process to quantify the expected value of said risk. 

Unlike the banking industry, the insurance industry, especially in the US, has been rather stable for the past century or so, and while I agree that certain elements of Statutory Accounting, such as the holding of nominal reserves, may seem somewhat extreme with respect to other businesses, it has done rather well in ensuring a viable and solvent insurance industry. Why are we rushing into something which has neither the provenance (Basel) nor the track record (not even officially implemented in Europe) to justify adding a new accounting and solvency standard.

Why method of moments doesn't always work

A number of years ago, someone asked me "why does my company need actuaries to fit curves, once I have the mean and standard deviation of my losses, isn't that enough?" I explained to him that not every distribution is completely determined by its mean and standard deviation (as the normal and lognormal are), and as at that point, I did not have "R" installed on my laptop, I demonstrated it to him in Excel. Having wanted to start blogging about "R", even ever so infrequently, I figured I'd toss together a little code to demonstrate.

The example I gave was to compare a gamma and a pareto distribution, each of which has mean 10,000 and a CV of 150% (making the standard deviation 15,000). I will spare all of you the algebra, but suffice to say, that using the Klugman-Panjer-Wilmot parameterization (which is used by most casualty actuaries in the past 20 years or so) the parameters of the gamma would be theta (R's scale) = 22500 and alpha (R's shape) = 4/9. The equivalent pareto would have theta (R's scale) = 26000 and alpha (R's shape) = 3.6.

Graphing the two (and Hadley, please forgive me for using default R' plotting, I left my ggplot book in the office; mea culpa) you can easily see how the distributions are rather different.

 

To make things easier for me, I used the actuar  package to do the graphing:

library(actuar)
curve(dpareto(x, shape=3.6, scale=26000), from=0, to=100000, col="blue")
curve(dgamma(x, shape=4/9, scale=22500), from=0, to=100000, add=TRUE, col="green")

Created by Pretty R at inside-R.org

Obviously, the tails of the distributions, and thus the survival function at a given loss size, is different for the two, notwithstanding their sharing identical first two moments. So, this was just a brief but effective visualization as to how the first two moments do not contain all the information needed to find a "best fit," and why we like to use distributional fitting methods (maximum likelihood, maximum spacing, various minimum distance metrics like Cramer-von Mises, etc.) to get a better understanding of the potential underlying loss processes.

Actuaries in the media…

…well at least in cartoons. Unfortunately, even we are not immune from politics.

http://d.yimg.com/a/p/uc/20090910/largeimagepo090909.gif