Mathematical finance has always fascinated me. Somehow, the concepts of risk neutral pricing, Brownian motion have been the bedrock of many a pricing models.
Somehow, this mathematics tries to project into the future - whether it is for the equity prices or the term structure. The past is summed up literally in the underlying volatility figures (if implied volatility are not used) and the risk-free rate (or actual returns in risk management). We know about the GARCH, EWMA etc models of volatility and its various variants, which digests the historical information. Somehow, can the future be so precisely summed up by just a couple of figures?

Statistics is a different field. It looks at past data and churns out a certain pattern recognition (regression aka. regret?) Then all it says is so and so dependent variable depends on so and so independent variables. Can it claim to project into the future?
The convergence of insurance and credit risk into the financial community will put more importance on acturial science. The Basle II accord on credit risk is targeted to be completed by 2005? But a lack of data hampers modeling efforts. Esp, so as the 2 most common - structural and reduced form approaches are difficult from a parameterisation standpoint. The rating agencies go around it through a statistical approach – like Moody’s RiskCalc. Will we one day see a convergence of the concepts from these 2 fields?
Just a little notti thought.

I think actuaries and quants have a lot to learn from each other. At the moment all the technology flow is going to the actuaries, from the quants, and little is going the other way.

When I was a lad, becoming an actuary was seen as the ultimate goal for the best math students at university. Unfortunately, once the insurance companies got their hands on the best mathematicians they totally ruined and confused them with their archaic institutes and their pre-Newton math conventions...have you ever tried putting any math into 'words'? It's incomprehensible! Well, that's what actuaries seemed to be doing!

It's only been in the last eight, or even fewer years, that actuaries have put option theory, for example, on their exam syllabi. There's some jealousy here, I sense. Actuaries have been around for ever, whereas quants are the new kids on the block.

P

A few years ago I read Professor Wilkie's seminal paper on modelling asset prices for insurance companies. Although it is interesting (and challenging to think of in terms of real world returns rather than risk neutral ones!) the basic technique is an application of standard Time Series techniques. This is based on the premise that sooner or later equities will outperform bonds. This is fine for a long view (I suppose) but tells you nothing of the probability of intervening bankruptcy. (Of course I am not suggesting that actuaries ignore this, of course they do stress tests etc - perhaps Equitable's weren't very good).

Personally I find mainstream statistics as being more of an educator for financial mathematics. If you compute your VaR, why not compute confidence intervals for this estimator? And if you do, why not use bootstrap to compute this rather than assuming normal confidence intervals? And how about computing confidence intervals for regression statistics, and so on.

Mark

It's always good to learn from other fields, and there is much in statistics and actuarial science that finance people could put to good use. However, much of the progress in finance has come from ignoring good statistical and actuarial practice.

For example, you ask why not put a confidence interval around VaR. It's good statistical practice whenever you make an estimate, to also estimate the error. However, VaR is supposed to incorporate all uncertainty, including uncertainty of estimation (whether it does in practice is another question). Putting a confidence interval on it would mislead people about what it is.

A statitician says her prediction was correct if the distribution of errors is what was expected. This leads to a lot of happy statisticians with angry clients, sort of like the old surgeon's joke "the operation was successful but the patient died." Finance people have to measure success by making or losing money. You can't trade a confidence interval.

Resampling and bootstrapping have an important place in finance, but parametric techniques will always be paramount. The reason is that money adds. You cannot either ignore or overinterpret "outliers," you have to add up your total P&L.

I agree that there is more to finance than mean and standard deviation, but it's amazing how much you can explain with just these two concepts. Since money adds, the mean is essential. Since time period returns are very close to independent, and it's a big world of trading opportunities, and money adds, the higher order moments can usually be diversified away either through time or space.

My first financial job in 1981 was in capital markets for Prudential insurance. My job was to price actuarial contracts, for example, Prudential would bid for a cash payment today in return for paying the retirement benefits (for something called a "defined benefit plan" that went extinct in the last geologic age) of 1,000 40-year old workers. The actuaries would analyze the plan, project the employment events and mortality of the workers, and come up with a set of projected cash outflows. I was supposed to give them a price to bid to the plan sponsor. If we won the plan, I was supposed to select investments (in some cases, dedicated portfolios, I selected the actual investments; in most cases the plans were combined in "Separate Accounts" of similar plans, I would then set investment parameters like equity percentage and bond duration of these accounts).

I argued that I needed more than one set of most-likely cash flows from the actuaries, I needed to know how those flows changed with respect to inflation and the company stock (these were the most important determinants for individual plans) and general mortality and the economy (these were the most important systematic risks). Then I should not be setting static parameters or picking buy-and-hold investments, but dynamically hedging things.

The actuaries fundamentally didn't understand this, despite my extraordinary lucid and passionate presentations. Their profession was built on zero-beta risk. Their understanding of an insurance company was you made bets with people, collected the expected present value of the payoff at the risk-free rate, added your profit and trusted to diversification and the New York State Insurance Commission to prevent you from going broke. In some ways this was realistic in an era of regulated insurance costs. But you can see how annoying it was to someone fresh out of a quantitative finance PhD program.

On the investment side, the old-line traders who ran the portfolios wanted nothing to do with computer models or complex strategies. They wanted some money to run and a stable benchmark to beat. Their profession, in those days, said that their job was to make money by spotting superior securities and trading opportunities, and that the rest of the insurance company existed only to give them money to make more money with.

Fortunately the one actuary I saw eye-to-eye with got appointed Chief Actuary of Prudential (an honor a medievalist would understand), and I got a free hand. $3 billion of asset-liability dynamic hedging done with homebrew programs on a first-generation IBM PC in Visicalc and BASIC plus a few Fortran programs I wrote for a time-sharing mainframe. In those time-share days I got in the habit of prefacing all my file names with "AA," both for "Aaron" and to be first in a sort. The program for pricing a Savings Protector Contract was AASPC.BAS. Thirteen years later, I happened to see the output of a Pru pricing of a Stable Value Product (the successor to savings protectors). This 1990's era, Oracle/C++ professional implementation was still called AASPC.

This history inclines me to fight the introduction of actuarial concepts into finance. They are useful, but before importing them you have to understand why they aren't natives.

Putting a confidence interval on it would mislead people about what it is.

i think a lot of people have already been misled about what it is.

My point exactly, although I do accept it is confusing to have a confidence interval for a confidence interval (in effect). But I don't think it is reason not to quote the uncertainty in your estimate.

BTW I disagree about the parametric approach. I think more and more we will see non-parametric approaches eg copulas instead of correlations (how else can you deal with increased correlation in melt-downs), more emphasis on modelling factors (credit spreads, implieds) that are even more non-normal than equities and bonds and so on.

Mark

An actuary is a highly trained professional who will assure you that a tossed coin will come to rest on its edge.

Actuaries are overly fixated on future value probability distributions, but (as someone trained as an actuary, bear in mind) I also think that quants are overly fixated on price, as though this were a divinely given quantity rather than being largely a reflection of people's perceptions of, um, future value probability distributions.

i thought correlation was a weak statistical measure. if so, why is it so widely used?

Come on, jungle, you're smarter than that! ...because it's easy...that's always the answer!

P

p,

do you use MSN messenger? there is a very good crying emoticon that would be apropos here - i was hoping that wasn't the answer.

When I was a lad, becoming an actuary was seen as the ultimate goal for the best math students at university. Unfortunately, once the insurance companies got their hands on the best mathematicians they totally ruined and confused them with their archaic institutes and their pre-Newton math conventions...have you ever tried putting any math into 'words'? It's incomprehensible! Well, that's what actuaries seemed to be doing!***********A few comments - 1. placing confidence intervals on VaR is perfectly fine. You may confuse some, but graphs with confidence bands ought to overcome that. It is especially important when we are looking at tail probabilities - unless some sort of importance sampling, etc. has been used.2. most actuaries I have met are not that sophisticated mathematically. (I passed a few exams and worked in an actuarial firm before leaving for a phd in OR. Now work in asset mgt. with several actuaries). 3. Actuarial estimates seem to always be based on history - and, the main goal is to satisfy regulators as opposed to being correct or making money.4. The RiskLab in Switzerland has an article on actuarial vs. mathematical finance.5. I entered the actuarial profession precisely because it dealt with math and was "ranked" as the best overall job.6. As for putting things into words - none of the non-quantitative people I work with are used to writing things down. Nothing is defined, everyone talks loosely, and you never know if someone is BSing although you feel they are. As soon as you say "let's write this down and define some variables", they back away. I give credit for intuition and experience, but the non-quants don't seem to know their own business. Anyone share my frustration??

btw, RiskLab also has several articles on copulas.

Ko,Could you tell me why you, in your career plan, choose to work as an actuary in insurance business, rather than quant. in Street ?

Ko,Could you tell me why you, in your career plan, choose to work as an actuary in insurance business, rather than quant. in Street ? >>J,First, let me point out that I used the "quote" function incorrectly,and the first part of my last message is a quote from Paul.Also, see #2 from last message.As a poor naive math undergrad years ago, uncertain about whether to go to grad school, I decided to work for a few years. Chose actuarial work - paid well, I didn't really know about quant. finance (Dad's an accountant and I thought that was all there was to finance), and a friend worked in the field.I became bored very quickly. Left after two years to pursue a phd in OR (the most useful/general math modeling degree??). I learned about CMU's program - not where I was, though - thought the stuff was interesting, bought Hull to get acquainted and steered my coursework towards stochastics.I find myself working in credit risk for the asset mgt. branch of a large insurance company. So, a good number of my coworkers are actuaries, but I don't have to do that work. It's a happy ending. I do miss out on the experience of working within a large (5+) quant group, though.

i thought correlation was a weak statistical measure. if so, why is it so widely used? >>I think this is like asking, if fat is bad for you, why do people eat it?Food is not good or bad. Your body needs fat as well as other nutrients. But there's a right amount, and given the choice, far more people overconsume than underconsume.Statistical measures are also not good or bad, but certain are habitually overused. Correlation has the Central Limit Theorem behind it, if your risk is sufficiently evenly distributed among sufficiently many sufficiently independent risk factors, only correlation matters. That is reasonable for computing, say, a 90% confidence interval for a large, diverse equity basket. It is unreasonable for other situations.Two bad reasons people use correlation is that it's easy to calculate (this was a real consideration before computers, silly today) and easy to analyze mathematically.