"Quants have ruled the financial roost. But this might just be the time for actuaries to fight back. "

Via Alea, Paul Wilmot on Actuaries Vs Quants:

"Those working in the two fields of actuarial science and quantitative finance have not always been totally appreciative of each others’ skills. Actuaries have been dealing with randomness and risk in finance for centuries. Quants are the relative newcomers, with all their fancy stochastic mathematics. Rather annoyingly for actuaries, quants come along late in the game and thanks to one piece of insight in the early ‘70s completely change the face of the valuation of risk. The insight I refer to is the concept of dynamic hedging, first published by Black, Scholes and Merton in 1973. Before 1973 derivatives were being valued using the “actuarial method,” i.e. in a sense relying, as actuaries always have, on the Central Limit Theorem. Since 1973 and the publication of the famous papers, all that has been made redundant. Quants have ruled the financial roost.

But this might just be the time for actuaries to fight back."

First, read this:

"Black–Scholes in practice

Results using the Black–Scholes model differ from real world prices due to simplifying assumptions of the model. One significant limitation is that in reality security prices do not follow a strict stationary log-normal process, nor is the risk-free interest actually known (and is not constant over time). The variance has been observed to be non-constant leading to models such as GARCH to model volatility changes. Pricing discrepancies between empirical and the Black-Scholes model have long been observed in options that are far out-of-the-money, and these correspond to the likelihood of extreme price changes. While these are very rare when price changes are normally distributed, they are observed in practice and can be modeled as a temporary increase in volatility.

Nevertheless, Black–Scholes pricing is widely used in practice ^[1], for it is easy to calculate and explicitly model the relationship of all the variables. It is a useful approximation, particularly when analyzing the directionality that prices move when crossing critical points. It is used both as a quoting convention and a basis for more refined models. Although volatility is not constant, results from the model are often useful in practice and helpful in setting up hedges in the correct proportions to minimize risk. Even when the results are not completely accurate, they serve as a first approximation to which adjustments can be made.

Additionally, rather than assuming a volatility a priori and computing prices from it, one can use the model to solve for volatility, which gives the implied volatility of an option at given prices, durations and exercise prices. Solving for volatility over a given set of durations and strike prices one can construct an implied volatility surface. In this application of the Black–Scholes model, a coordinate transformation from the price domain to the volatility domain is obtained. Rather than quoting option prices in terms of dollars per unit (which are hard to compare across strikes and tenors), option prices can thus be quoted in terms of implied volatility, which leads to trading of volatility in option markets."

Notice the phrases:

"differ from real world prices due to simplifying assumptions of the model."
"nor is the risk-free interest actually known"
"and these correspond to the likelihood of extreme price changes. "
" is widely used in practice ^[1], for it is easy to calculate and explicitly model the relationship of all the variables. It is a useful approximation"
" Even when the results are not completely accurate, they serve as a first approximation to which adjustments can be made."
" which gives the implied volatility of an option at given prices, durations and exercise prices."

Now, unless you want to actually learn how to use these models, these phrases give you enough of an understanding to see that these models are only tools. They are used to model very risky products, in many cases. That should be enough to let a person know that these are very risky models, intended for a very limited number of investors. At least, that's what I see.

For the Central Limit Theorem, I pulled out this graph, which shows that you get a graph telling you how likely various events are:

"Probability mass function of the sum of 1,000 terms

The following image shows the result of a simulation based on the example presented in this page. The extraction from the uniform distribution is repeated 1,000 times, and the results are summed.

Since the simulation is based on the Monte Carlo method, the process is repeated 10,000 times. The results shows that the distribution of the sum of 1,000 uniform extractions resembles the bell-shaped curve very well."

"I am putting the finishing touches to this article a few days after the first anniversary of the “day that quant died.” In early August 2007 a number of high-profile and previously successful quantitative hedge funds suffered large losses. People said that their models “just stopped working.” The year since has been occupied with a lot of soul searching by quants, how could this happen when they’ve got such incredible models?"

Here's a philosophical question: How can a model just stop working?

"In my view the main reason why quantitative finance is in a mess is because of complexity and obscurity."

Neither of these are good. A good result would be simplifying complexity and obscurity, not adding to it.

"Quants are making their models increasingly complicated, in the belief that they are making improvements. This is not the case. More often than not each ‘improvement’ is a step backwards."

Also not good.

"If this were a proper hard science then there would be a reason for trying to perfect models. But finance is not a hard science, one in which you can conduct experiments for which the results are repeatable. Finance, thanks to it being underpinned by human beings and their wonderfully irrational behaviour, is forever changing. It is therefore much better to focus your attention on making the models robust and transparent rather than ever more intricate."

Robust? I agree with this. Human Agency underpins this whole enterprise.

"As I mentioned in a recent wilmott.com blog, there is a maths sweet spot in quant finance. The models should not be too elementary so as to make it impossible to invent new structured products, but nor should they be so abstract as to be easily misunderstood by all except their inventor (and sometimes even by him), with the obvious and financially dangerous consequences. I teach on the Certificate in Quantitative Finance and in that our goal is to make quant finance practical, understandable and, above all, safe."

I hope that it works.

"When banks sell a contract they do so assuming that it is going to make a profit. They use their complex models, with sophisticated numerical solutions, to come up with the perfect value. Having gone to all that effort for that contract they then throw it into the same pot as all the others and risk manage en masse. The funny thing is that they never know whether each individual contract has “washed its own face.” Sure they know whether the pot has made money, their bonus is tied to it. But each contract? It makes good sense to risk manage all contracts together but it doesn’t make sense to go to such obsessive detail in valuation when ultimately it’s the portfolio that makes money, especially when the basic models are so dodgy. The theory of quant finance and the practice diverge. Money is made by portfolios, not by individual contracts."

How about looking at the individual contracts?

"In other words, quants make money from the Central Limit Theorem, just like actuaries, it’s just that quants are loath to admit it! Ironic."

How the hell do you tell who's making the money for you if it's all thrown into a pot and undifferentiated?

"It’s about time that actuaries got more involved in quantitative finance. They could bring some common sense back into this field. We need models which people can understand and a greater respect for risk. Actuaries and quants have complementary skill sets. What high finance needs now are precisely those skills that actuaries have, a deep understanding of statistics, an historical perspective, and a willingness to work with data."

And a penchant for making money and avoiding catastrophes. Good luck!