Sorry, I’ve been away for a while. Too much to do, not
enough sleep, etc. Which is a shame; after all there is an embarrassment of
riches or rather topics to bitch about out there! In fact, part of the reason
why I have not been more prolific lately is that I just cannot seem to keep up
with what going on out there. Too many crises, acts of muppetry or reasons to
gawk incredulously to even begin to gather my thoughts before the next one is
up on the agenda. It’s stressful! Anyway, enough prevarication let us move on.
The first thing I have to do is to make sure that you
understand that I DO NOT regularly (or even occasionally) read The Guardian. I
strictly limit myself to articles and columns recommended to me by concerned
friends. Thus I was confronted with a piece on the pitfalls of mathematical
modeling in finance that was on the face of it actually reasonably well thought
out. Please find aforementioned piece here.
Shame, however, that in the end the author managed to not only conflate about
three or four different problems that plague the world of finance but also
missed out a number of glaring problems with the thrust of his argument and
then finally came up with the weirdest and most hackneyed remedy to the mess we
are in that only a dyed-in-the-wool materialist dialectic type Marxist who
sadly doesn’t really understand Marx (or possibly did not read him to the end).
Right, so what are my points of contention?
Number one: Black-Scholes is not the all there is to
financial modeling – Despite the somewhat excessive use of big names, a
historical narrative that goes back to the beginning of the 20th
century mathematics and features super numerate Frenchmen and cryptic terms
such as “Brownian motion” the Black-Scholes model is not really all there is to
quantitative finance. In fact, it’s used for a very specific purpose, namely
valuing options. And granted, therein lies a challenge. And it is open to
abuse. And it can, if misused, bring about all manner of financial ruin.
However, it didn’t really bring about the credit crunch all by itself (granted
the author indemnifies himself a bit by phrasing the thrust of his argument in
such a manner as to avoid stating that B-S [yes, funny(ish) acronym] is
directly responsible for the credit crunch and merely “opened” the field, but
the implication is pretty blunt). For that one needs all manner of other
mathematical chimeras that defy easy comprehension: Gaussian cupolas, mean
reversion theorems, VAR, Monte Carlo simulations, the list goes on and on. Just
burrowing into the history of one particular type of financial modeling
technique doesn’t really make for a comprehensive argument about the use of
mathematical models in finance. Especially if that history is bereft of it’s
proper context and leaves out a cautionary tale that is known industry wide.
Which leads me to my next point.
Number two: Long Term Capital Management … Kaboom! Rather
gamely, the author informs us, that the brains that developed the B-S formula
(or rather the surviving part, seeing that Mr. Black passed away a before it
could come to pass) were awarded the Nobel prize for economics in 1997. What he
fails to mention is that Myron Scholes and Robert Merton (who didn’t author the
model but refined it) basically lost their shirts when the investment company
they co-founded – not overly prophetically named Long Term Capital Management –
demonstrated the limits of the usefulness of their theoretical acumen by
imploding. The fact that LCTM peaked and then died in 1998, the year following
the award of the Nobel prize, does actually make me think that whoever is in
charge of the universe does have a wicked sense of irony. At any rate, that
story has been and remains a constant reminder for any option trader to not
rely on B-S derived option valuations too much. I bet you; even the most
illiterate option desk in the city has a copy of this book lying around
somewhere.
 |
| John Meriwhether, Robert C. Merton and Myron Scholes as seen by themselves. |
 |
| John Meriwhether, Robert C. Merton and Myron Scholes as seen by the financial industry. |
Number three: Derivatives are not simply bets on bets –
Another thing that really annoys me about that article is the obtuseness with
which derivatives are simply described as “investments in investments, bets about bets”. I’d expect
that kind of definition from a dreadlocked tramp at the Occupy camp outside St
Paul’s, not from a Emeritus
Professor of Mathematics at Warwick University and a Fellow of the Royal
Society who has written over 80 books, and has won three gold medals for his
work on the public understanding of science. With this standard of work, I do
wonder who awarded those gold medals? Derivatives do cover a humongous range of
different financial products, which across all different types do share one –
and only one – characteristic: Their value is determined not intrinsically, but
through observation of another, underlying asset. It is derived; hence the name
derivative. And yes, they can be bets upon bets. But they are not necessarily
so. To say so is a bit like asserting that hammers are instruments of murder.
They certainly can be, but I’m not so sure that really comprehensively captures
the essence of what a derivative is. To be fair, derivatives are a bit more
complex than hammers. They also can wreak havoc on a larger scale. But the
analogy does work. Oh, and please spare me the Warren Buffet comment.
Number four: More models are NOT the answer!!! – The single
most mind-boggling thing about the whole article really is the conclusion.
Namely, that the answer to the travails of the world of modern finance lies in
an increase in the reliance on mathematical models. I’m not quite clear how the
factually somewhat compromised but still largely coherent rant about the
inadequacy and misuse of mathematical models in the world of derivatives
finance leads to the conclusion that more rather than less emphasis needs to be
put on developing ever more complex models. I mean, he does get one thing
right: model abuse is at the heart of a rotten system. How that model abuse is
remedied by use of more intricate (and by implication less well understood)
models is beyond me. I daresay trying to make it more academic is not the
answer. But then again, Emeritus
Professor of Mathematics at Warwick University tactfully failed to mention that
his esteemed and academically minded colleagues’ venture into the world of
finance did end with a bang and not a chest beating roar of triumph. Personally
I think finance should be run more like Tazerball:
And I think next I’ll try and
write something about pirates!
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