Chapter 2: FAQs 117
the scientist the question of calibration becomes one
concerning the existence of arbitrage. If you are a hedge
fund looking for prop trading opportunities with vanillas
then calibration is precisely what youdon’twant to do.
And robustness would be nice, but maybe the financial
world is so unstable that models can never be robust.
To the practitioner he needs to be able to price quickly
to get the deal done and to manage the risk. If he is
in the business of selling exotic contracts then he will
invariably be calibrating, so that he can say that his
prices are consistent with vanillas. As long as the model
isn’t too inaccurate or sensitive, and he can add a suf-
ficient profit margin, then he will be content. So to the
practitioner speed and ability to calibrate to the market
are the most important.
The scientist and the practitioner have conflicting inter-
ests. And the practitioner usually wins.
And what could be faster than a closed-form solution?
This is why practitioners tend to favour closed forms.
They also tend to be easier to understand intuitively
than a numerical solution. The Black–Scholes formulæ
are perfect for this, having a simple interpretation in
terms of expectations, and using the cumulative distri-
bution function for the Gaussian distribution.
Such is the desire for simple formulæ that people often
use the formulæ for the wrong product. Suppose you
want to price certain Asian options based on an arith-
metic average. To do this properly in the Black–Scholes
world you would do this by solving a three-dimensional
partial differential equation or by Monte Carlo simula-
tion. But if you pretend that the averaging is geometric
and not arithmetic then often there are simple closed-
form solutions. So use those, even though they must
be wrong. The point is that they will probably be less