116 Frequently Asked Questions In Quantitative Finance
Why Do Quants Like Closed-Form
Solutions?
Short Answer
Because they are fast to compute and easy to under-
stand.
Example
The Black–Scholes formulæ are simple and closed-form
and often used despite people knowing that they have
limitations, and despite being used for products for
which they were not originally intended.
Long Answer
There are various pressures on a quant when it comes
to choosing a model. What he’d really like is a model
that is
- robust: small changes in the random process for the
underlying don’t matter too much
- fast: prices and the greeks have to be quick to
compute for several reasons, so that the trade gets
done and you don’t lose out to a competitor, and so
that positions can be managed in real time as just
one small part of a large portfolio
- accurate: in a scientific sense the prices ought to be
good, perhaps matching historical data. This is
different from robust, of course
- easy to calibrate: banks like to have models that
match traded prices of simple contracts
There is some overlap in these. Fast may also mean
easy to calibrate, but not necessarily. Accurate and
robust might be similar, but again, not always.
From the scientific point of view the most important
of these is accuracy. The least important is speed. To
