192 Frequently Asked Questions In Quantitative Finance
that it might give prices that are inconsistent with the
market. For example, you are interested in buying a
certain option. You think volatility is 27%, so you use
that number to price the option, the price you get is
$15. However, the market price of that option is $19.
Are you still interested in buying it? You can either
decide that the option is incorrectly priced or that your
volatility estimate is wrong.
The other method is to assume, effectively, that there is
information in the market prices of traded instruments.
In the above example we ask what volatility must we
put into a formula to get the ‘correct’ price of $19. We
then use that number to price other instruments. In this
case we have calibrated our model to an instantaneous
snapshot of the market at one moment in time, rather
than to any information from the past.
Calibration is common in all markets, but is usually
more complicated than in the simple example above.
Interest rate models may have dozens of parameters or
even entire functions to be chosen by matching with the
market.
Calibration can therefore often be time consuming. Cal-
ibration is an example of an inverse problem, in which
we know the answer (the prices of simple contracts)
and want to find the problem (the parameters). Inverse
problems are notoriously difficult, for example being
very sensitive to initial conditions.
Calibration can be misleading, since it suggests that
your prices are correct. For example if you calibrate a
model to a set of vanilla contracts, and then calibrate
a different model to the same set of vanillas, how do
you know which model is better? Both correctly price
vanillas today. But how will they perform tomorrow?
Will you have to recalibrate? If you use the two different
