322 Frequently Asked Questions In Quantitative Finance
gral (in the same number of dimensions as there are underly-
ings). This amounts to a numerical quadrature problem which
is easily achieved by Monte Carlo or quasi Monte Carlo meth-
ods. The theory may be straightforward but the practice is not
since the price will depend on the correlations between all of
the underlyings, and these parameters are usually quite fickle.
Parisian option is a barrier option for which the barrier
feature (knock in or knock out) is only triggered after the
underlying has spent a certain prescribed time beyond the
barrier. The effect of this more rigorous triggering criterion
is to smooth the option value (and delta and gamma) near
the barrier to make hedging somewhat easier. It also makes
manipulation of the triggering, by manipulation of the underly-
ing asset, much harder. In the classical Parisian contract the
‘clock’ measuring the time outside the barrier is reset when
the asset returns to within the barrier. In the Parisian contract
the clock is not reset but continues ticking as long as the
underlying is beyond the barrier. These contracts are strongly
path dependent and can be valued either by Monte Carlo sim-
ulation or by finite-difference solution of a three-dimensional
partial differential equation.
Pass through is a security which collects payments on various
underlying securities and then passes the amounts on to
investors. They are issued by Special Purpose Vehicles and
can be made to avoid appearing on balance sheets. This
achieves a variety of purposes, some rather nefarious.
Passport option is a call option on the trading account of an
individual trader, giving the holder the amount in his account
at the end of the horizon if it is positive, or zero if it is
negative. For obvious reasons they are also called perfect
trader options. The terms of the contract will specify what the
underlying is that the trader is allowed to trade, his maximum
long and short position, how frequently he can trade and for
how long. To price these contracts requires a small knowledge
of stochastic control theory. The governing partial differential
equation is easily solved by finite differences. Monte Carlo
would be quite difficult to implement for pricing purposes.
Since the trader very quickly moves into or, more commonly,
