312 Frequently Asked Questions In Quantitative Finance
Basket option has a payoff that depends on more than one
underlying. A modest example would be an option that gives
you at expiration the value of the higher performing out of
two stocks. Another example would be a contract that pays
the average of the values of 20 stocks at expiration provided
that value is above a specified strike level. These contracts
can be valued straightforwardly by Monte Carlo simulation as
long as there is no early exercise feature. You would not use
finite-difference methods because of the high dimensionality.
If the contract is European, non path dependent with all of
the underlyings following lognormal random walks with con-
stant parameters then there is a closed-form formula for the
value of the contract, and this can be calculated by numerical
integration (quadrature). Basket options are popular in for-
eign exchange for those with exposure to multiple exchange
rates. They can also be used as options on your own index.
Although pricing these contracts can be theoretically straight-
forward they depend crucially on the correlation between
the underlyings. These correlations can be very difficult to
estimate since they can be quite unstable.
Bermudan option is one where the holder has the right to
exercise on certain dates or periods rather than only at
expiration (European exercise) or at any time (American
exercise). Bermudan options cannot be worth less than their
European equivalent and cannot be worth more than their
American equivalent.
Binary option has a payoff that is discontinuous. For example
a binary call pays off a specified amount if the underlying ends
above the strike at expiration and is otherwise worthless. A
one-touch pays off the specified amount as soon as the strike
is reached, it can be thought of as an American version of the
European binary. These contracts are also called digitals.
Break/Cancellable forward is a forward contract, usually FX,
where the holder can terminate the contract at certain times
if they so wish.
Coupe option is a periodic option in which the strike gets reset
to the worst of the underlying and the previous strike. Similar
to a cliquet option, but cheaper.
