314 Frequently Asked Questions In Quantitative Finance
Chooser option is an option on an option, therefore a second-
order option. The holder has the right to decide between
getting a call or a put, for example, on a specified date. The
expiration of these underlying options is further in the future.
Other similar contracts can be readily imagined. The key to
valuing such contracts is the realization that the two (or more)
underlying options must first be valued, and then one values
the option on the option. This means that finite-difference
methods are the most natural solution method for this kind
of contract. There are some closed-form formulæ for simple
choosers when volatility is at most time dependent.
Cliquet option is a path-dependent contract in which amounts
are locked in at intervals, usually linked to the return on some
underlying. These amounts are then accumulated and paid off
at expiration. There will be caps and/or floors on the locally
locked-in amounts and on the global payoff. Such contracts
might be referred to as locally capped, globally floored, for
example. These contracts are popular with investors because
they have the eternally appreciated upside participation and
the downside protection, via the exposure to the returns and
the locking in of returns and global floor. Because of the
locking in of returns and the global cap/floor on the sum of
returns, these contracts are strongly path dependent. Typically
there will be four dimensions, which may in special cases
be reduced to three via a similarity reduction. This puts
the numerical solution on the Monte Carlo, finite difference
border. Neither are ideal, but neither are really inefficient
either. Because these contracts have a gamma that changes
sign, the sensitivity is not easily represented by a simple vega
calculation. Therefore, to be on the safe side, these contracts
should be priced using a variety of volatility models so as to
see the true sensitivity to the model.
Constant Maturity Swap (CMS) is a fixed-income swap. In the
vanilla swap the floating leg is a rate with the same maturity
as the period between payments. However, in the CMS the
floating leg is of longer maturity. This apparently trivial differ-
ence turns the swap from a simple instrument, one that can
be valued in terms of bonds without resort to any model, into
a model-dependent instrument.
