316 Frequently Asked Questions In Quantitative Finance
CMOs are interest rate risk and prepayment risk, therefore it
is important to have a model representing prepayment.
Compound option is an option on an option, such as a call on a
put which would allow the holder the right to buy a specified
put at a later date for a specified amount. There is no element
of choice in the sense of which underlying option to buy (or
sell).
Contingent premium option is paid for at expiration only if
the option expires in the money, not up front. If the option
expires below the strike, for a call, then nothing is paid, but
then nothing is lost. If the asset is just slightly in the money
then the agreed premium is paid, resulting in a loss for the
holder. If the underlying ends up significantly in the money
then the agreed premium will be small relative to the payoff
and so the holder makes a profit. This contract can be valued
as a European vanilla option and a European digital with the
same strike. This contract has negative gamma below the
strike (for a call) and then positive gamma at the strike and
above, so its dependence on volatility is subtle. The holder
clearly wants the stock to end up either below the strike (for
a call) or far in the money. A negative skew will lower the
price of this contract.
Convertible bond is a bond issued by a company that can,
at the choosing of the holder, be converted into a speci-
fied amount of equity. When so converted the company will
issue new shares. These contracts are a hybrid instrument,
being part way between equity and debt. They are appealing
to the issuer since they can be issued with a lower coupon
than straight debt, yet do not dilute earnings per share. If
they are converted into stock that is because the company
is doing well. They are appealing to the purchaser because
of the upside potential with the downside protection. Of
course, that downside protection may be limited because
these instruments are exposed to credit risk. In the event of
default the convertible bond ranks alongside debt, and above
equity.
These instruments are best valued using finite-difference meth-
ods because that takes into account the optimal conversion
time quite easily. One must have a model for volatility and
