320 Frequently Asked Questions In Quantitative Finance
according to the value of some financial quantity or index
over the life of the swap. The level of this principal may be
determined by the level of an interest rate on the payments
dates. Or the principal may be determined by a non-fixed
income index. In the first example we would only need a fixed-
income model, in the second we would also need a model
for this other quantity, and its correlation with interest rates.
In an index amortizing rate swap the principal typically can
amortize on each payment date. On later payment dates this
principal can then be amortized again, starting from its cur-
rent level at the previous payment date andnotbased on
its original level. This makes this contract very path depen-
dent. The contract can be priced in either a partial differential
equation framework based on a one- or two-factor spot-rate
based model, or using Monte Carlo simulations and a Libor
market-type model.
Interest rate swap is a contract between two parties to ex-
change interest on a specified principal. The exchange may
be fixed for floating or floating of one tenor for floating of
another tenor. Fixed for floating is a particularly common form
of swap. These instruments are used to convert a fixed-rate
loan to floating, or vice versa. Usually the interval between the
exchanges is set to be the same as the tenor of the floating
leg. Furthermore, the floating leg is set at the payment date
before it is paid. This means that each floating leg is equiv-
alent to a deposit and a withdrawal of the principal with an
interval of the tenor between them. Therefore all the floating
legs can be summed up to give one deposit at the start of
the swap’s life and a withdrawal at maturity. This means that
swaps can be valued directly from the yield curve without
needing a dynamic model. When the contract is first entered
into the fixed leg is set so that the swap has zero value. The
fixed leg of the swap is then called the par swap rate and is
a commonly quoted rate. These contracts are so liquid that
they define the longer-maturity end of the yield curve rather
than vice versa.
Inverse floater is a floating-rate interest-rate contract where
coupons go down as interest rates go up. The relationship is
linear (up to any cap or floor) andnotan inverse one.
