A constant maturity swap (CMS) is a
swap that allows the purchaser to fix the
duration of received flows on a swap.
The floating leg of an interest rate swap typically resets against a published index. The floating leg of a constant maturity swap fixes against a point on the swap curve on a periodic basis.
A constant maturity swap is an interest rate swap where the interest rate on one leg is reset periodically, but with reference to a market swap rate rather than
LIBOR
The London Inter-Bank Offered Rate (Libor ) was an interest rate average calculated from estimates submitted by the leading Bank, banks in London. Each bank estimated what it would be charged were it to borrow from other banks. It was the prim ...
. The other leg of the swap is generally LIBOR, but may be a fixed rate or potentially another constant maturity rate. Constant maturity swaps can either be single currency or
cross currency swaps. Therefore, the prime factor for a constant maturity swap is the shape of the forward implied
yield curve
In finance, the yield curve is a graph which depicts how the Yield to maturity, yields on debt instruments – such as bonds – vary as a function of their years remaining to Maturity (finance), maturity. Typically, the graph's horizontal ...
s. A single currency constant maturity swap versus LIBOR is similar to a series of
differential interest rate fixes (or "DIRF") in the same way that an interest rate swap is similar to a series of
forward rate agreements. Valuation of constant maturity swaps depend on volatilities of different forward rates and therefore requires a stochastic yield curve model or some approximated methodology like a
convexity adjustment, see for example Brigo and Mercurio (2006).
Example
A customer believes that the six-month
LIBOR
The London Inter-Bank Offered Rate (Libor ) was an interest rate average calculated from estimates submitted by the leading Bank, banks in London. Each bank estimated what it would be charged were it to borrow from other banks. It was the prim ...
rate will fall relative to the three-year swap rate for a given currency. To take advantage of this curve steepening, he buys a constant maturity swap paying the six-month LIBOR rate and receiving the three-year swap rate.
References
*
Damiano Brigo and
Fabio Mercurio
Fabio Mercurio (born 26 September 1966) is an Italian mathematician, internationally known for a number of results in mathematical finance.
Main results
Mercurio worked during his Ph.D. on incomplete markets theory using dynamic mean-variance hed ...
(2006). ''Interest-Rate Models: Theory and Practice - with Smile, Inflation and Credit'', Springer Verlag, 2nd ed. 2006.
Constant Maturity Swaps, Forward Measure and LIBOR Market Model Dariusz Gatarek.
External links
Swaps (finance)
{{Derivatives market