A constant maturity swap, also known as a CMS, is a

swap Swap or SWAP may refer to: Finance * Swap (finance), a derivative in which two parties agree to exchange one stream of cash flows against another * Barter Science and technology * Swap (computer programming), exchanging two variables in t ...

that allows the purchaser to fix the

duration Duration may refer to: * The amount of time elapsed between two events * Duration (music) – an amount of time or a particular time interval, often cited as one of the fundamental aspects of music * Duration (philosophy) – a theory of time and ...

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 is an interest-rate average calculated from estimates submitted by the leading banks in London. Each bank estimates what it would be charged were it to borrow from other banks. The resulting average rate is u ...

. 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 swap A cross is a geometrical figure consisting of two intersecting lines or bars, usually perpendicular to each other. The lines usually run vertically and horizontally. A cross of oblique lines, in the shape of the Latin letter X, is termed a sa ...

s. 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 yields on debt instruments - such as bonds - vary as a function of their years remaining to maturity. Typically, the graph's horizontal or x-axis is a time line of months or ye ...

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

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 Damiano Brigo (born Venice, Italy 1966) is an applied mathematician and Chair in Mathematical Finance at Imperial College London. He is known for research in filtering theory and mathematical finance. Main results Brigo started his work with the ...

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