Modifying the LMM to price constant maturity swaps

Ting Pin Wu, Son Nan Chen

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


Within the framework of the LIBOR market model, this article presents a new approach for finding the approximate distribution of constant maturity swap (CMS) rates under forward martingale measures. With this approach, many popular CMS-type interest rate derivatives, such as CMS, CMS caps, CMS floors, CMS steepeners, and CMS range accruals, can be priced under the LIBOR market model and their risk can be managed consistently with LIBOR-type interest rate derivatives. We use this approximation to price three types of CMSs, namely, CMS-for-CMS, CMSfor-LIBOR, and CMS-for-fixed CMSs. The resulting pricing formulas are shown to be robustly accurate and time saving by comparison with Monte Carlo simulations based on the market data over a recent three-year period.

Original languageEnglish
Pages (from-to)20-32
Number of pages13
JournalJournal of Derivatives
Issue number2
StatePublished - Dec 2010


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