CMS Spread Options and Similar Options in Multi-Factor HJM Framework

Abstract

Constant maturity swaps (CMS), CMS spreads and similar products are analyzed in multi-factor HJM models. For Gaussian models, which include some Libor Market Models and the G2 model, explicit approximated formula are provided. The approximations are done through two different approaches: an exact solution to an approximated equation and an approximated solution to the exact equation. The first approach has been used previously in the literature for other models, the second is new. The approximations provide prices with error less than 0.02 basis point for the best approach; this is better than the previous literature and negligible in practice. The approach can be used to price standard CMS and CMS spreads and also for similar exotic products.

Keywords: Constant Maturity Swap, CMS spread, multi-factor, HJM

JEL Classification: G13, E43, C63