The derivatives of the constant maturity swap (CMS) are evaluated by the LIBOR market model (LMM) implemented by Monte Carlo methods in the previous researches. 1n this paper, we derive an approximated dynamic process of the forward-swap rate (FSR) under LMM. Based on the approximated dynamics for the FSR under one factor model, CMS spread options and CMS ratchet options are valued by the no-arbitrage method in approximated analytic formulas. In the numerical analysis, the relative errors between the Monte Carlo simulations and the approximated closed form formulas are very small for CMS spread options and CMS ratchet options and we also provide an efficient hedging method for these products under one factor LMM.
Journal of the Chinese Statistical Association, 48(3) , 161-189