The efficient pricing of CMS and CMS spread derivatives

Abstract

Two popular products on the interest rate market are Constant Maturity Swap (CMS) derivatives and CMS spread derivatives. This thesis focusses on the efficient pricing of CMS and CMS spread derivatives, in particular the pricing of CMS and CMS spread options. The notional values for these products are usually quite large, so even small errors when pricing these products can lead to substantial losses. Therefore, the pricing of these products has to be accurate. It is possible to use sophisticated models (e.g. Libor Market Model) to price these products, however the downside is that these models generally have high computational costs; they are not very efficient. To efficiently price CMS options the Terminal Swap Rate (TSR) approach can be used. From this approach TSR models are obtained, we will consider four different TSR models. Two of these TSR models are established in the literature, the other two TSR models are developed in this thesis. The main advantages of a TSR model is that the computational costs are low and that it has good numerical tractability. To price CMS spread options the copula approach is usually used. With the copula approach a pricing formula can be obtained for efficient valuations of CMS spread options. The copula that is considered in this thesis is the Gaussian copula. The TSR models are also a key component in the copula approach, because the marginal distributions are obtained with the help of a TSR model. Furthermore, an alternative approach is considered for the pricing of CMS spread options. The CMS spread options are priced with a relatively simple stochastic volatility model, the displaced diffusion SABR model. The displaced diffusion SABR model is obtained by applying the Markovian projection method to a modification of a two-dimensional version of the well-established SABR model. The calibration of the two-dimensional SABR model is performed with the help of the TSR approach.