Constant Maturity Credit Default Swaps (CMCDS) are similar to the common Credit Default Swap (CDS), offering the investor protection in exchange of a periodically paid spread. In contrast to the CDS spread, which is fixed through out the maturity of the CDS, the spread of a CMCDS is floating and is indexed to a reference CDS with a fixed time to maturity at reset dates. The floating spread is proportional to the constant maturity CDS market spread. The maturity of the CMCDS and of the reference CDS does not have to be the same.
The aim of this paper is to present a Monte Carlo method for estimating the participation rate based on single sided L¶evy models. We set up a firm's value model where the value is driven by the exponential of a Levy process with positive drift and only negative jumps. These single sided firm's value models allow us to calculate the default probabilities fast by a double Laplace inversion technique presented in Rogers (2000) and Madan and Schoutens (2007).
The fast calculation of the default probabilities implies a fast calculation of CDS values which is important for calibration. The models ability to calibrate on a CDS term structure has already been proven in Madan and Schoutens (2007). Based on the single sided firm's value model JÄonsson and Schoutens (2007) present how a dynamic spread generator can be set up that allows pricing of exotic options on single name CDS by Monte Carlo simulations.
The paper is organized as follows. In the following section we present the mechanics and valuation of Constant Maturity Credit Default Swaps. In Section 3 the singel sided firm's value model is introduced. The Monte Carlo algorithm and numerical results are given in Section 4. The paper ends with conclusions.