Abstract
In this paper, under the reduced form framework and “Bottom Up” method, a model for pricing a basket Loan-only Credit Default Swap (LCDS), with the negative correlation between prepayment and default, is established. A general pricing formula for it is obtained, where one factor CIR (Cox-Ingersoll-Ross) and ICIR (Inversed CIR) models are used to describe the negative correlation between prepayment and default. In this situation, the positivity of prepayment and default intensity processes are guaranteed. Numerical computations are presented.
Highlights
IntroductionDuring the last twenty years, the market for credit derivatives has experienced rapid development with the increasingly prominent importance of derivatives which leads to the evolution and innovation of the credit market
During the last twenty years, the market for credit derivatives has experienced rapid development with the increasingly prominent importance of derivatives which leads to the evolution and innovation of the credit market.The international financial crisis began in the year 2008 shocked the financial market even the global economy
A general pricing formula for it is obtained, where one factor CIR (Cox-Ingersoll-Ross) and ICIR (Inversed CIR) models are used to describe the negative correlation between prepayment and default
Summary
During the last twenty years, the market for credit derivatives has experienced rapid development with the increasingly prominent importance of derivatives which leads to the evolution and innovation of the credit market. Academic studies usually analyze the risks of interest rate, prepayment, default etc., which are related to the asset securitization products by building mathematical models They try to use methods of stochastic processes, partial differential equations and statistics etc. As a result, many new methods and techniques have been developed within the reduced-form framework in recent years, especially for pricing basket CDS, CDO and LCDS etc. We use a factor model to describe the correlation of the prepayment and default among the references This model is developed step by step from Pricing a basket CDS, the simplest basket LCDS (two references) to large-scale basket LCDS to obtain the formulae.
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