Abstract and Keywords
This article develops a methodology for valuing the counterparty credit risk inherent in credit default swaps, and presents a multi-dimensional extension of Merton's model (Merton 1974), where the joint dynamics of the firm's values are driven by a multi-dimensional jump-diffusion process. Applying the Fast Fourier Transform and finite-difference methods, it develops a forward induction procedure for calibrating the model, and a backward induction procedure for valuing credit derivatives in 1D and 2D. Jump size distributions of two types are considered, namely, discrete negative jumps (DNJs) and exponential negative jumps (ENJs), and showed that, for joint bivariate dynamics, the model with ENJs produces a noticeably lower implied Gaussian correlation than the one produced by the model with DNJs, although for both jump specifications the corresponding marginal dynamics fit the market data adequately. Based on these observations, and given the high level of the default correlation among financial institutions (above 50 per cent), the model with DNJs, albeit simple, seems to provide a more realistic description of default correlations and, thus, the counterparty risk, than a more sophisticated model with ENJs.
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