Article

Credit Value Adjustment in the Extended Structural Default Model

Alexander Lipton and Andrew Rennie

in The Oxford Handbook of Credit Derivatives

Published in print January 2011 | ISBN: 9780199546787
Published online September 2012 | | DOI: http://dx.doi.org/10.1093/oxfordhb/9780199546787.013.0012

Series: Oxford Handbooks in Finance

 Credit Value Adjustment in the Extended Structural Default Model

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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.

Keywords: credit default swaps; valuation; counterplay credit risk; Merton; credit derivatives; jump size distributions

Article.  29896 words. 

Subjects: Economics ; Financial Markets ; Econometric and Statistical Methods and Methodology: General

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