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Credit Derivative Evaluation and CVA under the Benchmark Approach

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Abstract

In this paper, we discuss how to model credit risk under the benchmark approach. Firstly we introduce an affine credit risk model. We then show how to price credit default swaps (CDSs) and introduce credit valuation adjustment (CVA) as an extension of CDSs. In particular, our model can capture right-way - and wrong-way exposure. This means, we capture the dependence structure of the default event and the value of the transaction under consideration. For simple contracts, we provide closed-form solutions. However, due to the fact that we allow for a dependence between the default event and the value of the transaction, closed-form solutions are difficult to obtain in general. Hence we conclude this paper with a reduced form model, which is more tractable.

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  • Jan Baldeaux & Eckhard Platen, 2013. "Credit Derivative Evaluation and CVA under the Benchmark Approach," Research Paper Series 324, Quantitative Finance Research Centre, University of Technology, Sydney.
    • Handle: RePEc:uts:rpaper:324
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    References listed on IDEAS

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    1. Nicola Bruti-Liberati, 2007. "Numerical Solution of Stochastic Differential Equations with Jumps in Finance," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 1, July-Dece.
    2. Eckhard Platen, 2002. "A Benchmark Framework for Integrated Risk Management," Research Paper Series 82, Quantitative Finance Research Centre, University of Technology, Sydney.
    3. Eckhard Platen, 2006. "A Benchmark Approach To Finance," Mathematical Finance, Wiley Blackwell, vol. 16(1), pages 131-151, January.
    4. Andrea Pallavicini & Daniele Perini & Damiano Brigo, 2011. "Funding Valuation Adjustment: a consistent framework including CVA, DVA, collateral,netting rules and re-hypothecation," Papers 1112.1521, arXiv.org, revised Dec 2011.
    5. Long, John Jr., 1990. "The numeraire portfolio," Journal of Financial Economics, Elsevier, vol. 26(1), pages 29-69, July.
    6. Mark Craddock & Kelly A. Lennox, 2010. "Lie Symmetry Methods for Multidimensional Linear, Parabolic PDES and Diffusions," Research Paper Series 274, Quantitative Finance Research Centre, University of Technology, Sydney.
    7. Ke Du & Eckhard Platen, 2016. "Benchmarked Risk Minimization," Mathematical Finance, Wiley Blackwell, vol. 26(3), pages 617-637, July.
    8. Eckhard Platen & Renata Rendek, 2012. "Approximating the numéraire portfolio by naive diversification," Journal of Asset Management, Palgrave Macmillan, vol. 13(1), pages 34-50, February.
    9. Damiano Brigo & Kyriakos Chourdakis, 2009. "Counterparty Risk For Credit Default Swaps: Impact Of Spread Volatility And Default Correlation," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 12(07), pages 1007-1026.
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    More about this item

    Keywords

    Credit derivatives; credit valuation adjustment; benchmark approach; affine processes; real world pricing;
    All these keywords.

    JEL classification:

    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General

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