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Credit derivative evaluation and CVA under the benchmark approach. (English) Zbl 1368.91178
Summary: 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.
91G40 Credit risk
Full Text: DOI
[1] Baldeaux, J., & Platen, E. (2013). Functionals of multidimensional diffusions with applications to finance. Bocconi & Springer Series. · Zbl 1401.60001
[2] Bielecki, T., Brigo, D., & Patras, F. (2011). Credit risk frontiers: Subprime crisis, pricing and hedging, CVA, MBS, ratings, and liquidity. New York: Wiley.
[3] Brigo, D; Chourdakis, K, Counterparty risk for credit default swaps: impact of spread volatility and default correlation, International Journal of Theoretical and Applied Finance, 12, 1007-1026, (2009) · Zbl 1187.91206
[4] Burgard, CZ; Kjaer, M, Funding cost adjustment for derivatives, Asia Risk, 2011, 63-67, (2011)
[5] Cesari, G., Aquilina, J., Charpillon, N., Filipović, Z., Lee, G., & Manda, I. (2009). Modelling, pricing, and hedging counterparty credit exposure. Berlin: Springer. · Zbl 1188.91001
[6] Crépey, S. (2011). A BSDE approach to counterparty risk under funding constraints. University de Evry (working paper).
[7] Du, K., & Platen, E. (2012a). Benchmarked risk minimization. University of Technology, Sydney (working paper). · Zbl 1386.91124
[8] Du, K., & Platen, E. (2012b). Forward and futures contracts on commodities under the benchmark approach. University of Technology, Sydney (working paper).
[9] Filipović, D. (2009). Term-structure models. Berlin: Springer Finance. · Zbl 1184.91002
[10] Kelly, JR, A new interpretation of information rate, Bell Systems Technology Journal, 35, 917-926, (1956)
[11] Lennox, K. (2011). Lie symmetry methods for multi-dimensional linear parabolic PDEs and diffusions. Ph. D. thesis, UTS, Sydney.
[12] Long, JB, The numeraire portfolio, Journal on Financial Economics, 26, 29-69, (1990)
[13] Musiela, M., & Rutkowski, M. (2005). Martingale methods in financial modelling (2nd ed.)., Volume 36 of Applied Mathematics Berlin: Springer. · Zbl 1058.60003
[14] Pallavicini, A., Perini, D., & Brigo, D. (2011). Funding valuation adjustment: A consistent framework including CVA, DVA, collateral, netting rules and re-hypothecation. Imperial College, London (working paper).
[15] Platen, E. (2002). A benchmark framework for integrated risk management. Technical report, University of Technology, Sydney. QFRG Research Paper 82. · Zbl 1191.91048
[16] Platen, E., & Bruti-Liberati, N. (2010). Numerical solution of SDEs with jumps in finance. Berlin: Springer. · Zbl 1225.60004
[17] Platen, E., & Heath, D. (2010). A benchmark approach to quantitative finance. Berlin: Springer Finance. · Zbl 1104.91041
[18] Platen, E; Rendek, R, Approximating the numeraire portfolio by naive diversification, Journal of Asset Management, 13, 34-50, (2012)
[19] Tang, D; Wang, Y; Zhou, Y, Counterparty risk for credit default swaps with states related default intensity processes, International Journal of Theoretical and Applied Finance, 14, 1335-1353, (2011) · Zbl 1233.91290
[20] Wu, L. (2012). CVA and FVA under margining. Hong Kong University of Science and Technology (working paper).
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