Valuation of CDS counterparty risk under a reduced-form model with regime-switching shot noise default intensities

Abstract

We study the counterparty risk for a credit default swap (CDS) in a regime-switching market driven by an underlying continuous-time Markov chain. We model the default dependence via some correlated Cox processes with regime-switching shot noise intensities containing common shock. Under the proposed model, the general bilateral counterparty risk pricing formula for CDS contracts with the possibility of joint defaults is presented. Based on some expressions for the conditional Laplace transform of the integrated intensity processes, semi-analytical solution for the bilateral credit valuation adjustment (CVA) is derived. When the model parameters satisfy some conditions, explicit formula for the bilateral CVA at time 0 is also given.

Keywords

Credit default swap (CDS) / bilateral credit valuation adjustment / Markov chain / common shock / regime-switching shot noise process

References

[1] BieleckiT R, RutkowskiM. Credit Risk: Modeling, Valuation and Hedging.Berlin: Springer, 2004

[2] BieleckiT, CrépeyS, JeanblancM, ZargariB. Valuation and hedging of CDS counterparty exposure in a Markov copula model.Int J Theor Appl Finance, 2012, 15(1): 1–39

[3] BrigoD, CapponiA. Bilateral counterparty risk with application to CDSs.Risk, 2010, 23(3): 85–90

[4] BuffingtonJ, ElliottR J. American options with regime switching.Int J Theor Appl Finance, 2002, 5: 497–514

[5] CesariG, AquilinaJ, Niels CharpillonN, FilipovicZ, LeeG, MandaI. Modelling, Pricing, and Hedging Counterparty Credit Exposure: A Technical Guide.Berlin: Springer,2010

[6] CoxD R, IshamV. The virtual waiting time and related processes.Adv Appl Probab, 1986, 18: 558–573

[7] CrépeyS, JeanblancM, ZargariB. Counterparty risk on a CDS in a Markov chain copula model with joint defaults.In: Recent Advances in Financial Engineering 2009. Singapore: World Scientific Publishing, 2010, 91–126

[8] DassiosA, JangJ. Pricing of catastrophe reinsurance and derivatives using the Cox process with shot noise intensity.Finance Stoch,2003, 7(1): 73–95

[9] DongY H, YuenK C, WuC F. Unilateral counterparty risk valuation of CDS using a regime-switching intensity model.Statist Probab Lett, 2014, 85: 25–35

[10] DuffieD, FilipovicD, SchachermayerW. Affine processes and applications in finance.Ann Appl Probab, 2003, 13(3): 984–1053

[11] ElliottR J. New finite dimensional filters and smoothers for noisily observed Markov chains.IEEE Trans Inform Theory, 1993, 39: 265–271

[12] ElouerkhaouiY. Pricing and hedging in a dynamic credit model.Int J Theor Appl Finance, 2007, 10(4): 703–731

[13] GieseckeK. A simple exponential model for dependent defaults.J Fixed Income, 2003, 13(3): 74–83

[14] GieseckeK, LongstaffF A, SchaeferS, StrebulaevI. Corporate bond default risk: A 150-year perspective.Journal of Financial Economics, 2011, 102: 233–250

[15] GregoryJ. Counterparty Credit Risk: The New Challenge for Global Financial Markets.New York: Wiley, 2010

[16] GuoX. Information and option pricings.Quant Finance, 2001, 1: 38–44

[17] LindskogF, McNeilA. Common Poisson shock models: applications to insurance and credit risk modelling.Astin Bull, 2003, 33: 209–238

[18] LiptonA, SeppA. Credit value adjustment for credit default swaps via the structural default model.Journal of Credit Risk, 2009, 5(2): 123–146

[19] NaikV. Option valuation and hedging strategies with jumps in the volatility of asset returns.The Journal of Finance, 1993, 48: 1969–1984

[20] SiuT K. Bond pricing under a Markovian regime-switching jump-augmented Vasicek model via stochastic flows.Appl Math Comput,2010, 216: 3184–3190

[21] ZhouC S. An analysis of default correlation and multiple defaults.The Review of Financial Studies, 2001, 14(2): 555–576

RIGHTS & PERMISSIONS

Higher Education Press and Springer-Verlag GmbH Germany