Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
Hostname: page-component-65f69f4695-kc48j Total loading time: 0 Render date: 2025-06-27T06:46:19.817Z Has data issue: false hasContentIssue false

19 - Pricing and Mitigation of Counterparty Credit Exposures

from PART VI - COUNTERPARTY RISK AND SYSTEMIC RISK

Published online by Cambridge University Press:  05 June 2013

By
Agostino Capponi
Edited by
Jean-Pierre Fouque  and
Joseph A. Langsam
Agostino Capponi
Affiliation:
Purdue University
Jean-Pierre Fouque
Affiliation:
University of California, Santa Barbara
Joseph A. Langsam
Affiliation:
University of Maryland, College Park
Get access

Summary

Abstract We analyze the market price of counterparty risk and develop an arbitrage-free pricing valuation framework, inclusive of collateral mitigation. We show that the adjustment is given by the sum of option payoff terms, depending on the netted exposure, i.e. the difference between the on-default exposure and the predefault collateral account. We specialize our analysis to Interest Rates Swaps (IRS) and Credit Default Swaps (CDS) as underlying portfolio, and perform a numerical study to illustrate the impact of default correlation, collateral margining frequency, and collateral re-hypothecation on the resulting adjustment. We also discuss problems of current research interest in the counterparty risk community.

Keywords Counterparty Risk, Systemic Risk, Credit Default Swaps, Interest Rates Swaps, Default Correlation, Stochastic Intensity, Collateral Margining. AMS Classification Codes: 60H10, 60J60, 60J75, 62H20, 91B70. JEL Classification Codes: C15, C63, C65, G12, G13.

Introduction

Basel II defines the counterparty credit risk as the amount that a financial institution would lose in the event that one of its counterparties defaults before the final settlement of the transaction. Unlike a firm's exposure to credit risk through a loan, where the exposure to credit risk is unilateral and only the lending bank faces the risk of loss, the counterparty credit risk creates a bilateral risk of loss, when both parties are default sensitive. Such risk is embedded in all financial contracts which are traded over the counter, where the credit quality of counterparties plays a key role.

Information

Type
Chapter
Information
Handbook on Systemic Risk , pp. 485 - 511
Publisher: Cambridge University Press
Print publication year: 2013

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Book purchase

Temporarily unavailable

References

Amini, H., Cont, R., and Minca, A. (2011). Stress testing the resilience of financial networks. International Journal of Theoretical and Applied Finance 14.Google Scholar
Assefa, S., Bielecki, T., Crépey, S., and Jeanblanc, M. (2009). CVA computation for counterparty risk assesment in credit portfolio. In Credit Risk Frontiers: Subprime crisis, Pricing and Hedging, CVA, MBS, Ratings and Liquidity, T., Bielecki, D., Brigo and F., Patras (eds). Wiley.Google Scholar
Belanger, A., Shreve, S., and Wong, D. (2004). A general framework for pricing credit risk. Mathematical Finance 14 317-350.CrossRefGoogle Scholar
BIS Basel III: A global regulatory framework for more resilient banks and banking systems. Available at www.bis.org.
Bielecki, T., and Crepey, S. (2011). Dynamic hedging of counterparty exposure. In The Musiela Festschrift, T., Zariphopoulou, M., Rutkowski, and Y., Kabanov, (eds). Springer-Verlag.Google Scholar
Bielecki, T., and Rutkowski, M. (2001). Credit Risk: Modeling, Valuation and Hedging. Springer-Verlag.Google Scholar
Bielecki, T., Jeanblanc, M., and Rutkowski, M. (2008). Pricing and trading credit default swaps in a hazard process model. Annals of Applied Probability 18 2495-2529.CrossRefGoogle Scholar
Bielecki, T., Jeanblanc, M., and Rutkowski, M. (2010). Hedging of a credit default swaption in the CIR default intensity model. Finance and Stochastics 15 541-572.Google Scholar
Bielecki, T., Cialenco, I., and Iyigunler, I. (2011). Counterparty risk and the impact of collateralization. Available at http://arxiv.org/pdf/1104.2625v3.
Blanchet-Scalliet, C., and Patras, F. (2011). Structural counterparty risk valuation for CDS. In Credit Risk Frontiers: Subprime crisis, Pricing and Hedging, CVA, MBS, Ratings and Liquidity, T., Bielecki, D., Brigo and F., Patras (eds). Wiley.Google Scholar
Brigo, D., and Alfonsi, A. (2005). Credit default swap calibration and derivatives pricing with the SSRD stochastic intensity model. Finance and Stochastics 9 29-42.CrossRefGoogle Scholar
Brigo, D., and Capponi, A. (2010). Bilateral counterparty risk with application to CDSs. Risk Magazine, March issue.Google Scholar
Brigo, D., Chourdakis, K. (2009). Counterparty risk for credit default swaps: Impact of spread volatility and default correlation. International Journal of Theoretical and Applied Finance, 12 (7) 1007–1026.CrossRefGoogle Scholar
Brigo, D., and Mercurio, F. (2006). Interest Rate Models: Theory and Practice – with Smile, Inflation and Credit, Second Edition. Springer Verlag.Google Scholar
Brigo, D., and Pallavicini, A. (2007). Counterparty Risk under Correlation between Default and Interest Rates. In Numerical Methods for Finance, Miller, J., Edelman, D., and Appleby, J. (eds). Chapman and Hall.Google Scholar
Brigo, D., Capponi, A., and Pedrescu, M. (2011). Liquidity modeling for credit default swaps: an overview. In Credit Risk Frontiers: Subprime crisis, Pricing and Hedging, CVA, MBS, Ratings and Liquidity, T., Bielecki, D., Brigo and F., Patras (eds). WileyGoogle Scholar
Brigo, D., Capponi, A., Pallavicini, A., and Papatheodorou, V. (2011). Collateral margining in arbitrage-free counterparty valuation adjustment including re-hypotecation and netting. Available at arxiv.org/pdf/1101.3926.
Brigo, D., Capponi, A., Pallavicini, A. (2012). Arbitrage-free bilateral counterparty risk valuation under collateralization and application to Credit Default Swaps. Mathematical Finance, DOI: 10.1111/j.1467-9965.2012.00520.x.Google Scholar
Capponi, A., and Larsson, M. (2012). Default and systemic risk in equilibrium. Mathematical Finance, DOI: 10.1111/mafi.12009.Google Scholar
Canabarro, E., and Duffie, D. (2004). Measuring and marking counterparty risk. Chapter 9 of ALMof Financial Institutions, Leo, Tilman (ed). Institutional Investor Books.Google Scholar
Cesari, G., Aquilna, J., Charpillon, N., Filipovic, Z., and Lee, G. (2011). Modelling, Pricing, and Hedging Counterparty Credit Exposure. Springer Verlag.Google Scholar
Crépey, S. (2011). A BSDE approach to counterparty risk under funding constraints. Preprint available at http://grozny.maths.univ-evry.fr/pages_perso/crepey/papers/Counterparty_Funding-Crepey-SUBMITTED.pdf.
Crépey, S., Jeanblanc, M., and B., Zargari. (2010). CDS with counterparty risk in a Markov chain copula model with joint defaults. In Recent Advances in Financial Engineering, M., Kijima, C., Hara, Y., Muromachi and K., Tanaka, (eds). World Scientific Publishing Co. Pte.Google Scholar
Cvitanić, J., Ma, J., and Zhang, J. (2010). Law of large numbers for self-exciting correlated defaults. Preprint available at http://www.hss.caltech.edu/~cvitanic/PAPERS/cmz2011.pdf.
Dai Pra, P., Runggaldier, W., Sartori, E., and Tolotti, M. (2009). Large portfolio losses: a dynamic contagion model, Annals of Applied Probability 19 (1) 347–394.CrossRefGoogle Scholar
Dai Pra, P., and Tolotti, . (2009). Heterogeneous credit portfolios and the dynamics of the aggregate losses. Stochastic Processes and their Applications 119 2913-2944.CrossRefGoogle Scholar
Duffie, D., and Huang, M. (1996). Swap rates and credit quality. Journal of Finance 51 921-950.CrossRefGoogle Scholar
Duffie, D., and Zhu, H. (2010). Does a central clearing counterparty reduce counterparty risk?Review of Asset Pricing Studies 1 74-95.Google Scholar
Fujii, M., and Takahashi, A. (2011). Collateralized CDS and default dependence – implications for the central clearing. Working paper, SSRN.com, 2011.
Chan-Lau, J., Espinosa-Vega, M., and Sole, J. (2009). Assessing the systemic implications of financial linkages. Global Financial Stability Report, International Monetary Fund.Google Scholar
Giesecke, K., and Kim, B. (2011). Systemic risk: what defaults are telling us. Management Science 57 1387-1405.CrossRefGoogle Scholar
Giesecke, K., and Weber, S. (2006). Credit contagion and aggregate losses. Journal of Economic Dynamics and Control 30 741-767.CrossRefGoogle Scholar
Giesecke, K., Spiliopoulos, K., and Sowers, R. (2011). Default clustering in large portfolios: typical and atypical events. Working Paper, Stanford University.
Glasserman, P (2003). Monte Carlo Methods in Financial Engineering. Springer-Verlag.CrossRefGoogle Scholar
ISDA Credit Support Annex. Available at www.isda.com.
ISDA Guidelines for Collateral Practitioners. Available at www.isda.com.
ISDA Credit Support Protocol (2002). Available at www.isda.com.
ISDA Close-Out Amount Protocol (2009). Available at www.isda.com.
ISDA Margin survey. Available at www.isda.com.
ISDA. Market review of OTC derivative bilateral collateralization Practices (2010). Available at www.isda.com.
Jarrow, R., and Yu, F. (2001). Counterparty risk and the pricing of defaultable securities. Journal of Finance 56 1765-1799.CrossRefGoogle Scholar
Jouanin, J., Rapuch, G., Riboulet, G., and Roncalli, T. (2001). Modelling dependence for credit derivatives with copulas. Working paper. Groupe de Recherche Operationnelle. Credit Lyonnais.
Leung, S.Y., and Kwok, Y. K. (2005). Credit default swap valuation with counterparty risk. The Kyoto Economic Review 74 25-15.Google Scholar
Lipton, A., and Sepp, A. (2009). Credit value adjustment for credit default swaps via the structural default model. Journal of Credit Risk 5 123-146.CrossRefGoogle Scholar
Nathanaël, B. (2010). The Basel Committee's December 2009 Proposals on Counterparty Risk. Federal Reserve/FSA presentation at the International Workshop on Counterparty Risk Management and Application of CVA, Bank of Japan, June 14, 2010.
Pykhtin, M. (2009). Modeling credit exposure for collateralized counterparties. Journal of Credit Risk 5 3-27.CrossRefGoogle Scholar
Walker, M. (2006). Credit default swaps with counterparty risk: a calibrated Markov model. Journal of Credit Risk 2 31-49.CrossRefGoogle Scholar
Weeber, P., and Robson, E. S. (2009). Market practices for settling derivatives in bankruptcy. ABI Journal 9 34-35.Google Scholar

Save book to Kindle

To save this book to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×