Arbitrage Opportunities in CDS Term Structure: Theory and Implications for OTC Derivatives

Brummelhuis, Raymond and Luo, Zhongmin (2018): Arbitrage Opportunities in CDS Term Structure: Theory and Implications for OTC Derivatives.

Abstract

Absence-of-Arbitrage (AoA) is the basic assumption underpinning derivatives pricing theory. As part of the OTC derivatives market, the CDS market not only provides a vehicle for participants to hedge and speculate on the default risks of corporate and sovereign entities, it also reveals important market-implied default-risk information concerning the counterparties with which financial institutions trade, and for which these financial institutions have to calculate various valuation adjustments (collectively referred to as XVA) as part of their pricing and risk management of OTC derivatives, to account for counterparty default risks. In this study, we derive No-arbitrage conditions for CDS term structures, first in a positive interest rate environment and then in an arbitrary one. Using an extensive CDS dataset which covers the 2007-09 financial crisis, we present a catalogue of 2,416 pairs of anomalous CDS contracts which violate the above conditions. Finally, we show in an example that such anomalies in the CDS term structure can lead to persistent arbitrage profits and to nonsensical default probabilities. The paper is a first systematic study on CDS-term-structure arbitrage providing model-free AoA conditions supported by ample empirical evidence.

• Item Type: MPRA Paper
• Language: English
• Keywords: Arbitrage; Asset pricing; OTC derivatives; CVA; XVA; Valuation adjustment; Counterparty credit risk
• Subjects: C - Mathematical and Quantitative Methods > C4 - Econometric and Statistical Methods: Special Topics; C - Mathematical and Quantitative Methods > C4 - Econometric and Statistical Methods: Special Topics > C45 - Neural Networks and Related Topics; C - Mathematical and Quantitative Methods > C5 - Econometric Modeling; C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C58 - Financial Econometrics; C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling; G - Financial Economics > G0 - General > G01 - Financial Crises

References

[1] Bai J. and Collin-Dufresne P., November 2013, ”The CDS-Bond Basis”, AFA 2013 San Diego Meetings Paper, Georgetown Univ., Dept. of Finance and Ecole Polytechnique Federale de´Lausanne. [2] Banks for Int’l Settlements, July 2017, Statistical release: OTC derivatives statistics at end June 2017. [3] Battalio, R. and Schultz P., 2011, ”Regulatory Uncertainty and Market Liquidity: The 2008 Short Sale Ban’s Impact on Equity Option Markets”, Journal of Finance, Vol66. [4] Biswas G., Nikolova S. and Stahel C., 2015, ”The Transaction Costs of Trading Corporate Credit”, SSRN. [5] Bjork, T., 2004, Arbitrage Theory in Continuous Time, Oxford Univ. Press. [6] Brigo, D., Morini M. and Pallavicini A., 2013, Counterparty Credit Risk, Collateral and Funding: With Pricing Cases for All Asset Classes, John Wiley and Sons Ltd. [7] Brigo, D., Capponi A., Pallavicini A., 2014, ”Arbitrage-free Bilateral Counterparty risk valuation under collateralization and application to credit default swaps”, Mathematical Finance, Vol:24. [8] Brigo, D., and Mercurio F., Interest Rate Models Theory and Practice, with Smile, Inflation and Credit, 2nd Edition, Springer-Verlag, Page 775. [9] Brigo, D., Francischello, M., and Pallavicini, A., November 2015, ”Invariance, existence and uniqueness of solutions of nonlinear valuation PDEs and FBSDEs inclusive of credit risk, collateral and funding costs”, https://arxiv.org/abs/1506.00686. [10] Brummelhuis, R. and Z. Luo. 2018a. ”CDS Proxy Construction via Machine Learning Techniques: Methodology and Results”. forthcoming, Journal of Financial Data Science. [11] Brummelhuis, R. and Z. Luo. 2018b. ”CDS Proxy Construction via Machine Learning Techniques: Parametrization, Correlation and Benchmarking”. forthcoming, Journal of Financial Data Science. [12] Brummelhuis, R. and Z. Luo. 2017. ”CDS Rate Construction Methods by Machine Learning Techniques”. SSRN Journals. https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2967184. [13] Burgard, C. and Kjaer, M., 2011, ”Partial differential equation representations of derivatives with bilateral counterparty risk and funding costs”. The Journal of Credit Risk 7(3), 75–93. [14] Crepey, S., Gerboud, R., Grbac, Z., and Ngor, N., 2013, ”Counterparty risk and funding: The four wings of TVA”. Int’l Journal of Theoretical & Applied Finance 16, 1350006. [15] Delbaen, F. and Schachermayer, W., 1994, ”A General Version of the Fundamental Theorem on Asset Pricing”. Mathematishe Annalen 300, 463-520. [16] Delbaen, F. and W. Schachermayer, 2006, The Mathematics of Arbitrage. Springer Finance, xvi+371 p., ISBN 3-540-21992-7 (2006). [17] Green, A., Kenyon C. and Dennis C., 2014, ”KVA: Capital Valuation Adjustment”, Risk, 27.12. [18] Green, A. and C. Kenyon. 2015. ”MVA: Initial Margin Valuation Adjustment by Replication and Regression”. Risk 28(5). [19] Jarrow R., Li H, Ye X. and Hu M., 2018, ”Exploring Mispricing in the Term Structure of CDS Spreads”, forthcoming, Review of Finance, rfy014, https://doi.org/10.1093/rof/rfy014. [20] Kapadia N. and Pu X., 2012, ”Limited arbitrage between equity and credit markets”, Journal of Financial Economics 105 (2012) 542564 [21] O’Kane, D., 2008, Modelling single-name and multi-name Credit Derivatives, John Wiley & Sons Ltd.