Top

Published in:

2017 | OriginalPaper | Chapter

5. Credit Derivatives and Counterparty Credit Risk

Author : Jiří Witzany

Published in: Credit Risk Management

Publisher: Springer International Publishing

Activate our intelligent search to find suitable subject content or patents.

search-config

AI-assisted search

Off

Abstract

Financial derivatives are generally contracts whose financial payoffs depend on the prices of certain underlying assets. The contracts are traded Over the Counter (OTC), or in a standardized form on organized exchanges. The most popular derivative types are forwards, futures, options, and swaps. The underlying assets are, typically, interest rate instruments, stocks, foreign currencies, or commodities. The reasons for entering into a derivative contract might be hedging, speculation, or arbitrage. Compared to on-balance sheet instruments, derivatives allow investors and other market participants to hedge their existing positions, or to enter into new exposures with no, or very low, initial investment. This is an advantage in the case of hedging, but at the same time, in the case of a speculation, a danger, since large risks could be taken too easily. Derivatives are sometimes compared to electricity; something that is very useful if properly used, but extremely dangerous if used irresponsibly. In spite of those warnings, the derivatives market has grown tremendously in recent decades, with OTC outstanding notional amounts exceeding 650 trillion USD, as of the end of 2014, and exchange traded derivatives’ annual turnover exceeding 1450 trillion USD in 2014.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

previous chapter Portfolio Credit Risk

next chapter Conclusion

In this case, the conditional default probability n can be calculated recursively with respect to, the number of borrowers in the portfolio, essentially adding them one by one, see Brigo et al. (2010).

Let \( {v}_1=0\;\mathrm{and}\ {v}_2=v \), then according to the two-increasingness property \( C\left({u}_2,v\right)-C\left({u}_1,v\right)\ge 0 \) whenever \( {u}_2\ge {u}_1 \).

If C is the copula given by two random variables X ₁, X ₂ and if α ₁, α ₂ are two increasing continuous functions, then C is also the copula given by α ₁(X ₁), α ₂(X ₂).

The left-hand side of the inequality follows from the copula properties (b) and (c) setting \( {u}_2={v}_2=1 \), \( {u}_1=u \), and \( {v}_1=v \). The right-hand side of the inequality follows from the fact that C is increasing in both variables and from (b).

Nevertheless, for any \( \mathbf{u}\in {\left[0,1\right]}^n \) there is a copula C so that \( \max \left({u}_1+\cdots +{u}_n-1,0\right)\le C\left(\mathbf{u}\right) \). Therefore it is the best lower bound (Nelsen 1999).

That is q(t)Δt is the probability of default over the period \( \left[t,t+\Delta t\right] \).

\( S(t)= \Pr \left[\tau >t\right] \) is defined as the probability that default does not take place until time t.

Implicitly assuming that \( \Pr \left[{\tau}_C={\tau}_I\right]=0 \).

The TED spread is the difference between the interest rates on interbank loans (USD Libor) and on short-term U.S. government debt (“T-bills”).

Baran, J. (2016). Post-crisis valuation of derivatives. Doctoral Thesis. Faculty of Finance and Accounting, University of Economics in Prague, p. 84.

Baran, J., & Witzany, J. (2013). Konstrukce výnosových křivek v pokrizovém období. In J. Málek (Ed.), Risk management 2012 (pp. 69–100). Praha: Oeconomica.

BCBS. (2006a, June). International convergence of capital measurement and capital standards. A Revised Framework Comprehensive Version.

BCBS. (2009a, July). Enhancements to the basel II framework BCBS.

BCBS. (2010, December). Basel III: A global regulatory framework for more resilient banks and banking systems.

Brigo, D., & Pallavicini, A. (2008). Counterparty risk and contingent CDS valuation under correlation between interest-rates and default (SSRN Working Paper). p. 19. Retrieved from SSRN: http://ssrn.com/abstract=926067

Brigo, D., Pallavicini, A., & Torresetti R. (2006a). The dynamical generalized-poisson loss model, part one. Introduction and CDO calibration. Short version to appear in Risk Magazine. Retrieved from www.ssrn.com

Brigo, D., Pallavicini, A., & Torresetti, R. (2006b). The dynamical generalized-poisson loss model, part two. Calibration stability and spread dynamics extensions. Short version to appear in Risk Magazine. Retrieved from www.ssrn.com

Brigo, D., Pallavicini, A., & Torresetti, R. (2010). Credit models and the crisis: A journey into CDOs, copulas, correlations and dynamic models (p. 143). Chichester: Wiley.

Cantor, R., Hamilton, D. T., Ou, S., & Varma, P. (2005). Default and recovery rates of corporate bond issuers, 1920–2004. Moody’s Investor Service, Special Comment, Global Credit Research.

Černý, J., & Witzany, J. (2015). Interest rate swap credit valuation adjustment. The Journal of Derivatives, 23(2), 24–35.CrossRef

Cherubini, U., Luciano, E., & Vecchiato, W. (2004). Copula methods in finance (Willey Finance, p. 293). Hoboken, NJ: Willey.CrossRef

Cox, J. C., Ingersoll, J., & Ross, S. (1985). A theory of the term structure of interest rates. Econometrica, 53, 385–407.CrossRef

Crépey, S., Bielecki, T. R., & Brigo, D. (2014). Counterparty risk and funding: A tale of two puzzles. Boca Raton, FL: CRC Press.

Duffie, D., & Singleton, K. J. (2003). Credit risk—Pricing, measurement, and management (p. 396). Princeton, NJ: Princeton University Press.

Fong, H. G. (Ed.). (2006). The credit market handbook—Advanced modeling issues (Wiley Finance, p. 233). Hoboken, NJ: Wiley.

Gapko, P., & Smid, M. (2012). Dynamic multi-factor credit risk model with fat-tailed factors. Czech Journal of Economics and Finance, 62(2), 125–140.

Gregory, J. (2010). Counterparty credit risk (p. 424). Chichester: Wiley.

Gregory, J. (2015). The XVA challenge: Counterparty credit risk, funding, collateral, and capital. Chichester: Wiley.CrossRef

Heath, D., Jarrow, R., & Morton, A. (1992). Bond pricing and the term structure of interest rates: A new methodology for contingent claims valuation. Econometrica, 60, 77–106.CrossRef

Hull, J. C. (2009). Options, futures, and other derivatives (7th ed.). Upper Saddle River, NJ: Pearson/Prentice Hall.

Hull, J. C., & White, A. D. (2004). Valuation of a CDO and an n-th to default CDS without Monte Carlo simulation. The Journal of Derivatives, 12(2), 8–23.CrossRef

Hull, J. C., & White, A. (2006). Valuing credit derivatives using an implied copula approach. Journal of Derivatives, 14, 8–28.CrossRef

Hull, J., & White, A. (2012a). LIBOR vs. OIS: The derivatives discounting dilemma. Journal of Investment Management, 11(3), 14–27.

Hull, J., & White, A. (2012b). The FVA debate. Risk, 25, 83.

Hull, J., & White, A. (2012c, October). The FVA debate continued. Risk Magazine, 52.

Hull, J., & White, A. (2014). Valuing derivatives: Funding value adjustments and fair value. Financial Analysts Journal, 70(3), 46–56.CrossRef

ISDA. (2015). ISDA margin survey 2015. International Swaps and Derivatives Association. http://www2.isda.org/functional-areas/research/surveys/margin-surveys/

Kolman, M. (2013, August 31). Selected one-factor methods to price synthetic CDOs (VŠE Working Paper). p. 32.

Kolman, M. (2014). A one-factor copula-based model for credit portfolios. The Journal of Risk, 17(2), 93.CrossRef

Lando, D. (1988). Cox process and credit-risky securities. Review of Derivatives Research, 2, 99–120.

Lando, D. (2005). Credit risk modeling—Theory and applications (p. 310). Princeton, NJ: Princeton University Press.

Li David, X. (1999). On default correlation: A copula approach. Retrieved from SSRN 187289.

Nelsen, R. B. (1999). An introduction to copulas (Lecture notes in statistics 2nd ed., p. 269). New York: Springer.CrossRef

Pykhtin, M. (2012). Model foundations of the Basel III standardised CVA charge. Risk, 25(7), 60–66.

Sklar, A. (1959). Fonctions de repartition à n dimensions et leurs marges. Publications de l’Institut de Statistique de L’Université de Paris, 8, 229–231.

Torresetti, R., Brigo, D., & Pallavicini, A. (2006). Implied correlation in CDO tranches: A paradigm to be handled with care. Retrieved from SSRN 946755.

Vasicek, O. A. (1977). An equilibrium characterization of the term structure. Journal of Financial Economics, 5, 177–188.CrossRef

Vrins, F. D. (2009). Double t copula pricing of structured credit products: Practical aspects of a trustworthy implementation. Journal of Credit Risk, 3, 95–109.

Walker, M. (2006). CDO models—towards the next generation: Incomplete markets and term structure (Working Paper). Retrieved from www.defaultrisk.com

Witzany, J. (2013a). Financial derivatives, valuation, hedging and risk management (p. 374). Prague: Oeconomica.

Witzany, J. (2013b). A Note on the vasicek’s model with the logistic distribution. Ekonomický časopis, 10, 1053–1066.

Zhou, C. (2001). The term structure of credit spreads with jump risk. Journal of Banking and Finance, 25, 2015–2040.CrossRef

Title: Credit Derivatives and Counterparty Credit Risk
Author: Jiří Witzany
Publisher: Springer International Publishing
Book: Credit Risk Management
Print ISBN: 978-3-319-49799-0

Electronic ISBN: 978-3-319-49800-3

Copyright Year: 2017
DOI: https://doi.org/10.1007/978-3-319-49800-3_5