Pricing Financial Derivatives Subject to Multilateral Credit Risk and Collateralization

Xiao, Tim (2019): Pricing Financial Derivatives Subject to Multilateral Credit Risk and Collateralization.

Abstract

This article presents a new model for valuing financial contracts subject to credit risk and collateralization. Examples include the valuation of a credit default swap (CDS) contract that is affected by the trilateral credit risk of the buyer, seller and reference entity. We show that default dependency has a significant impact on asset pricing. In fact, correlated default risk is one of the most pervasive threats in financial markets. We also show that a fully collateralized CDS is not equivalent to a risk-free one. In other words, full collateralization cannot eliminate counterparty risk completely in the CDS market.

• Item Type: MPRA Paper
• Language: English
• Keywords: asset pricing; credit risk modeling; collateralization; comvariance; comrelation; correlation, CDS.
• Subjects: G - Financial Economics > G1 - General Financial Markets > G12 - Asset Pricing ; Trading Volume ; Bond Interest Rates; G - Financial Economics > G1 - General Financial Markets > G13 - Contingent Pricing ; Futures Pricing; M - Business Administration and Business Economics ; Marketing ; Accounting ; Personnel Economics > M2 - Business Economics > M21 - Business Economics; P - Economic Systems > P4 - Other Economic Systems > P45 - International Trade, Finance, Investment, and Aid

References

Arora, Navneet, Priyank Gandhi, and Francis A. Longstaff (2009), “Counterparty credit risk and the credit default swap market,” Working paper, UCLA.

Brigo, D., A. Pallavicini, and R. Torresetti (2011), “Credit Models and the Crisis: default cluster dynamics and the Generalized Poisson Loss model,” Journal of Credit Risk, 6: 39-81.

Brigo, D., and Capponi, A., 2008, Bilateral counterparty risk valuation with stochastic dynamical models and application to Credit Default Swaps, Working paper.

Collin-Dufresne, P., R. Goldstein, and J. Helwege (2003), “Is credit event risk priced? Modeling contagion via the updating of beliefs,” Working paper, Haas School, University of California, Berkeley.

Das, S., D. Duffie, N. Kapadia, and L. Saita (2007), “Common failings: How corporate defaults are correlated,” Journal of Finance, 62: 93-117.

Das, S., L. Freed, G. Geng, N. Kapadia (2006), “Correlated default risk,” Journal of Fixed Income, 16: 7-32.

Davis, M., and V. Lo (2001), “Infectious defaults,” Quantitative Finance, 1: 382-387.

Bielecki, T., I. Cialenco and I. Iyigunler, (2013) “Collateralized CVA valuation with rating triggers and credit migrations,” International Journal of Theoretical and Applied Finance, 16 (2).

Crepey, S. (2015) “Bilateral counterparty risk under funding constraints – part II: CVA,” Mathematical Finance, 25(1), 23-50.

Deardorff, Alan V. (1982): “The general validity of the Heckscher-Ohlin Theorem,” American Economic Review, 72 (4): 683-694.

Duffie, D., A. Eckner, G. Horel, and L. Saita (2009), “Frailty correlated default,” Journal of Finance, 64: 2089-2123.

Duffie, D., and K. Singleton (1999), “Modeling term structure of defaultable bonds,” Review of Financial Studies, 12: 687-720.

ECB (2009), “Credit default swaps and counterparty risk,” European central bank.

FinPricing, 2013, Investment banking solution, https://finpricing.com/product.html

Fuijii, M. and A. Takahahsi (2012), “Collateralized CDS and default dependence – Implications for the central clearing,” Journal of Credit Risk, 8(3): 97-113.

Giesecke, K. (2004), “Correlated default with incomplete information,” Journal of Banking and Finance, 28: 1521-1545.

Gregory, Jon, 2009, Being two-faced over counterparty credit risk, RISK, 22, 86-90.

Hull, J. and A. White (2004), “Valuation of a CDO and a nth to default CDS without Monte Carlo simulation,” Journal of Derivatives, 12: 8-23.

Hull, J. and A. White (2014), “Collateral and Credit Issues in Derivatives Pricing,” Journal of Credit Risk, 10 (3), 3-28.

ISDA (2013), “ISDA margin survey 2013.”

Jarrow, R., and S. Turnbull (1995), “Pricing derivatives on financial securities subject to credit risk,” Journal of Finance, 50: 53-85.

Jarrow, R., and F. Yu (2001), “Counterparty risk and the pricing of defaultable securities,” Journal of Finance, 56: 1765-99.

Johannes, M. and S. Sundaresan (2007), “The impact of collateralization on swap rates,” Journal of Finance, 62: 383-410.

J. P. Morgan (1999), “The J. P. Morgan guide to credit derivatives,” Risk Publications.

Koopman, S., A. Lucas, and B. Schwaab (2011), “Modeling frailty-correlated defaults using many macroeconomic covariates,” Journal of Econometrics, 162: 312-325.

Lando, D. and M. Nielsen (2010), “Correlation in corporate defaults: contagion or conditional independence?” Journal of Financial Intermediation, 19: 355-372.

Laurent, J. and J. Gregory (2005), “Basket default swaps, CDOs and factor copulas,” Journal of Risk, 7: 03-122.

Li, D. (2000), “On default correlation: A copula function approach,” Journal of Fixed Income, 9: 43-54.

Lipton, A., and Sepp, A., 2009, Credit value adjustment for credit default swaps via the structural default model, Journal of Credit Risk, 5(2), 123-146.

Longstaff, F., and E. Schwartz (2001): “Valuing American options by simulation: a simple least-squares approach,” The Review of Financial Studies, 14 (1): 113-147.

Madan, D., and H. Unal (1998), “Pricing the risks of default,” Review of Derivatives Research, 2: 121-160.

Piterbarg, V. (2010), “Funding beyond discounting: collateral agreements and derivatives pricing,” Risk Magazine, 2010 (2): 97-102.

Pykhtin, Michael, and Steven Zhu, 2007, A guide to modeling counterparty credit risk, GARP Risk Review, July/August, 16-22.

Teugels, J. (1990), “Some representations of the multivariate Bernoulli and binomial distributions,” Journal of Multivariate Analysis, 32: 256-268.

Zhang, G., and P. Jorion, (2007), “Good and bad credit contagion: Evidence from credit default swaps,” Journal of Financial Economics 84: 860–883.