Bao, Qunfang and Chen, Si and Liu, Guimei and Li, Shenghong (2010): Unilateral CVA for CDS in Contagion model: With volatilities and correlation of spread and interest.
Download (289Kb) | Preview
The price of financial derivative with unilateral counterparty credit risk can be expressed as the price of an otherwise risk-free derivative minus a credit value adjustment(CVA) component that can be seen as shorting a call option, which is exercised upon default of counterparty, on MtM of the derivative. Therefore, modeling volatility of MtM and default time of counterparty is key to quantification of counterparty risk. This paper models default times of counterparty and reference with a particular contagion model with stochastic intensities that is proposed by Bao et al. 2010. Stochastic interest rate is incorporated as well to account for positive correlation between spread and interest. Survival measure approach is adopted to calculate MtM of risk-free CDS and conditional survival probability of counterparty in defaultable environment. Semi-analytical solution for CVA is attained. Affine specification of intensities and interest rate concludes analytical expression for pre-default value of MtM. Numerical experiments at the last of this paper analyze the impact of contagion, volatility and correlation on CVA.
|Item Type:||MPRA Paper|
|Original Title:||Unilateral CVA for CDS in Contagion model: With volatilities and correlation of spread and interest|
|Keywords:||Credit Value Adjustment, Contagion Model, Stochastic Intensities and Interest, Survival Measure, Aﬃne Speciﬁcation|
|Subjects:||G - Financial Economics > G1 - General Financial Markets > G12 - Asset Pricing; Trading volume; Bond Interest Rates
C - Mathematical and Quantitative Methods > C6 - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling > C63 - Computational Techniques; Simulation Modeling
C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C15 - Statistical Simulation Methods: General
G - Financial Economics > G1 - General Financial Markets > G13 - Contingent Pricing; Futures Pricing
|Depositing User:||Qunfang Bao|
|Date Deposited:||19. Jan 2011 20:54|
|Last Modified:||15. Feb 2013 21:04|
Bao, Q. F., Li, S. H., \& Liu, G. M.(2010). Survival Measures and Interacting Intensity Model: with Applications in Guaranteed Debt Pricing. Zhejiang University, Working Paper.
Blanchet-Scalliet, CH., Patras, F.(2008). Counterparty risk valuation for CDS. Working paper.
Brigo, D., Chourdakis, K.(2008). Counterparty risk for credit default swaps: impact of spread and default correlation. Working paper.
Collin-Dufresene, P., Goldstein, R. S., \& Hugonnier, J.(2004). A general formula for valuing defaultable securities. Econometrica, 77, 1277–1307.
Crepey, S., Jeanblanc, M., Zargari, B.(2009). CDS with counterparty risk in a Markov chain copula model with joint defaults. Working paper.
Gregory, J.(2010). Counterparty credit risk: the new challenge for global financial markets. Wiely Finance.
Huge, B., Lando, D.(1999). Swap pricing with two-sided default risk an a rating-based model. European Finance Review, 3, 239-268.
Hull, J., White, A.(2001). Valuting credit default swaps II: modeling default correlation. The Journal of Derivatives, 8(3),12-22.
Jarrow, R., Yu, F.(2001). Counterparty risk and the pricing of defaultable securities. Journal of Finance, 56, 1765-1800.
Leung, S. Y., Kwok, Y. K.(2005). Credit default swap valuation with counterparty risk, Kyoto Economics Review, 74, 25-45.
Leung, K. S., Kwok, Y. K.(2009). Counterparty risk for credit default swaps: Markov chain interacting intensities model with stochastic intensity. Asia-Pacific Finan Markets, 16, 169–181.
Schonbucher P.(1998). A LIBOR Market Model with Default Risk. Bonn University, Working paper.
Walker, M. B.(2006). Credit default swaps with counterparty risk: A calibrated Markov model. Journal of Credit Risk, 2(1), 31–49.
Yu, F.(2005). Default correlation in reduced-form models. Journal of Investment Management, 3(4), 33–42.
Yu, F.(2007). Correlated defaults in intensity-based models.Mathmatical Finance, 17, 155–173.