Fathi, Abid and Nader, Naifar (2007): Price Calibration of basket default swap: Evidence from Japanese market.
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The aim of this paper is the price calibration of basket default swap from Japanese market data. The value of this instruments depend on the number of factors including credit rating of the obligors in the basket, recovery rates, intensity of default, basket size and the correlation of obligors in the basket. A fundamental part of the pricing framework is the estimation of the instantaneous default probabilities for each obligor. Because default probabilities depend on the credit quality of the considered obligor, well-calibrated credit curves are a main ingredient for constructing default times. The calibration of credit curves take into account internal information on credit migrations and default history. We refer to Japan Credit Rating Agency to obtain rating transition matrix and cumulative default rates. Default risk is often considered as a rare-event and then, many studies have shown that many distributions have fatter tails than those captured by the normal distribution. Subsequently, the choice of copula and the choice of procedures for rare-event simulation govern the pricing of basket credit derivatives. Joshi and Kainth (2004) introduced an Importance Sampling technique for rare-event that forces a predetermined number of defaults to occur on each path. We consider using Gaussian copula and t-student copula and study their impact on basket credit derivative prices. We will present an application of the Canonical Maximum Likelihood Method (CML) for calibrating t-student copula to Japanese market data.
|Item Type:||MPRA Paper|
|Original Title:||Price Calibration of basket default swap: Evidence from Japanese market|
|Keywords:||Basket Default Swaps, Credit Curve, Monte Carlo method, Gaussian copula, t-student copula, Japanese market data, CML, Importance Sampling|
|Subjects:||G - Financial Economics > G1 - General Financial Markets > G19 - Other|
|Date Deposited:||29. Nov 2007 13:40|
|Last Modified:||12. Feb 2013 15:05|
Abid, F and N. Naifar (2005), “The impact of stock returns volatility on credit default swap rates: a copula study”, International Journal of Theoretical and Applied Finance, Vol.8, No.8 pp: 1135-1155. Abid, F and N. Naifar (2006), “Credit default swap rates and equity volatility: a nonlinear relationship”, The Journal of Risk Finance, Volume 7, Number 4, August 2006, p: 348-371. Abid, F and N. Naifar (2007), “Copula based simulation procedures for pricing basket Credit Derivatives”, Working Paper, MODESFI. http://papers.ssrn.com/sol3/papers.cfm?abstract_id=980024 Altman, E., Resti, A., and A. Sironi (2003), “Default Recovery Rates in Credit Risk Modeling: A Review of the Literature and Empirical Evidence”, Working Paper, Stern School of Business, New York, U.S.A. Altman, E., Brady. B., Resti, A., and A. Sironi (2005), “The Link between Default and Recovery Rates: Theory, Empirical Evidence, and Implications”, Journal of Business, 2005, vol. 78, no. 6, p:2203-2227. Bakshi, G., Madan, D., and F. Zhang (2006), “Recovery Risk in Defaultable Debt Models: Empirical Comparisons and Implied Recovery Rates”, Working Paper, FDIC Center for Financial Research. Bouyé, E., Durrleman, V., Nikeghbali, A., Riboulet, G., and T. Roncalli (2000), “Copulas for finance: A reading guide and some applications”, Working Paper, GRO, Crédit Lyonnais, Paris.
Elizalde, A., (2005), “Credit Risk Models I: Default Correlation in Intensity Models”, Working Paper, CEMFI and UPNA. Embrechts, P., A. McNeil and D. Straumann (1999), “Correlation and dependence in risk management: properties and pitfalls”, in Risk Management: Value at Risk and Beyond, M. Dempster, Ed. (Cambridge: Cambridge University Press)., Frey, R. and A. McNeil (2001), “Modelling Dependent Defaults”, Working Paper, University of Zurich. Frieweld, N., (2004), “Modeling correlated defaults in a reduced form approach using copulas”, DIPLOMARBEIT. http://gutmannpcenter.univie.ac.at/html/wwd/creation_of_knowledge/master_thesis_grants_docs/DA_Nils%20Friewald.pdf Genest, C., and J. MacKay (1986), “The joy of copulas: Bivariate distributions with uniform marginals”, The American Statisticien, 40, p.280-283. Genest, C., K. Ghoudi, and L. P. Rivest (1995), “A semiparametric estimation procedure of dependence parameters in multivariate families of distributions”. Biometrika 82 (3), p.543-552. Giese, G., (2003), “ Enhancing CreditRisk+”, Risk, Vol. 16, No. 4, pp. 73-77, 2003. Giesecke, K., (2004), “Successive Correlated Defaults in a Structural Model”, Guha, R., (2002), “Recovery of Face Value at Default: Theory and Empirical Evidence”, Working Paper, London Business School. Jarrow, R. A. (2001), “Default parameter estimation using market prices”, Financial Analysts Journal, Vol 57, no. 5, p:75–92. Joe, H. (1997), “Multivariate models and dependence concepts”, chapman & Hall, London. Joshi, M.S., and D. Kainth (2004), “Rapid and accurate development of prices and Greeks for nth to default credit swaps in the Li model”, Quantitative Finance, Vol 4, Issue 3, pp. 266-275. Jouanin, J-F., G. Riboulet and T. Roncalli (2001), “Beyond conditionnally independent defaults”, Credit Lyonnais. Kreinin, A., and M. Sidelnikova (2001), “Regularization Algorithms for transition matrices”, Algo research Quaterly 4, pp:25-40. Laurent, J-P, “Pricing of basket default swaps and CDO tranches”, Isaac Newton Institute for Mathematical Sciences, City Event "Credit", 2005. Li, D., (2000), “On default correlation: a copula function approach”, Journal of Fixed Income 9, (2000) 43-54.
Hull, J and A. White, (2001) “Valuing Credit Default Swaps II: Modeling Default Correlations”, Journal of Derivatives, Vol. 8, No. 3, (Spring 2001), pp. 12-22. Hull, J., Predescu, M. & White, A. (2005), The Valuation of Correlation-dependent Credit Derivatives Using a Structural Model. Working Paper, Joseph L. Rotman School of Management, University of Toronto. Huschens, H., Konstantin V., and R. Wania. (2004), “Estimation of Default Probabilities and Default Correlations”, Working Paper, Technische Universität Dresden, Kim, G., Silvapulle, M. J., and P. Silvapulle (2007), “Comparison of semiparametric and parametric methods for estimating copulas”, Computational Statistics & Data Analysis, Volume 51, Issue 6 (March 2007), P: 2836-2850. Mashal, R., & M. Naldi. (2002), “Pricing multiname credit derivatives: heavy tailed hybrid approach”, Working Paper, Columbia Graduate School of Business et Quantitative Credit Reaseach, Lehman Brothers Inc. Mashal, R. and A. Zeevi (2002), “Beyond correlation: Extreme Co-movements Between Financial Assets”, Working Paper, Columbia Graduate School of Business. Merrick J. Jr. (2000), “Crisis Dynamics of Implied Default Recovery Ratios: Evidence from Russia and Argentina”, The Journal of Banking and Finance 25, (1921-1939). Moody’s Special Comment(2003), “Recovery Rates on Defaulted Corporate Bonds and Preferred Stocks, 1982–2003” Decembre 2003. Navarro, R. S., (2005), “Default Recovery Rates and Implied Default Probability Estimations: Evidence from the Argentinean Crisis”, Document de recherche, EPEE. Nelsen, R. ( 1999), “An Introduction to Copulas”, Springer Verlag, New York. Noris, J., 1998. Markov Chains. Cambridge University Press. Pan, J and K. J. Singleton (2006), “Default and Recovery Implicit in the Term Structure of Sovereign CDS Spreads”, Working paper Schweizer, B., and E.F. Wolff ( 1981), “ On nonparametric measures of dependence for random variables”, Annals of Statististics 9, p.870-885. Sironi, A., Altman, E.I., Brady, B., and A. Resti (2002), “The Link Between Default and Recovery Rates: Implications for Credit Risk Models and Procyclicality”, Working paper. Bocconi University. Sklar, A. (1959), “Fonctions de répartition à n dimensions et leurs marges”, vol. 8. Publications de l’Institut de Statistique de l’Université de Paris, Paris, p. 229-231. Tavakoli, J.M (2003), “Collateralised debt obligations and structured finance”, John Wiley & Sons, Inc., Hoboken, New Jersey. Wong, D., (2000), “Copula from the limit of multivariate binary model”, Working Paper, Bank of America Corporation. www.defaultrisk.com/pp_corr_25.htm Zeng, B. and J. Zhang (2001), “Modeling credit correlation: Equity correlation is not enough!”, KMV LLC.