Pricing k^threalization derivatives and collateralized debt obligation with multivariate Fréchet copula

Abstract

Copula method has been widely applied to model the correlation among underlying assets in financial market. In this paper, we propose to use the multivariate Fréchet copula family presented in J. P. Yang et al. [Insurance Math. Econom., 2009, 45: 139–147] to price multivariate financial instruments whose payoffs depend on the k^th realization of the underlying assets and collateralized debt obligation (CDO). The advantage of the multivariate Fréchet copula is discussed. Empirical study shows that such copula family gives a better fitting to CDO’s market price than Gaussian copula for some derivatives.

Keywords

Multivariate Fréchet copula / k^th realization derivative / order statistics / collateralized debt obligation (CDO)

References

[1] Chen Z, Glasserman P. Fast pricing of basket default swaps. Operations Research, 2008, 56: 286–303

[2] Credit Suisse Financial Products. CreditRisk⁺: A credit risk management framework. Technical Report, 1997,

[3] Hull J, White A. Valuing credit default swaps II: Modeling default correlations. Journal of Derivatives, 2001, 8: 12–21

[4] Hull J, White A. Valuation of a CDO and an n^th to default CDS without Monte Carlo simulation. Journal of Derivatives, 2004, 12: 8–23

[5] Johnson H. Options on maximum or the minimum of several assets. Journal of Financial and Quantitative Analysis, 1987, 22: 277–283

[6] Joshi M, Kainth D. Rapid and accurate development of prices and Greeks for n^th to default credit swaps in the Li model. Quantitative Finance, 2004, 4: 266–275

[7] Laurent J P, Gregory J. Basket default swap, CDO’s and factor copula. Journal of Risk, 2005, 7: 103–122

[8] Li D X. On default correlation: a copula approach. Journal of Fixed Income, 2000, 9: 43–54

[9] Meaney J. Dealing with the volatility smile of Himalayan options. In: Vanmaele M, Deelstra G, Schepper A D, Dhaene J, Reynaerts H, Schoutens W, Goethem P V, eds. 5th Actuarial and Financial Mathematics Day in 2007. Wetteren: Universa Press, 2007

[10] Meneguzzo D, Vecchiato W. Copula sensitivity in collateralized debt obligations and basket default swaps. Journal of Futures Markets, 2004, 24: 37–70

[11] Ouwehand P, West G. Pricing rainbow options. Wilmott Magazine, 2006, (1): 74–80

[12] Yang J P, Cheng S H, Zhang L H. Bivariate copula decomposition in terms of comonotonicity, countermonotonicity and independence. Insurance Math Econom, 2006, 39: 267–284

[13] Yang J P, Qi Y C, Wang R D. A class of multivariate copulas with bivariate Frechet marginal copulas. Insurance Math Econom, 2009, 45: 139–147

[14] Youn H, Shemyakin A. Statistical aspects of joint life insurance pricing. In: 1999 Proceedings of the Business and Statistics Section of the Amer Statist Assoc. 1999, 34–38

RIGHTS & PERMISSIONS

Higher Education Press and Springer-Verlag Berlin Heidelberg