Based on the framework of [7], we discuss pricing bilateral counterparty risk of CDS, where each individual default intensity is modeled by a shifted CIR process with jump （3CIR＋＋）, and the correlation between the...Based on the framework of [7], we discuss pricing bilateral counterparty risk of CDS, where each individual default intensity is modeled by a shifted CIR process with jump （3CIR＋＋）, and the correlation between the default times is modeled by a copula function. We present a semi-analytical formula for pricing bilateral counterparty risk of CDS, which is more convenient to compute through calculating multiple numerical integration or using Monte-Carlo simulation without simulating default times. Moreover, we obtain simpler formulae under FGM copulas, Bernstein copulas and CA＇B copulas, which can be applied for speeding up the computation and reducing the pricing error. Numerical results under FGM copulas and CA＇B copulas show that our method performs better both in computation speed and accuracy.展开更多
This paper discusses the correlation structure between London Interbank Offered Rates （LIBOR） by using the copula function. We start from one simplified model of A. Brace, D. Gatarek, and M. Musiela （1997） and fin...This paper discusses the correlation structure between London Interbank Offered Rates （LIBOR） by using the copula function. We start from one simplified model of A. Brace, D. Gatarek, and M. Musiela （1997） and find out that the copula function between two LIBOR rates can be expressed as a sum of an infinite series, where the main term is a distribution function with Gaussian copula. Partial differential equation method is used for deriving the copula expansion. Numerical results show that the copula of the LIBOR rates and Gaussian copula are very close in the central region and differ in the tail, and the Gaussian copula approximation to the copula function between the LIBOR rates provides satisfying results in the normal situation.展开更多
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 Frechet copula family presented in J. P. Yang et al. [Insur...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 Frechet 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 Frechet 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.展开更多
In actuarial science, Panjer recursion （1981） is used in insurance to compute the loss distribution of the compound risk models. When the severity distribution is continuous with density function, numerical calculat...In actuarial science, Panjer recursion （1981） is used in insurance to compute the loss distribution of the compound risk models. When the severity distribution is continuous with density function, numerical calculation for the compound distribution by applying Panjer recursion will involve an approxi- mation of the integration. In order to simplify the numerical algorithms, we apply Bernstein approximation for the continuous severity distribution function and obtain approximated recursive equations, which are used for computing the approximated values of the compound distribution. The theoretical error bound for the approximation is also obtained. Numerical results show that our algorithm provides reliable results.展开更多
基金supported by the National Natural Science Foundation of China(Grants No.11671021,11271033)National Social Science Fund of China(Grant No.16ZDA052)
文摘Based on the framework of [7], we discuss pricing bilateral counterparty risk of CDS, where each individual default intensity is modeled by a shifted CIR process with jump （3CIR＋＋）, and the correlation between the default times is modeled by a copula function. We present a semi-analytical formula for pricing bilateral counterparty risk of CDS, which is more convenient to compute through calculating multiple numerical integration or using Monte-Carlo simulation without simulating default times. Moreover, we obtain simpler formulae under FGM copulas, Bernstein copulas and CA＇B copulas, which can be applied for speeding up the computation and reducing the pricing error. Numerical results under FGM copulas and CA＇B copulas show that our method performs better both in computation speed and accuracy.
基金The authors thank the referees for their valuable comments. Yang＇s research was partly supported by the Key Program of National Natural Science Foundation of China （Grant No. 11131002） and the National Natural Science Foundation of China （Grants No. 11271033）. Zheng＇s research was supported by the Ng-Jhit-Cheong Foundation.
文摘This paper discusses the correlation structure between London Interbank Offered Rates （LIBOR） by using the copula function. We start from one simplified model of A. Brace, D. Gatarek, and M. Musiela （1997） and find out that the copula function between two LIBOR rates can be expressed as a sum of an infinite series, where the main term is a distribution function with Gaussian copula. Partial differential equation method is used for deriving the copula expansion. Numerical results show that the copula of the LIBOR rates and Gaussian copula are very close in the central region and differ in the tail, and the Gaussian copula approximation to the copula function between the LIBOR rates provides satisfying results in the normal situation.
文摘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 Frechet 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 Frechet 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.
文摘In actuarial science, Panjer recursion （1981） is used in insurance to compute the loss distribution of the compound risk models. When the severity distribution is continuous with density function, numerical calculation for the compound distribution by applying Panjer recursion will involve an approxi- mation of the integration. In order to simplify the numerical algorithms, we apply Bernstein approximation for the continuous severity distribution function and obtain approximated recursive equations, which are used for computing the approximated values of the compound distribution. The theoretical error bound for the approximation is also obtained. Numerical results show that our algorithm provides reliable results.
