In this paper, we study the price of catastrophe Options with counterparty credit risk in a reduced form model. We assume that the loss process is generated by a doubly stochastic Poisson process, the share price proc...In this paper, we study the price of catastrophe Options with counterparty credit risk in a reduced form model. We assume that the loss process is generated by a doubly stochastic Poisson process, the share price process is modeled through a jump-diffusion process which is correlated to the loss process, the interest rate process and the default intensity process are modeled through the Vasicek model： We derive the closed form formulae for pricing catastrophe options in a reduced form model. Furthermore, we make some numerical analysis on the explicit formulae.展开更多
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 provides a methodology for valuing a credit default swap (CDS) with considering a counterparty default risk. Using a structural framework, we study the correlation of the reference entity and the counterpar...This paper provides a methodology for valuing a credit default swap (CDS) with considering a counterparty default risk. Using a structural framework, we study the correlation of the reference entity and the counterparty through the joint distribution of them. The default event discussed in our model is associated to whether the minimum value of the companies in stochastic processes has reached their thresholds (default barriers). The joint probability of minimums of correlated Brownian motions solves the backward Kolmogorov equation, which is a two dimensional partial differential equation. A closed pricing formula is obtained. Numerical methodology, parameter analysis and calculation examples are implemented.展开更多
This paper considers an improved model of pricing defaultable bonds under the assumption that the interest rate satisfies the Vasicek model driven by fractional Brownian motion(fBm for short)based on the counterparty ...This paper considers an improved model of pricing defaultable bonds under the assumption that the interest rate satisfies the Vasicek model driven by fractional Brownian motion(fBm for short)based on the counterparty risk framework of Jarrow and Yu(2001). The authors use the theory of stochastic analysis of f Bm to derive pricing formulas for the defaultable bonds and study how the counterparty risk, recovery rate, and the Hurst parameter affect the values of the defaultable bonds.Numerical experiment results are presented to demonstrate the findings.展开更多
To investigate the impact of microstructure interdependency of a counterparty explicitly, a geometric function is introduced in one firm's default intensity to reflect the attenuation behavior of the impact of its...To investigate the impact of microstructure interdependency of a counterparty explicitly, a geometric function is introduced in one firm's default intensity to reflect the attenuation behavior of the impact of its counterparty firm's default. The general joint distribution and marginal distributions of default times are derived by employing the change of measure. The fair premium of a vanilla CDS (credit default swap) is obtained in continuous and discrete contexts, respectively. The swap premium in a discrete context is similar to the accumulated interest during the period between two payment days, and the short rate is the swap rate in a continuous context.展开更多
Regime switching,which is described by a Markov chain,is introduced in a Markov copula model.We prove that the marginals（X,H^i）,i = 1,2,3 of the Markov copula model（X,H） are still Markov processes and have marting...Regime switching,which is described by a Markov chain,is introduced in a Markov copula model.We prove that the marginals（X,H^i）,i = 1,2,3 of the Markov copula model（X,H） are still Markov processes and have martingale property.In this proposed model,a pricing formula of credit default swap（CDS） with bilateral counterparty risk is derived.展开更多
We apply to the concrete setup of a bank engaged into bilateral trade portfolios the XVA theoretical framework of Albanese and Crepey(2017),whereby´so-called contra-liabilities and cost of capital are charged by ...We apply to the concrete setup of a bank engaged into bilateral trade portfolios the XVA theoretical framework of Albanese and Crepey(2017),whereby´so-called contra-liabilities and cost of capital are charged by the bank to its clients,on top of the fair valuation of counterparty risk,in order to account for the incompleteness of this risk.The transfer of the residual reserve credit capital from shareholders to creditors at bank default results in a unilateral CVA,consistent with the regulatory requirement that capital should not diminish as an effect of the sole deterioration of the bank credit spread.Our funding cost for variation margin(FVA)is defined asymmetrically since there is no benefit in holding excess capital in the future.Capital is fungible as a source of funding for variation margin,causing a material FVA reduction.We introduce a specialist initial margin lending scheme that drastically reduces the funding cost for initial margin(MVA).Our capital valuation adjustment(KVA)is defined as a risk premium,i.e.the cost of remunerating shareholder capital at risk at some hurdle rate.展开更多
This paper proposes an approximate analytical solution method to calculate counterparty credit risk exposures.Compared with the Standard Approach for measuring Counterparty Credit Risk and the Internal Modeling Method...This paper proposes an approximate analytical solution method to calculate counterparty credit risk exposures.Compared with the Standard Approach for measuring Counterparty Credit Risk and the Internal Modeling Method provided by Basel Committee,the proposed method significantly improves the calculation efficiency based on sacrificing a little accuracy.Taking Forward Rate Agreement as an example,this article derives the exact expression for Expected Exposure.By approximating the distribution of Forward Rate Agreement’s future value to a normal distribution,the approximate analytical expression for Potential Future Exposure is derived.Numerical results show that this method is reliable and is robust under different parameters.展开更多
基金supported by the National Natural Science Foundation of China(11371274)
文摘In this paper, we study the price of catastrophe Options with counterparty credit risk in a reduced form model. We assume that the loss process is generated by a doubly stochastic Poisson process, the share price process is modeled through a jump-diffusion process which is correlated to the loss process, the interest rate process and the default intensity process are modeled through the Vasicek model： We derive the closed form formulae for pricing catastrophe options in a reduced form model. Furthermore, we make some numerical analysis on the explicit formulae.
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.
文摘This paper provides a methodology for valuing a credit default swap (CDS) with considering a counterparty default risk. Using a structural framework, we study the correlation of the reference entity and the counterparty through the joint distribution of them. The default event discussed in our model is associated to whether the minimum value of the companies in stochastic processes has reached their thresholds (default barriers). The joint probability of minimums of correlated Brownian motions solves the backward Kolmogorov equation, which is a two dimensional partial differential equation. A closed pricing formula is obtained. Numerical methodology, parameter analysis and calculation examples are implemented.
基金supported by the National Natural Science Foundation of China under Grant Nos.11471051 and 11871010supported by the National Social Science Foundation of China under Grant No.16ZDA033
文摘This paper considers an improved model of pricing defaultable bonds under the assumption that the interest rate satisfies the Vasicek model driven by fractional Brownian motion(fBm for short)based on the counterparty risk framework of Jarrow and Yu(2001). The authors use the theory of stochastic analysis of f Bm to derive pricing formulas for the defaultable bonds and study how the counterparty risk, recovery rate, and the Hurst parameter affect the values of the defaultable bonds.Numerical experiment results are presented to demonstrate the findings.
基金The National Basic Research Program of China (973 Program)(No.2007CB814903)the National Natural Science Foundationof China (No.70671069)
文摘To investigate the impact of microstructure interdependency of a counterparty explicitly, a geometric function is introduced in one firm's default intensity to reflect the attenuation behavior of the impact of its counterparty firm's default. The general joint distribution and marginal distributions of default times are derived by employing the change of measure. The fair premium of a vanilla CDS (credit default swap) is obtained in continuous and discrete contexts, respectively. The swap premium in a discrete context is similar to the accumulated interest during the period between two payment days, and the short rate is the swap rate in a continuous context.
基金Supported by Jiangsu Government Scholarship for Overseas Studiesthe NNSF of China(Grant Nos.11401419,11301369,11371274)+1 种基金the CPSF(2014M561453)the NSF of Jiangsu Province(Grant Nos.BK20140279,BK20130260)
文摘Regime switching,which is described by a Markov chain,is introduced in a Markov copula model.We prove that the marginals（X,H^i）,i = 1,2,3 of the Markov copula model（X,H） are still Markov processes and have martingale property.In this proposed model,a pricing formula of credit default swap（CDS） with bilateral counterparty risk is derived.
基金The research of Stephane Cr´epey benefited from the support of the“Chair Markets´in Transition,”Fed´eration Bancaire Franc´¸aise,of the ANR project 11-LABX-0019 and from the EIF grant“Collateral management in centrally cleared trading.”。
文摘We apply to the concrete setup of a bank engaged into bilateral trade portfolios the XVA theoretical framework of Albanese and Crepey(2017),whereby´so-called contra-liabilities and cost of capital are charged by the bank to its clients,on top of the fair valuation of counterparty risk,in order to account for the incompleteness of this risk.The transfer of the residual reserve credit capital from shareholders to creditors at bank default results in a unilateral CVA,consistent with the regulatory requirement that capital should not diminish as an effect of the sole deterioration of the bank credit spread.Our funding cost for variation margin(FVA)is defined asymmetrically since there is no benefit in holding excess capital in the future.Capital is fungible as a source of funding for variation margin,causing a material FVA reduction.We introduce a specialist initial margin lending scheme that drastically reduces the funding cost for initial margin(MVA).Our capital valuation adjustment(KVA)is defined as a risk premium,i.e.the cost of remunerating shareholder capital at risk at some hurdle rate.
基金supported by the National Natural Science Foundation of China under grant 62025306。
文摘This paper proposes an approximate analytical solution method to calculate counterparty credit risk exposures.Compared with the Standard Approach for measuring Counterparty Credit Risk and the Internal Modeling Method provided by Basel Committee,the proposed method significantly improves the calculation efficiency based on sacrificing a little accuracy.Taking Forward Rate Agreement as an example,this article derives the exact expression for Expected Exposure.By approximating the distribution of Forward Rate Agreement’s future value to a normal distribution,the approximate analytical expression for Potential Future Exposure is derived.Numerical results show that this method is reliable and is robust under different parameters.
