The use of credit default swaps （CDSs） has become increasingly popular over time. Between 2002 and 2007, gross notional amounts outstanding grew from below S2 trillion to nearly S60 trillion. The recent crisis has r...The use of credit default swaps （CDSs） has become increasingly popular over time. Between 2002 and 2007, gross notional amounts outstanding grew from below S2 trillion to nearly S60 trillion. The recent crisis has revealed several shortcomings in CDS market practices and structure. In addition, management of counterparty risk has proved insufficient, as has in some instances the settlement of contracts following a credit event. However, past problems should not distract from the potential benefits of these instruments. In particular, CDSs help complete markets, as they provide an effective means to hedge and trade credit risk. CDSs allow financial institutions to better manage their exposures, and investors benefit from an enhanced investment universe. The purpose of this paper is to present a complete and practical exposition of the CDS market and to explore how the development of the CDS market has played an important role in the credit risk markets. Currently, the CDS market is transforming into a more stable system. Various measures are being put in place to help enhance market transparency and mitigate operational and systemic risk. In particular, central counterparties have started to operate, which will eventually lead to an improved management of individual as well as system-wide risks.展开更多
A hyperbolic function is introduced to reflect the attenuation effect of one firm＇s default to its partner. If two firms are competitors （copartners）, the default intensity of one firm will decrease （increase） ab...A hyperbolic function is introduced to reflect the attenuation effect of one firm＇s default to its partner. If two firms are competitors （copartners）, the default intensity of one firm will decrease （increase） abruptly when the other firm defaults. As time goes on, the impact will decrease gradually until extinct. In this model, the joint distribution and marginal distributions of default times are derived by employing the change of measure, and the fair swap premium of a credit default swap （CDS） can be valued.展开更多
This paper discusses the valuation of the Credit Default Swap based on a jump market, in which the asset price of a firm follows a double exponential jump diffusion process, the value of the debt is driven by a geomet...This paper discusses the valuation of the Credit Default Swap based on a jump market, in which the asset price of a firm follows a double exponential jump diffusion process, the value of the debt is driven by a geometric Brownian motion, and the default barrier follows a continuous stochastic process. Using the Gaver-Stehfest algorithm and the non-arbitrage asset pricing theory, we give the default probability of the first passage time, and more, derive the price of the Credit Default Swap.展开更多
In modem financial markets, the credit default swap （CDS） market has supplanted the bond market as the industry gauge for a borrower＇s credit quality. Therefore, it is very important to value CDS accurately by gett...In modem financial markets, the credit default swap （CDS） market has supplanted the bond market as the industry gauge for a borrower＇s credit quality. Therefore, it is very important to value CDS accurately by getting closer to more realistic pricing models. So far there have been no models for extracting forward-looking credit information to value CDS. In current practice, historical data is used in a credit default swap pricing model. One of the reasons was the difficulty when the market for credit derivatives was small, to extract forward-looking credit information such as recovery rates and default probabilities from traded securities. Since the CDS market has undergone rapid expansion in recent years, the possibilities of extracting forward-looking credit information have increased. Our work significantly extends Das and Hanouma （2009） where a flexible jump-to-default model was introduced to obtain implied recovery rates. We improve the flexible jump-to-default model where forecasted forward-looking hazard rates and recovery rates can be extracted using stock prices, stock volatilities and data from credit default markets to forecast CDS spreads. Instead of using exogenously assumed constant recovery rates and default probabilities from a credit rating agency, we use forward-looking hazard rates and recovery rates to price and forecast CDS spreads. We also compare out-of-sample market CDS spreads with our forecasted CDS spreads to check how well our model performs. Our model fit the market CDS spreads very well across all time to maturity CDS contracts except in some extreme cases when there is a big jump in CDS spreads.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
We study the counterparty risk for a credit default swap （CDS） in a regime-switching market driven by an underlying continuous-time Markov chain. We model the default dependence via some correlated Cox processes wit...We study the counterparty risk for a credit default swap （CDS） in a regime-switching market driven by an underlying continuous-time Markov chain. We model the default dependence via some correlated Cox processes with regime-switching shot noise intensities containing common shock. Under the proposed model, the general bilateral counterparty risk pricing formula for CDS contracts with the possibility of joint defaults is presented. Based on some expressions for the conditional Laplace transform of the integrated intensity processes, semi-analytical solution for the bilateral credit valuation adjustment （CVA） is derived. When the model parameters satisfy some conditions, explicit formula for the bilateral CVA at time 0 is also given.展开更多
This paper mainly studies the pricing of credit default swap(CDS) with the loan as the reference asset,and gives a model based on the obtained conclusions. In the contract of CDS, we consider that the default of the p...This paper mainly studies the pricing of credit default swap(CDS) with the loan as the reference asset,and gives a model based on the obtained conclusions. In the contract of CDS, we consider that the default of the protection's seller is correlated with the stochastic interest rate following Vasicek model and the default state of the reference firm. We give the pricing formula of CDS and analyze the effect of the contagious risk between the counterparties on the pricing of CDS.展开更多
文摘The use of credit default swaps （CDSs） has become increasingly popular over time. Between 2002 and 2007, gross notional amounts outstanding grew from below S2 trillion to nearly S60 trillion. The recent crisis has revealed several shortcomings in CDS market practices and structure. In addition, management of counterparty risk has proved insufficient, as has in some instances the settlement of contracts following a credit event. However, past problems should not distract from the potential benefits of these instruments. In particular, CDSs help complete markets, as they provide an effective means to hedge and trade credit risk. CDSs allow financial institutions to better manage their exposures, and investors benefit from an enhanced investment universe. The purpose of this paper is to present a complete and practical exposition of the CDS market and to explore how the development of the CDS market has played an important role in the credit risk markets. Currently, the CDS market is transforming into a more stable system. Various measures are being put in place to help enhance market transparency and mitigate operational and systemic risk. In particular, central counterparties have started to operate, which will eventually lead to an improved management of individual as well as system-wide risks.
基金the National Basic Research Program of China(973 Program)(No.2007CB814903)the National Natural Science Foundation of China(No.70671069)
文摘A hyperbolic function is introduced to reflect the attenuation effect of one firm＇s default to its partner. If two firms are competitors （copartners）, the default intensity of one firm will decrease （increase） abruptly when the other firm defaults. As time goes on, the impact will decrease gradually until extinct. In this model, the joint distribution and marginal distributions of default times are derived by employing the change of measure, and the fair swap premium of a credit default swap （CDS） can be valued.
基金Supported by The National Natural Science Foundation of China(71261015)Humanity and Social Science Youth Foundation of Education Ministry in China(10YJC630334)Program for Innovative Research Team in Universities of Inner Mongolia Autonomous Region
文摘This paper discusses the valuation of the Credit Default Swap based on a jump market, in which the asset price of a firm follows a double exponential jump diffusion process, the value of the debt is driven by a geometric Brownian motion, and the default barrier follows a continuous stochastic process. Using the Gaver-Stehfest algorithm and the non-arbitrage asset pricing theory, we give the default probability of the first passage time, and more, derive the price of the Credit Default Swap.
文摘In modem financial markets, the credit default swap （CDS） market has supplanted the bond market as the industry gauge for a borrower＇s credit quality. Therefore, it is very important to value CDS accurately by getting closer to more realistic pricing models. So far there have been no models for extracting forward-looking credit information to value CDS. In current practice, historical data is used in a credit default swap pricing model. One of the reasons was the difficulty when the market for credit derivatives was small, to extract forward-looking credit information such as recovery rates and default probabilities from traded securities. Since the CDS market has undergone rapid expansion in recent years, the possibilities of extracting forward-looking credit information have increased. Our work significantly extends Das and Hanouma （2009） where a flexible jump-to-default model was introduced to obtain implied recovery rates. We improve the flexible jump-to-default model where forecasted forward-looking hazard rates and recovery rates can be extracted using stock prices, stock volatilities and data from credit default markets to forecast CDS spreads. Instead of using exogenously assumed constant recovery rates and default probabilities from a credit rating agency, we use forward-looking hazard rates and recovery rates to price and forecast CDS spreads. We also compare out-of-sample market CDS spreads with our forecasted CDS spreads to check how well our model performs. Our model fit the market CDS spreads very well across all time to maturity CDS contracts except in some extreme cases when there is a big jump in CDS spreads.
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The authors thank the anonymous referees for valuable comments to improve the earlier version of the paper. The research of Yinghui Dong was supported by the Natural Science Foundation of Jiangsu Province （Grant No. BK20170064） and QingLan project. The research of Kam Chuen Yuen was supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China （Project No. HKU17329216）, and the CAE 2013 research grant from the Society of Actuaries-any opinions, finding, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the SOA. The research of Guojing Wang was supported by the National Natural Science Foundation of China （Grant No. 11371274）.
文摘We study the counterparty risk for a credit default swap （CDS） in a regime-switching market driven by an underlying continuous-time Markov chain. We model the default dependence via some correlated Cox processes with regime-switching shot noise intensities containing common shock. Under the proposed model, the general bilateral counterparty risk pricing formula for CDS contracts with the possibility of joint defaults is presented. Based on some expressions for the conditional Laplace transform of the integrated intensity processes, semi-analytical solution for the bilateral credit valuation adjustment （CVA） is derived. When the model parameters satisfy some conditions, explicit formula for the bilateral CVA at time 0 is also given.
基金the National Natural Science Foundation of China(No.11271259)the China Postdoctoral Science Foundation(No.2014M551297)+1 种基金the Innovation Program of Shanghai Municipal Education Commission(No.13YZ125)the Funding Scheme for Training Young Teachers in Shanghai Colleges(No.ZZshjr12010)
文摘This paper mainly studies the pricing of credit default swap(CDS) with the loan as the reference asset,and gives a model based on the obtained conclusions. In the contract of CDS, we consider that the default of the protection's seller is correlated with the stochastic interest rate following Vasicek model and the default state of the reference firm. We give the pricing formula of CDS and analyze the effect of the contagious risk between the counterparties on the pricing of CDS.
