In this paper a generalized defaultable bond pricing formula is derived by assuming that there exists a defaultable forward rate term structure and that firms in the economy interact when default occurs.Generally,The ...In this paper a generalized defaultable bond pricing formula is derived by assuming that there exists a defaultable forward rate term structure and that firms in the economy interact when default occurs.Generally,The risk-neutral default intensity λ Q is not equal to the empirical or actual default intensity λ.This paper proves that multiple default intensities are invariant under equivalent martingale transformation,given a well-diversified portfolio corresponding to the defaultable bond.Thus one can directly apply default intensities and fractional losses empirically estimated to the evaluation of defaultable bonds or contingent claims.展开更多
With the increase of China’s bond issuance and slowdown of the economic growth,the potential credit risks such as bond default in the bond market are gradually emerging.The frequent occurrence of bond defaults and th...With the increase of China’s bond issuance and slowdown of the economic growth,the potential credit risks such as bond default in the bond market are gradually emerging.The frequent occurrence of bond defaults and the problem of false credit ratings make bond investors and market participants more cautious about the credit ratings issued by rating agencies.Based on the default bonds from 2016 to 2019,this paper analyzes the adjustment of rating of defaulted bonds by rating agencies before default.It also compares the impact of both the regulatory events and the entrance of international agencies on timeless of credit ratings on default bonds.At the same time,the divergence of rating timeliness between different rating agencies is compared.The research shows that after the unified supervision of regulators and the punishment of Dagong Global Credit Rating Co.Ltd in 2018,the timeliness of rating agencies'downgrading of defaulted bonds has increased significantly;Compared with other rating agencies,the timeliness of rating agencies owned by international rating agencies are better.展开更多
The pricing of corporate bond with the default correlation was studied when the corporate holded the share of other corporates . On the basis of stochastic interest rate, the model of firm's bond with default corr...The pricing of corporate bond with the default correlation was studied when the corporate holded the share of other corporates . On the basis of stochastic interest rate, the model of firm's bond with default correlation was established by means of reduced form and partial differential equations (PDE). Also, the close form formula for the pricing of the firm's bond was obtained. Finally, some numerical examples were given to illustrate how our models work.展开更多
China’s credit bond market has rapidly expanded in recent years.However,since 2014,the number of credit bond defaults has been increasing rapidly,posing enormous potential risks to the stability of the financial mark...China’s credit bond market has rapidly expanded in recent years.However,since 2014,the number of credit bond defaults has been increasing rapidly,posing enormous potential risks to the stability of the financial market.This study proposed a deep learning approach to predict credit bond defaults in the Chinese market.A convolutional neural network(CNN)was selected as the classification model and to reduce the extreme imbalance between defaulted and non-defaulted bonds,and a generative adversarial network(GAN)was used as the oversampling model.Based on 31 financial and 20 non-financial indicators,we collected Wind data on all credit bonds issued and matured or defaulted from 2014 to 2021.The experimental results showed that our GAN+CNN approach had superior predictive performance with an area under the curve(AUC)of 0.9157 and precision of 0.8871 compared to previous research and other commonly used classification models-including the logistic regression,support vector machine,and fully connected neural network models-and oversampling techniques-including the synthetic minority oversampling technique(SMOTE)and Borderline SMOTE model.For one-year predictions,indicators of solvency,capital structure,and fundamental properties of bonds are proved to be the most important indicators.展开更多
This study considers an optimal investment and reinsurance problem involving a defaultable security for an insurer in an ambiguous environment.In other words,the insurer is ambiguous about the insurance claim that is ...This study considers an optimal investment and reinsurance problem involving a defaultable security for an insurer in an ambiguous environment.In other words,the insurer is ambiguous about the insurance claim that is exponentially distributed with an uncertain rate parameter.The insurer can purchase proportional reinsurance and invest its wealth in three assets:a risk-free asset,a risky asset,the price process of which satisfies the Heston local-stochastic volatility model,and a defaultable corporate bond.For the optimal investment–reinsurance objective with a smooth ambiguity utility proposed by Klibanoff,P.,Marinacci,M.,and Mukerji,S.[A smooth model of decision making under ambiguity,Econometrica,2005,73(6):1849-1892],the equilibrium strategy is introduced and the extended Hamilton–Jacobi–Bellman equation is established through a stochastic control approach.However,the analytical solution of the strategy under the Heston local-stochastic volatility model cannot be obtained because of the complicated nonlinearity of the partial differential equation.In this study,we employ a perturbation method to derive an asymptotic solution for the post-and pre-default cases.In addition,we present a sensitivity analysis to explain the impact of model parameters on the equilibrium investment–reinsurance strategy.展开更多
Convertible bond gives holder the right to choose a conversion strategy to maximize the bond value, and issuer also has the right to minimize the bond value in order to maximize equity value. When there is default occ...Convertible bond gives holder the right to choose a conversion strategy to maximize the bond value, and issuer also has the right to minimize the bond value in order to maximize equity value. When there is default occurring, conversion and calling strategies are invalid. In the framework of reduced form model, we reduce the price of convertible bond to variational inequalities, and the coefficients of variational inequalities are unbounded at the original point. Then the existence and uniqueness of variational inequality are proven. Finally, we prove that the conversion area, the calling area and the holding area are connected subsets of the state space.展开更多
基金National Natural Science Foundation of China(70 0 71 0 1 2 )
文摘In this paper a generalized defaultable bond pricing formula is derived by assuming that there exists a defaultable forward rate term structure and that firms in the economy interact when default occurs.Generally,The risk-neutral default intensity λ Q is not equal to the empirical or actual default intensity λ.This paper proves that multiple default intensities are invariant under equivalent martingale transformation,given a well-diversified portfolio corresponding to the defaultable bond.Thus one can directly apply default intensities and fractional losses empirically estimated to the evaluation of defaultable bonds or contingent claims.
文摘With the increase of China’s bond issuance and slowdown of the economic growth,the potential credit risks such as bond default in the bond market are gradually emerging.The frequent occurrence of bond defaults and the problem of false credit ratings make bond investors and market participants more cautious about the credit ratings issued by rating agencies.Based on the default bonds from 2016 to 2019,this paper analyzes the adjustment of rating of defaulted bonds by rating agencies before default.It also compares the impact of both the regulatory events and the entrance of international agencies on timeless of credit ratings on default bonds.At the same time,the divergence of rating timeliness between different rating agencies is compared.The research shows that after the unified supervision of regulators and the punishment of Dagong Global Credit Rating Co.Ltd in 2018,the timeliness of rating agencies'downgrading of defaulted bonds has increased significantly;Compared with other rating agencies,the timeliness of rating agencies owned by international rating agencies are better.
基金National Key Basic Research Program of China (973 program) (No. 2007CB814903)Shanghai Leading Academic Discipline Project,China ( No. S30405)the Research Program of Shanghai Normal University,China (No. SK201211)
文摘The pricing of corporate bond with the default correlation was studied when the corporate holded the share of other corporates . On the basis of stochastic interest rate, the model of firm's bond with default correlation was established by means of reduced form and partial differential equations (PDE). Also, the close form formula for the pricing of the firm's bond was obtained. Finally, some numerical examples were given to illustrate how our models work.
基金supported in part by the Emerging Interdisciplinary Project of Central University of Finance and Economics,Beijing,China.
文摘China’s credit bond market has rapidly expanded in recent years.However,since 2014,the number of credit bond defaults has been increasing rapidly,posing enormous potential risks to the stability of the financial market.This study proposed a deep learning approach to predict credit bond defaults in the Chinese market.A convolutional neural network(CNN)was selected as the classification model and to reduce the extreme imbalance between defaulted and non-defaulted bonds,and a generative adversarial network(GAN)was used as the oversampling model.Based on 31 financial and 20 non-financial indicators,we collected Wind data on all credit bonds issued and matured or defaulted from 2014 to 2021.The experimental results showed that our GAN+CNN approach had superior predictive performance with an area under the curve(AUC)of 0.9157 and precision of 0.8871 compared to previous research and other commonly used classification models-including the logistic regression,support vector machine,and fully connected neural network models-and oversampling techniques-including the synthetic minority oversampling technique(SMOTE)and Borderline SMOTE model.For one-year predictions,indicators of solvency,capital structure,and fundamental properties of bonds are proved to be the most important indicators.
基金isupported by the National Natural Science Foundation of China(Grant Nos.11871010 and 11971040)the Fundamental Research Funds for the Central Universities(Grant No.2019XD-A11)The work of Weilin Xiao is supported by the Humanities and Social Sciences of Ministry of Education Planning Fund of China(Grant No.23YJA630102).
文摘This study considers an optimal investment and reinsurance problem involving a defaultable security for an insurer in an ambiguous environment.In other words,the insurer is ambiguous about the insurance claim that is exponentially distributed with an uncertain rate parameter.The insurer can purchase proportional reinsurance and invest its wealth in three assets:a risk-free asset,a risky asset,the price process of which satisfies the Heston local-stochastic volatility model,and a defaultable corporate bond.For the optimal investment–reinsurance objective with a smooth ambiguity utility proposed by Klibanoff,P.,Marinacci,M.,and Mukerji,S.[A smooth model of decision making under ambiguity,Econometrica,2005,73(6):1849-1892],the equilibrium strategy is introduced and the extended Hamilton–Jacobi–Bellman equation is established through a stochastic control approach.However,the analytical solution of the strategy under the Heston local-stochastic volatility model cannot be obtained because of the complicated nonlinearity of the partial differential equation.In this study,we employ a perturbation method to derive an asymptotic solution for the post-and pre-default cases.In addition,we present a sensitivity analysis to explain the impact of model parameters on the equilibrium investment–reinsurance strategy.
基金Supported by the NNSF of China (10671144)NBRP of China (2007CB814903)
文摘Convertible bond gives holder the right to choose a conversion strategy to maximize the bond value, and issuer also has the right to minimize the bond value in order to maximize equity value. When there is default occurring, conversion and calling strategies are invalid. In the framework of reduced form model, we reduce the price of convertible bond to variational inequalities, and the coefficients of variational inequalities are unbounded at the original point. Then the existence and uniqueness of variational inequality are proven. Finally, we prove that the conversion area, the calling area and the holding area are connected subsets of the state space.
