将李群理论用于金融问题中出现的数学模型的微分方程,研究了Zero-Coupon bond pricing模型.求出了该模型的单参数李点对称及它相应的群伴随表达式,由此求得该模型允许的一维李群的子代数的最优系统并且利用最优系统构造该模型相应的微...将李群理论用于金融问题中出现的数学模型的微分方程,研究了Zero-Coupon bond pricing模型.求出了该模型的单参数李点对称及它相应的群伴随表达式,由此求得该模型允许的一维李群的子代数的最优系统并且利用最优系统构造该模型相应的微分方程的一些特殊的不同类的闭解.展开更多
This study examines the pricing of municipal bonds before and after a currency shock in Switzerland.Two approaches are used to decompose the municipal to treasuries bond spreads into liquidity,maturity,and default ris...This study examines the pricing of municipal bonds before and after a currency shock in Switzerland.Two approaches are used to decompose the municipal to treasuries bond spreads into liquidity,maturity,and default risk premiums.The first approach is the model of the cross-sectional instrumental variables,and the second approach is the model of the instrumental variables with panel data.This study examines the composition of spreads for both approaches,in three scenarios:before,throughout,and after the currency shock.The study performed Durbin-Wu-Hausman tests for each decisive model to verify endogeneity issues,including the Lagrangian Multiplier test,the Cragg-Donald Wald F statistic to confirm the relationship of instrumental and endogenous variables,and the structural break test(Bai-Perron test)to determine the existence of structural breaks in bond distortions.This study finds that the currency price distortions of the Swiss franc in January 2015 made long-run changes in the composition of the municipal bond spreads.This research contributes to the understanding of municipal bond pricing by showing that default risk accounts for a large portion of the municipal bond spread,while maturity risk plays a lesser role.According to our empirical findings,unexpected large currency price shocks may have long-term implications on the municipal bond spreads.展开更多
It is well known that economic policy uncertainty prompts the volatility of the high-yield bond market.However,the correlation between economic policy uncertainty and volatility of high-yield bonds is still not clear....It is well known that economic policy uncertainty prompts the volatility of the high-yield bond market.However,the correlation between economic policy uncertainty and volatility of high-yield bonds is still not clear.In this paper,we employ GARCH-MIDAS models to investigate their correlation with US economic policy uncertainty index and S&P high-yield bond index.The empirical studies show that mixed volatility models can effectively capture the realized volatility of high-yield bonds,and economic policy uncertainty and macroeconomic factors have significant effects on the long-term component of high-yield bonds volatility.展开更多
Convertible bonds are an important segment of the corporate bond market,however,as hybrid instruments,convertible bonds are difficult to value because they depend on variables related to the underlying stock,the fixed...Convertible bonds are an important segment of the corporate bond market,however,as hybrid instruments,convertible bonds are difficult to value because they depend on variables related to the underlying stock,the fixed-income part,and the interaction between these components.Besides,embedded options,such as conversion,call,and put provisions are often restricted to certain periods,may vary over time,and are subject to additional path-dependent features of the state variables.Moreover,the most challenging problem in convertible bond valuation is the underlying stock return process modeling as it retains various complex statistical properties.In this paper,we propose DeepPricing,a novel data-driven convertible bonds pricing model,which is inspired by the recent success of generative adversarial networks(GAN),to address the above challenges.The method introduces a new financial time-series generative adversarial networks(FinGAN),which is able to reproduce risk-neutral stock return process that retains the unique statistical properties such as the fat-tailed distributions,the long-range dependence,and the asymmetry structure etc.,and then transit to its risk-neutral distribution.Thus it is more flexible and accurate to capture the dynamics of the underlying stock return process and keep the rich set of real-world convertible bond specifications compared with previous model-driven models.The experiments on the Chinese convertible bond market demonstrate the effectiveness of DeepPricing model.Compared with the convertible bond market prices,our model has a better convertible bonds pricing performance than both model-driven models,i.e.Black-Scholes,the constant elasticity of variance,GARCH,and the state-of-the-art GAN-based models,i.e.FinGAN-MLP,FinGAN-LSTM.Moreover,our model has a better fitting capacity for higher-volatility convertible bonds and the overall convertible bond market implied volatility smirk,especially for equity-liked convertible bonds,convertible bonds trading in the bull market,and out-of-the-money convertible bonds.Furthermore,the Long-Short and Long-Only investment strategies based on our model earn a significant annualized return with 41.16%and 31.06%,respectively,for the equally-weighted portfolio during the sample period.展开更多
At present,further research and exploration on credit risks are being carried out in the global field,and increasingly profound modem credit risks are exposed to the bond market.This requires that we cannot ignore the...At present,further research and exploration on credit risks are being carried out in the global field,and increasingly profound modem credit risks are exposed to the bond market.This requires that we cannot ignore the impact of credit rating migration risk on bond pricing,so as to adapt to the sustainable and healthy development of the bond market under the new normal of China's economy.The innovation point of this paper is to try to analyze the pricing of Convertible bonds in China from the perspective of credit rating migration risk.Tsiveriotis and Femandes(1998)model is selected,and the credit risk in the model is assumed to be caused by the credit rating migration risk,and the credit spread is used to measure the credit rating migration risk.The research conclusion of this paper is as follows:First,it is valid to consider the risk of credit rating migration in the TF(1998)model.The market price of convertible bonds is on average 1.22% higher 1han the theoretical value of the model.In general,the theoretical value obtained from the model has little deviation from the market price,and has a good fitting degree.Second,from the Angle of credit rating,the selection of 32 samples of convertible bonds only empirical research shows that the credit rating of AA-convertible bonds average deviation rate is negative,suggest that the credit rating of AA-the phenomenon of convertible bonds value is underestimated,and AAA credit rating to AA,AA+,the average deviation rate of convertible bonds is positive,that credit rating AA(containing AA)more convertible bond value is overrated phenomenon,and the higher the credit rating of the average deviation rate of convertible bond,the greater the overvalued levels.It has certain guiding significance for participants in the convertible bond market.展开更多
In this paper, a new corporate bond pricing model with credit migration risk is proposed. This model sets different thresholds for the rising or falling of credit ratings, which forms a buffer zone that could reduce t...In this paper, a new corporate bond pricing model with credit migration risk is proposed. This model sets different thresholds for the rising or falling of credit ratings, which forms a buffer zone that could reduce the frequency of credit rating changes. Mathematically, this model is a system of partial differential equations with overlapping area. The existence, uniqueness, regularity and asymptotic behavior of the solution are obtained. Furthermore, a numerical scheme and its stability, convergence and accuracy are discussed in detail. Calibration and analysis of the parameters are also suggested.展开更多
文摘This study examines the pricing of municipal bonds before and after a currency shock in Switzerland.Two approaches are used to decompose the municipal to treasuries bond spreads into liquidity,maturity,and default risk premiums.The first approach is the model of the cross-sectional instrumental variables,and the second approach is the model of the instrumental variables with panel data.This study examines the composition of spreads for both approaches,in three scenarios:before,throughout,and after the currency shock.The study performed Durbin-Wu-Hausman tests for each decisive model to verify endogeneity issues,including the Lagrangian Multiplier test,the Cragg-Donald Wald F statistic to confirm the relationship of instrumental and endogenous variables,and the structural break test(Bai-Perron test)to determine the existence of structural breaks in bond distortions.This study finds that the currency price distortions of the Swiss franc in January 2015 made long-run changes in the composition of the municipal bond spreads.This research contributes to the understanding of municipal bond pricing by showing that default risk accounts for a large portion of the municipal bond spread,while maturity risk plays a lesser role.According to our empirical findings,unexpected large currency price shocks may have long-term implications on the municipal bond spreads.
基金This work was supported by National Natural Science Foundation of China(Nos.71461005,71561008)National Social Science Foundation of China(No.17BGL234)Innovation Project of Guangxi Graduate Education(No.YC-SW2017143).
文摘It is well known that economic policy uncertainty prompts the volatility of the high-yield bond market.However,the correlation between economic policy uncertainty and volatility of high-yield bonds is still not clear.In this paper,we employ GARCH-MIDAS models to investigate their correlation with US economic policy uncertainty index and S&P high-yield bond index.The empirical studies show that mixed volatility models can effectively capture the realized volatility of high-yield bonds,and economic policy uncertainty and macroeconomic factors have significant effects on the long-term component of high-yield bonds volatility.
基金supported by the Postdoctoral Science Foundation of China(Project No.2021M700055)。
文摘Convertible bonds are an important segment of the corporate bond market,however,as hybrid instruments,convertible bonds are difficult to value because they depend on variables related to the underlying stock,the fixed-income part,and the interaction between these components.Besides,embedded options,such as conversion,call,and put provisions are often restricted to certain periods,may vary over time,and are subject to additional path-dependent features of the state variables.Moreover,the most challenging problem in convertible bond valuation is the underlying stock return process modeling as it retains various complex statistical properties.In this paper,we propose DeepPricing,a novel data-driven convertible bonds pricing model,which is inspired by the recent success of generative adversarial networks(GAN),to address the above challenges.The method introduces a new financial time-series generative adversarial networks(FinGAN),which is able to reproduce risk-neutral stock return process that retains the unique statistical properties such as the fat-tailed distributions,the long-range dependence,and the asymmetry structure etc.,and then transit to its risk-neutral distribution.Thus it is more flexible and accurate to capture the dynamics of the underlying stock return process and keep the rich set of real-world convertible bond specifications compared with previous model-driven models.The experiments on the Chinese convertible bond market demonstrate the effectiveness of DeepPricing model.Compared with the convertible bond market prices,our model has a better convertible bonds pricing performance than both model-driven models,i.e.Black-Scholes,the constant elasticity of variance,GARCH,and the state-of-the-art GAN-based models,i.e.FinGAN-MLP,FinGAN-LSTM.Moreover,our model has a better fitting capacity for higher-volatility convertible bonds and the overall convertible bond market implied volatility smirk,especially for equity-liked convertible bonds,convertible bonds trading in the bull market,and out-of-the-money convertible bonds.Furthermore,the Long-Short and Long-Only investment strategies based on our model earn a significant annualized return with 41.16%and 31.06%,respectively,for the equally-weighted portfolio during the sample period.
文摘At present,further research and exploration on credit risks are being carried out in the global field,and increasingly profound modem credit risks are exposed to the bond market.This requires that we cannot ignore the impact of credit rating migration risk on bond pricing,so as to adapt to the sustainable and healthy development of the bond market under the new normal of China's economy.The innovation point of this paper is to try to analyze the pricing of Convertible bonds in China from the perspective of credit rating migration risk.Tsiveriotis and Femandes(1998)model is selected,and the credit risk in the model is assumed to be caused by the credit rating migration risk,and the credit spread is used to measure the credit rating migration risk.The research conclusion of this paper is as follows:First,it is valid to consider the risk of credit rating migration in the TF(1998)model.The market price of convertible bonds is on average 1.22% higher 1han the theoretical value of the model.In general,the theoretical value obtained from the model has little deviation from the market price,and has a good fitting degree.Second,from the Angle of credit rating,the selection of 32 samples of convertible bonds only empirical research shows that the credit rating of AA-convertible bonds average deviation rate is negative,suggest that the credit rating of AA-the phenomenon of convertible bonds value is underestimated,and AAA credit rating to AA,AA+,the average deviation rate of convertible bonds is positive,that credit rating AA(containing AA)more convertible bond value is overrated phenomenon,and the higher the credit rating of the average deviation rate of convertible bond,the greater the overvalued levels.It has certain guiding significance for participants in the convertible bond market.
基金the National Natural Science Foundation of China (Nos. 12071349)。
文摘In this paper, a new corporate bond pricing model with credit migration risk is proposed. This model sets different thresholds for the rising or falling of credit ratings, which forms a buffer zone that could reduce the frequency of credit rating changes. Mathematically, this model is a system of partial differential equations with overlapping area. The existence, uniqueness, regularity and asymptotic behavior of the solution are obtained. Furthermore, a numerical scheme and its stability, convergence and accuracy are discussed in detail. Calibration and analysis of the parameters are also suggested.
