This paper investigates the mean-reversion and volatile of credit spread time series by using regression and time series analysis in Chinese bond market. Then the Longstaff-Schwartz model and GARCH model are applied t...This paper investigates the mean-reversion and volatile of credit spread time series by using regression and time series analysis in Chinese bond market. Then the Longstaff-Schwartz model and GARCH model are applied to price credit spread put option. The authors compare the features of these two models by employing daily bond prices of government bonds and corporate bonds for the period 2010–2012 in Chinese bond market. The proposed results show that the higher the credit ratings of the corporate bonds are, the lower the prices of the credit spread options are.展开更多
This paper considers the problem of partially observed optimal control for forward-backward stochastic systems driven by Brownian motions and an independent Poisson random measure with a feature that the cost function...This paper considers the problem of partially observed optimal control for forward-backward stochastic systems driven by Brownian motions and an independent Poisson random measure with a feature that the cost functional is of mean-field type. When the coefficients of the system and the objective performance functionals are allowed to be random, possibly non-Markovian, Malliavin calculus is employed to derive a maximum principle for the optimal control of such a system where the adjoint process is explicitly expressed. The authors also investigate the mean-field type optimal control problem for the system driven by mean-field type forward-backward stochastic differential equations(FBSDEs in short) with jumps, where the coefficients contain not only the state process but also its expectation under partially observed information. The maximum principle is established using convex variational technique. An example is given to illustrate the obtained results.展开更多
This paper presents two new versions of uncertain market models for valuing vulnerable European call option.The dynamics of underlying asset,counterparty asset,and corporate liability are formulated on the basis of un...This paper presents two new versions of uncertain market models for valuing vulnerable European call option.The dynamics of underlying asset,counterparty asset,and corporate liability are formulated on the basis of uncertain differential equations and uncertain fractional differential equations of Caputo type,respectively,and the solution to an uncertain fractional differential equation of Caputo type is presented by employing the Mittag-Leffler function andα-path.Then,the pricing formulas of vulnerable European call option based on the proposed models are investigated as well as some algorithms.Some numerical experiments are performed to verify the effectiveness of the results.展开更多
Assume that there is additional market information in the financial market, which is represented by n given T-contingent claims. The special claims with observed prices at time 0 can only be traded at time 0. Hence, i...Assume that there is additional market information in the financial market, which is represented by n given T-contingent claims. The special claims with observed prices at time 0 can only be traded at time 0. Hence, investment opportunities increase. By means of the techniques developed by Gourierout et al. （1998）, the mixed hedging problem is considered, especially, the price of contingent claim and the optimal hedging strategy are obtained. An explicit description of the mean-variance efficient solution is given after arguing mean-variance efficient frontier problem.展开更多
基金supported by the National Natural Science Foundation of China under Grant Nos.71171012and 70901019Humanity and Social Science Foundation of Ministry of Education of China under Grant No.14YJA790075
文摘This paper investigates the mean-reversion and volatile of credit spread time series by using regression and time series analysis in Chinese bond market. Then the Longstaff-Schwartz model and GARCH model are applied to price credit spread put option. The authors compare the features of these two models by employing daily bond prices of government bonds and corporate bonds for the period 2010–2012 in Chinese bond market. The proposed results show that the higher the credit ratings of the corporate bonds are, the lower the prices of the credit spread options are.
基金supported by the National Natural Science Foundation of China under Grant Nos.11471051 and 11371362the Teaching Mode Reform Project of BUPT under Grant No.BUPT2015JY52+5 种基金supported by the National Natural Science Foundation of China under Grant No.11371029the Natural Science Foundation of Anhui Province under Grant No.1508085JGD10supported by the National Natural Science Foundation of China under Grant No.71373043the National Social Science Foundation of China under Grant No.14AZD121the Scientific Research Project Achievement of UIBE NetworkingCollaboration Center for China’s Multinational Business under Grant No.201502YY003A
文摘This paper considers the problem of partially observed optimal control for forward-backward stochastic systems driven by Brownian motions and an independent Poisson random measure with a feature that the cost functional is of mean-field type. When the coefficients of the system and the objective performance functionals are allowed to be random, possibly non-Markovian, Malliavin calculus is employed to derive a maximum principle for the optimal control of such a system where the adjoint process is explicitly expressed. The authors also investigate the mean-field type optimal control problem for the system driven by mean-field type forward-backward stochastic differential equations(FBSDEs in short) with jumps, where the coefficients contain not only the state process but also its expectation under partially observed information. The maximum principle is established using convex variational technique. An example is given to illustrate the obtained results.
基金supported by the National Natural Science Foundation of China under Grant Nos.11871010 and 11971040by the Fundamental Research Funds for the Central Universities under Grant No.2019XD-A11supported by the National Natural Science Foundation of China under Grant No.71073020.
文摘This paper presents two new versions of uncertain market models for valuing vulnerable European call option.The dynamics of underlying asset,counterparty asset,and corporate liability are formulated on the basis of uncertain differential equations and uncertain fractional differential equations of Caputo type,respectively,and the solution to an uncertain fractional differential equation of Caputo type is presented by employing the Mittag-Leffler function andα-path.Then,the pricing formulas of vulnerable European call option based on the proposed models are investigated as well as some algorithms.Some numerical experiments are performed to verify the effectiveness of the results.
基金the National Natural Science Foundation of China under Grant No.70471071Shanghai Leading Academic Discipline Project under Grant No.T0502Jiangsu Provinces Education Commission,National Natural Science Foundation Research Project under Grant No.07KJD110066.
文摘Assume that there is additional market information in the financial market, which is represented by n given T-contingent claims. The special claims with observed prices at time 0 can only be traded at time 0. Hence, investment opportunities increase. By means of the techniques developed by Gourierout et al. （1998）, the mixed hedging problem is considered, especially, the price of contingent claim and the optimal hedging strategy are obtained. An explicit description of the mean-variance efficient solution is given after arguing mean-variance efficient frontier problem.
