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
In this paper,we consider the price of catastrophe options with credit risk in a regime-switching model.We assume that the macroeconomic states are described by a continuous-time Markov chain with a finite state space...In this paper,we consider the price of catastrophe options with credit risk in a regime-switching model.We assume that the macroeconomic states are described by a continuous-time Markov chain with a finite state space.By using the measure change technique,we derive the price expressions of catastrophe put options.Moreover,we conduct some numerical analysis to demonstrate how the parameters of the model affect the price of the catastrophe put option.展开更多
Credit risk is one of the main risks the commercial banks faces all over the world,especially in the risk structure of the banks of China.In order to control credit risk more scientifically,we shall connect the qualit...Credit risk is one of the main risks the commercial banks faces all over the world,especially in the risk structure of the banks of China.In order to control credit risk more scientifically,we shall connect the qualitative analysis and the quantitative analysis.Put forward by J.P.Morgan Credit Metrics model is the application of the VaR in the field of credit risk,showing great advantage in quantitative bonds and credit risk of loan.This paper studies the Credit Metrics model and analyzes the hypothesis and framework of this model,attempting to explore the application of the model in China in order to promote the realization of the risk quantification of the commercial banks of China.展开更多
A credit-linked note(CLN)is a note paying an enhanced coupon to investors for bearing the credit risk of a reference entity.In this paper,we study the counterparty risk on CLNs under a Markov chain framework,and intro...A credit-linked note(CLN)is a note paying an enhanced coupon to investors for bearing the credit risk of a reference entity.In this paper,we study the counterparty risk on CLNs under a Markov chain framework,and introduce a Markov copula model to describe joint defaults between the reference entity underlying the CLN and CLN issuer.Assuming that the respective default intensities are directly and inversely proportional to the interest rate,which follows a CIR process,we obtain the explicit formulae for CLN values through a PDE approach.Finally,credit valuation adjustment(CVA)formula is derived to price counterparty credit risk.展开更多
An equivalent condition is derived for g-concave function defined by (static) g-expectation. Several extensions including quadratic generators and (g,h)-concavity are also considered.
In this paper,we propose a pricing model of airbag options with discrete monitoring,time-varying barriers,early exercise opportunities,and other popular features simultaneously.We show that the option value is a visco...In this paper,we propose a pricing model of airbag options with discrete monitoring,time-varying barriers,early exercise opportunities,and other popular features simultaneously.We show that the option value is a viscosity solution of a PDE system.In particular,a closed-form solution is obtained in the classic Black-Scholes economy with no early exercise opportunities.For the general case,we develop a numerical algorithm and conduct an extensive numerical analysis after calibrating the model to the CSI 500 index in China.Greek letters,dynamic hedging,and assessment of investing in airbag options are also studied.展开更多
In this paper,we give an overview of representation theorems for various static risk measures:coherent or convex risk measures, risk measures with comonotonic subadditivity or convexity, law-invariant coherent or conv...In this paper,we give an overview of representation theorems for various static risk measures:coherent or convex risk measures, risk measures with comonotonic subadditivity or convexity, law-invariant coherent or convex risk measures, risk measures with comonotonic subadditivity or convexity and respecting stochastic orders.展开更多
The contagion credit risk model is used to describe the contagion effect among different financial institutions. Under such a model, the default intensities are driven not only by the common risk factors, but also by ...The contagion credit risk model is used to describe the contagion effect among different financial institutions. Under such a model, the default intensities are driven not only by the common risk factors, but also by the defaults of other considered firms. In this paper, we consider a two-dimensional credit risk model with contagion and regime-switching. We assume that the default intensity of one firm will jump when the other firm defaults and that the intensity is controlled by a Vasicek model with the coefficients allowed to switch in different regimes before the default of other firm. By changing measure, we derive the marginal distributions and the joint distribution for default times. We obtain some closed form results for pricing the fair spreads of the first and the second to default credit default swaps （CDSs）. Numerical results are presented to show the impacts of the model parameters on the fair spreads.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
G-VaR,which is a type of worst-case value-at-risk(VaR),is defined as measuring risk incorporating model uncertainty.Compared with most extant notions of worst-case VaR,G-VaR can be computed using an explicit formula,a...G-VaR,which is a type of worst-case value-at-risk(VaR),is defined as measuring risk incorporating model uncertainty.Compared with most extant notions of worst-case VaR,G-VaR can be computed using an explicit formula,and can be applied to large portfolios of several hundred dimensions with low computational cost.We also apply G-VaR to robust portfolio optimization,thereby providing a tractable means to facilitate optimal allocations under the condition of market ambiguity.展开更多
In this paper, we consider the problem of optimal dividend payout and equity issuance for a company whose liquid asset is modeled by the dual of classical risk model with diffusion. We assume that there exist both pro...In this paper, we consider the problem of optimal dividend payout and equity issuance for a company whose liquid asset is modeled by the dual of classical risk model with diffusion. We assume that there exist both proportional and fixed transaction costs when issuing new equity. Our objective is to maximize the expected cumulative present value of the dividend payout minus the equity issuance until the time of bankruptcy,which is defined as the first time when the company＇s capital reserve falls below zero. The solution to the mixed impulse-singular control problem relies on two auxiliary subproblems： one is the classical dividend problem without equity issuance, and the other one assumes that the company never goes bankrupt by equity issuance.We first provide closed-form expressions of the value functions and the optimal strategies for both auxiliary subproblems. We then identify the solution to the original problem with either of the auxiliary problems. Our results show that the optimal strategy should either allow for bankruptcy or keep the company＇s reserve above zero by issuing new equity, depending on the model＇s parameters. We also present some economic interpretations and sensitivity analysis for our results by theoretical analysis and numerical examples.展开更多
This paper considers a correlated risk model with thinning-dependence structure. The au- thors investigate the optimal proportional reinsurance that maximizes the adjustment coefficient and the optimal proportional re...This paper considers a correlated risk model with thinning-dependence structure. The au- thors investigate the optimal proportional reinsurance that maximizes the adjustment coefficient and the optimal proportional reinsurance under mean variance principle for the proposed model. The au- thors derive the optimal solutions and the numerical illustrations to show the impact of the dependence among the classes of business on the optimal reinsurance arrangements.展开更多
We consider a two-dimensional reduced form contagion model with regime-switching interacting default intensities. The model assumes the intensities of the default times are driven by macro-economy described by a homog...We consider a two-dimensional reduced form contagion model with regime-switching interacting default intensities. The model assumes the intensities of the default times are driven by macro-economy described by a homogeneous Markov chain as well as the other default. By using the idea of ＇change of measure＇ and some closed-form formulas for the Laplace transforms of the integrated intensity processes, we derive the two-dimensional conditional and unconditional joint distributions of the default times. Based on these results, we give the explicit formulas for the fair spreads of the first-to-default and second-to-default credit default swaps （CDSs） on two underlyings.展开更多
In this paper, we consider a risk model in which each main claim may induce a delayed claim, called a by-claim. We assume that the time for the occurrence of a by-claim is random. We investigate the expected discounte...In this paper, we consider a risk model in which each main claim may induce a delayed claim, called a by-claim. We assume that the time for the occurrence of a by-claim is random. We investigate the expected discounted penalty function, and derive the defective renewal equation satisfied by it. We obtain some explicit results when the main claim and the by-claim are both exponentially distributed, respectively. We also present some numerical illustrations.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 Jiangsu University Philosophy and Social Science Research Project(Grant No.2019SJA1326).
文摘In this paper,we consider the price of catastrophe options with credit risk in a regime-switching model.We assume that the macroeconomic states are described by a continuous-time Markov chain with a finite state space.By using the measure change technique,we derive the price expressions of catastrophe put options.Moreover,we conduct some numerical analysis to demonstrate how the parameters of the model affect the price of the catastrophe put option.
文摘Credit risk is one of the main risks the commercial banks faces all over the world,especially in the risk structure of the banks of China.In order to control credit risk more scientifically,we shall connect the qualitative analysis and the quantitative analysis.Put forward by J.P.Morgan Credit Metrics model is the application of the VaR in the field of credit risk,showing great advantage in quantitative bonds and credit risk of loan.This paper studies the Credit Metrics model and analyzes the hypothesis and framework of this model,attempting to explore the application of the model in China in order to promote the realization of the risk quantification of the commercial banks of China.
基金the National Natural Science Foundation of China(11671291,71971031,U1811462).
文摘A credit-linked note(CLN)is a note paying an enhanced coupon to investors for bearing the credit risk of a reference entity.In this paper,we study the counterparty risk on CLNs under a Markov chain framework,and introduce a Markov copula model to describe joint defaults between the reference entity underlying the CLN and CLN issuer.Assuming that the respective default intensities are directly and inversely proportional to the interest rate,which follows a CIR process,we obtain the explicit formulae for CLN values through a PDE approach.Finally,credit valuation adjustment(CVA)formula is derived to price counterparty credit risk.
基金supported by the NSFC(11871050 and11401414)SF of Jiangsu Province(BK20160300+3 种基金BK2014029914KJB110022)supported by NSFC(11171186)the"111"project(B12023)
文摘An equivalent condition is derived for g-concave function defined by (static) g-expectation. Several extensions including quadratic generators and (g,h)-concavity are also considered.
基金supported by the the National Natural Science Foundation of China(No.11901416)Natural Science Foundation of Jiangsu Province(BK20190812)。
文摘In this paper,we propose a pricing model of airbag options with discrete monitoring,time-varying barriers,early exercise opportunities,and other popular features simultaneously.We show that the option value is a viscosity solution of a PDE system.In particular,a closed-form solution is obtained in the classic Black-Scholes economy with no early exercise opportunities.For the general case,we develop a numerical algorithm and conduct an extensive numerical analysis after calibrating the model to the CSI 500 index in China.Greek letters,dynamic hedging,and assessment of investing in airbag options are also studied.
基金supported by National Natural Science Foundation of China (Grant No.10571167)National Basic Research Program of China (973 Program) (Grant No.2007CB814902)Science Fund for Creative Research Groups (Grant No.10721101)
文摘In this paper,we give an overview of representation theorems for various static risk measures:coherent or convex risk measures, risk measures with comonotonic subadditivity or convexity, law-invariant coherent or convex risk measures, risk measures with comonotonic subadditivity or convexity and respecting stochastic orders.
基金Acknowledgements The authors cordially thank the anonymous reviewers for valuable comments to improve the earlier version of the paper. This work was supported by the National Natural Science Foundation of China （Grant Nos. 11371274, 11671291）, the Natural Science Foundation of Jiangsu Province （Grant No. BK20160300）, and the Open Project of Jiangsu Key Laboratory of Financial Engineering （Grant No. NSK2015-05）.
文摘The contagion credit risk model is used to describe the contagion effect among different financial institutions. Under such a model, the default intensities are driven not only by the common risk factors, but also by the defaults of other considered firms. In this paper, we consider a two-dimensional credit risk model with contagion and regime-switching. We assume that the default intensity of one firm will jump when the other firm defaults and that the intensity is controlled by a Vasicek model with the coefficients allowed to switch in different regimes before the default of other firm. By changing measure, we derive the marginal distributions and the joint distribution for default times. We obtain some closed form results for pricing the fair spreads of the first and the second to default credit default swaps （CDSs）. Numerical results are presented to show the impacts of the model parameters on the fair spreads.
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supported by Natural Science Foundation of China and Jiangsu Province(No.11871050,No.11971342,No.11401414,No.BK20140299,No.14KJB110022)。
文摘G-VaR,which is a type of worst-case value-at-risk(VaR),is defined as measuring risk incorporating model uncertainty.Compared with most extant notions of worst-case VaR,G-VaR can be computed using an explicit formula,and can be applied to large portfolios of several hundred dimensions with low computational cost.We also apply G-VaR to robust portfolio optimization,thereby providing a tractable means to facilitate optimal allocations under the condition of market ambiguity.
基金partially supported by grants of the National Natural Science Foundation of China(Nos.71231008,71201173,71301031,71471045)Natural Science Foundation of Guangdong Province of China(No.S2013010011959)the Post-Doctoral Foundation of China(Nos.2012M510195,2014T70796)
文摘In this paper, we consider the problem of optimal dividend payout and equity issuance for a company whose liquid asset is modeled by the dual of classical risk model with diffusion. We assume that there exist both proportional and fixed transaction costs when issuing new equity. Our objective is to maximize the expected cumulative present value of the dividend payout minus the equity issuance until the time of bankruptcy,which is defined as the first time when the company＇s capital reserve falls below zero. The solution to the mixed impulse-singular control problem relies on two auxiliary subproblems： one is the classical dividend problem without equity issuance, and the other one assumes that the company never goes bankrupt by equity issuance.We first provide closed-form expressions of the value functions and the optimal strategies for both auxiliary subproblems. We then identify the solution to the original problem with either of the auxiliary problems. Our results show that the optimal strategy should either allow for bankruptcy or keep the company＇s reserve above zero by issuing new equity, depending on the model＇s parameters. We also present some economic interpretations and sensitivity analysis for our results by theoretical analysis and numerical examples.
基金supported by the Research Fund for the Doctorial Program of Higher Education under Grant No.20093201110013Science and Technology Foundation of Fujian Education Department under Grant Nos.JA11208 and JB07153
文摘This paper considers a correlated risk model with thinning-dependence structure. The au- thors investigate the optimal proportional reinsurance that maximizes the adjustment coefficient and the optimal proportional reinsurance under mean variance principle for the proposed model. The au- thors derive the optimal solutions and the numerical illustrations to show the impact of the dependence among the classes of business on the optimal reinsurance arrangements.
基金Acknowledgements 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. BK20130260）, the National Natural Science Foundation of China （Grant No. 11301369）, and the China Postdoctoral Science Foundation （Grant No. 2013M540371）. The research of Guojing Wang was supported by the National Natural Science Foundation of China （Grant No. 11371274） and the Natural Science Foundation of Jiangsu Province （Grant No. BK2012613）.
文摘We consider a two-dimensional reduced form contagion model with regime-switching interacting default intensities. The model assumes the intensities of the default times are driven by macro-economy described by a homogeneous Markov chain as well as the other default. By using the idea of ＇change of measure＇ and some closed-form formulas for the Laplace transforms of the integrated intensity processes, we derive the two-dimensional conditional and unconditional joint distributions of the default times. Based on these results, we give the explicit formulas for the fair spreads of the first-to-default and second-to-default credit default swaps （CDSs） on two underlyings.
基金supported by 121 Young Doctorial Development Fund Project for Central University of Finance and Economics (No. QBJJJ201004)the 2011 research grant from the China Institute for Actuarial Science,Central University of Finance and Economics+2 种基金the Ministry of Education Project of Key Research Institute of Humanities and Social Sciences in Universities (No. 11JJD790004,No. 11JJD790053)The researchof Guojing Wang is supported by the Natural Science Foundation (No. KB2008155) of Jiangsu Province of Chinathe Research Fund for the Doctorial Program of Higher Education (No. 20093201110013)
文摘In this paper, we consider a risk model in which each main claim may induce a delayed claim, called a by-claim. We assume that the time for the occurrence of a by-claim is random. We investigate the expected discounted penalty function, and derive the defective renewal equation satisfied by it. We obtain some explicit results when the main claim and the by-claim are both exponentially distributed, respectively. We also present some numerical illustrations.
