This paper studies the critical exercise price of American floating strike lookback options under the mixed jump-diffusion model. By using It formula and Wick-It-Skorohod integral, a new market pricing model estab...This paper studies the critical exercise price of American floating strike lookback options under the mixed jump-diffusion model. By using It formula and Wick-It-Skorohod integral, a new market pricing model established under the environment of mixed jumpdiffusion fractional Brownian motion. The fundamental solutions of stochastic parabolic partial differential equations are estimated under the condition of Merton assumptions. The explicit integral representation of early exercise premium and the critical exercise price are also given, then the American floating strike lookback options factorization formula is obtained, the results is generalized the classical Black-Scholes market pricing model.展开更多
In this paper,we construct and analyze a Crank-Nicolson fitted finite volume scheme for pricing European options under regime-switching Kou’s jumpdiffusion model which is governed by a system of partial integro-diffe...In this paper,we construct and analyze a Crank-Nicolson fitted finite volume scheme for pricing European options under regime-switching Kou’s jumpdiffusion model which is governed by a system of partial integro-differential equations(PIDEs).We show that this scheme is consistent,stable and monotone as the mesh sizes in space and time approach zero,hence it ensures the convergence to the solution of continuous problem.Finally,numerical experiments are performed to demonstrate the efficiency,accuracy and robustness of the proposed method.展开更多
This paper generalizes European call options on the extremum of several risky assets in a Poisson-Gaussian model which allows both the risky assets and stochastic interest rates moving randomly with jump risks. The st...This paper generalizes European call options on the extremum of several risky assets in a Poisson-Gaussian model which allows both the risky assets and stochastic interest rates moving randomly with jump risks. The stochastic interest rate is assumed to follow an extended multi-factor HJM model with jumps. The authors provide explicitly the closed-form solutions of these options through the change of numeralre technique and examine the effects of both jump risks and stochastic interest rate on the option price with numerical experiment. The model can be seen as an extension of Stulz （1982）, Johnson （1987） and Lindset （2006）.展开更多
In this paper,we study the valuation of vulnerable European options incorporating the reduced-form approach,which models the credit default of the counterparty.We provide an analytical pricing model in which the compo...In this paper,we study the valuation of vulnerable European options incorporating the reduced-form approach,which models the credit default of the counterparty.We provide an analytical pricing model in which the components of the state processes,including the dynamics of the underlying asset value and the intensity process corresponding to the default event,are cross-exciting and they could facilitate the description of complex structure of events dependence.To illustrate how our model works,we present an application when the state variables follow specific affine jump-diffusion processes.Semi-analytical pricing formulae are obtained through a system of matrix Riccati equations.The derived formula can be implemented numerically,and we give numerical analysis to investigate the impact of the dynamic correlation between jump risk of the underlying asset value and default risk of the counterparty.展开更多
This paper analyzes Conditional Value-at-Risk(CVaR)based partial hedging and its applications on equity-linked life insurance contracts in a Jump-Diffusion market model with transaction costs.A nonlinear partial diffe...This paper analyzes Conditional Value-at-Risk(CVaR)based partial hedging and its applications on equity-linked life insurance contracts in a Jump-Diffusion market model with transaction costs.A nonlinear partial differential equation(PDE)that an option value process inclusive of transaction costs should satisfy is provided.In particular,the closed-form expression of a European call option price is given.Meanwhile,the CVaR-based partial hedging strategy for a call option is derived explicitly.Both the CVaR hedging price and the weights of the hedging portfolio are based on an adjusted volatility.We obtain estimated values of expected total hedging errors and total transaction costs by a simulation method.Furthermore,our results are implemented to derive target clients’survival probabilities and age of equity-linked life insurance contracts.展开更多
基金Supported by the Fundamental Research Funds of Lanzhou University of Finance and Economics(Lzufe2017C-09)
文摘This paper studies the critical exercise price of American floating strike lookback options under the mixed jump-diffusion model. By using It formula and Wick-It-Skorohod integral, a new market pricing model established under the environment of mixed jumpdiffusion fractional Brownian motion. The fundamental solutions of stochastic parabolic partial differential equations are estimated under the condition of Merton assumptions. The explicit integral representation of early exercise premium and the critical exercise price are also given, then the American floating strike lookback options factorization formula is obtained, the results is generalized the classical Black-Scholes market pricing model.
基金supported by the National Natural Science Foundation of China(Nos.11971354,and 11701221)the Special Basic Cooperative Research Programs of Yunnan Provincial Undergraduate Universities’Association(No.2019FH001-079)the Fundamental Research Funds for the Central Universities(No.22120210555).
文摘In this paper,we construct and analyze a Crank-Nicolson fitted finite volume scheme for pricing European options under regime-switching Kou’s jumpdiffusion model which is governed by a system of partial integro-differential equations(PIDEs).We show that this scheme is consistent,stable and monotone as the mesh sizes in space and time approach zero,hence it ensures the convergence to the solution of continuous problem.Finally,numerical experiments are performed to demonstrate the efficiency,accuracy and robustness of the proposed method.
基金Supported by the National Natural Science Foundation of China under Grant No. 40675023the "985" Project of Hunan Universitythe Guangxi Natural Science Foundation under Grant No. 0991091
文摘This paper generalizes European call options on the extremum of several risky assets in a Poisson-Gaussian model which allows both the risky assets and stochastic interest rates moving randomly with jump risks. The stochastic interest rate is assumed to follow an extended multi-factor HJM model with jumps. The authors provide explicitly the closed-form solutions of these options through the change of numeralre technique and examine the effects of both jump risks and stochastic interest rate on the option price with numerical experiment. The model can be seen as an extension of Stulz （1982）, Johnson （1987） and Lindset （2006）.
基金The work of Huawei Niu in this paper was supported by National Natural Science Foundation of China(71871120,71501099)Key Project of Philosophy and Social Science Research in Universities in Jiangsu Province(2018SJZDI101)+2 种基金Six Talent Peaks Project in Jiangsu Province(SZCY-012)and Qing Lan Project in Jiangsu ProvinceThe work of Yu Xing was supported by Natural Science Foundation for Youths of Jiangsu of China(BK20171072).
文摘In this paper,we study the valuation of vulnerable European options incorporating the reduced-form approach,which models the credit default of the counterparty.We provide an analytical pricing model in which the components of the state processes,including the dynamics of the underlying asset value and the intensity process corresponding to the default event,are cross-exciting and they could facilitate the description of complex structure of events dependence.To illustrate how our model works,we present an application when the state variables follow specific affine jump-diffusion processes.Semi-analytical pricing formulae are obtained through a system of matrix Riccati equations.The derived formula can be implemented numerically,and we give numerical analysis to investigate the impact of the dynamic correlation between jump risk of the underlying asset value and default risk of the counterparty.
基金Natural Sciences and Engineering Research Council of Canada(Grant No.RES0043487).
文摘This paper analyzes Conditional Value-at-Risk(CVaR)based partial hedging and its applications on equity-linked life insurance contracts in a Jump-Diffusion market model with transaction costs.A nonlinear partial differential equation(PDE)that an option value process inclusive of transaction costs should satisfy is provided.In particular,the closed-form expression of a European call option price is given.Meanwhile,the CVaR-based partial hedging strategy for a call option is derived explicitly.Both the CVaR hedging price and the weights of the hedging portfolio are based on an adjusted volatility.We obtain estimated values of expected total hedging errors and total transaction costs by a simulation method.Furthermore,our results are implemented to derive target clients’survival probabilities and age of equity-linked life insurance contracts.
