This paper proposes a dimension reduction technique on lattice model, an extension of the discrete CRR （1979） model, for option pricing. Applications are demonstrated on pricing some vulnerable options with the payo...This paper proposes a dimension reduction technique on lattice model, an extension of the discrete CRR （1979） model, for option pricing. Applications are demonstrated on pricing some vulnerable options with the payoff functions including two stochastic processes： the underlying stock price and the assets value of the option writer. Instead of building a bivariate tree structure for these correlated processes, a univariate binomial tree for the underlying stock price is only constructed. The proposed univariate binomial tree model is sufficient to undertake, though two underlying assets are involved.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
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
文摘This paper proposes a dimension reduction technique on lattice model, an extension of the discrete CRR （1979） model, for option pricing. Applications are demonstrated on pricing some vulnerable options with the payoff functions including two stochastic processes： the underlying stock price and the assets value of the option writer. Instead of building a bivariate tree structure for these correlated processes, a univariate binomial tree for the underlying stock price is only constructed. The proposed univariate binomial tree model is sufficient to undertake, though two underlying assets are involved.
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 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.
