Empirical studies show that more and more short-term rate models in capturing the dynamics cannot be described by those classic ones. So the mean-reverting γ-process was correspondingly proposed. In most cases, its c...Empirical studies show that more and more short-term rate models in capturing the dynamics cannot be described by those classic ones. So the mean-reverting γ-process was correspondingly proposed. In most cases, its coefficients do not satisfy the linear growth condition;even they satisfy the local Lipschitz condition. So we still cannot examine its existence of solutions by traditional techniques. This paper overcomes these difficulties. Firstly, through using the function Lyapunov, it has proven the existence and uniqueness of solutions for mean-reverting γ-process when the parameter . Secondly, when , it proves the solution is non-negative. Finally, it proves that there is a weak solution to the mean-reverting γ-process and the solution satisfies the track uniqueness by defining a function ρ. Therefore, the mean-reverting γ-process has the unique solution.展开更多
Assuming that oil price follows the stochastic processes of Geometric Brownian Motion （GBM） or the Mean-Reverting Process （MRP）, this paper takes the net present value （NPV） as an economic index and models the P...Assuming that oil price follows the stochastic processes of Geometric Brownian Motion （GBM） or the Mean-Reverting Process （MRP）, this paper takes the net present value （NPV） as an economic index and models the PSC in 11 different scenarios by changing the value of each contract element （i.e. royalty, cost oil, profit oil as well as income tax）. Then the NPVs are shown in probability density graphs to investigate the effect of different elements on contract economics. The results show that under oil price uncertainty the influence of profit oil and income tax on NPV are more significant than those of royalty and cost oil, while a tax holiday could improve the contractor＇s financial status remarkably. Results also show that MRP is more appropriate for cases with low future oil price volatility, and GBM is best for high future oil price volatility.展开更多
In this work we investigate the pricing of swing options in a model where the underlying asset follows a jump diffusion process.We focus on the derivation of the partial integro-differential equation(PIDE)which will b...In this work we investigate the pricing of swing options in a model where the underlying asset follows a jump diffusion process.We focus on the derivation of the partial integro-differential equation(PIDE)which will be applied to swing contracts and construct a novel pay-off function from a tree-based pay-off matrix that can be used as initial condition in the PIDE formulation.For valuing swing type derivatives we develop a theta implicit-explicit finite difference scheme to discretize the PIDE using a Gaussian quadrature method for the integral part.Based on known results for the classical theta-method the existence and uniqueness of solution to the new implicit-explicit finite difference method is proven.Various numerical examples illustrate the usability of the proposed method and allow us to analyse the sensitivity of swing options with respect to model parameters.In particular the effects of number of exercise rights,jump intensities and dividend yields will be investigated in depth.展开更多
文摘Empirical studies show that more and more short-term rate models in capturing the dynamics cannot be described by those classic ones. So the mean-reverting γ-process was correspondingly proposed. In most cases, its coefficients do not satisfy the linear growth condition;even they satisfy the local Lipschitz condition. So we still cannot examine its existence of solutions by traditional techniques. This paper overcomes these difficulties. Firstly, through using the function Lyapunov, it has proven the existence and uniqueness of solutions for mean-reverting γ-process when the parameter . Secondly, when , it proves the solution is non-negative. Finally, it proves that there is a weak solution to the mean-reverting γ-process and the solution satisfies the track uniqueness by defining a function ρ. Therefore, the mean-reverting γ-process has the unique solution.
基金financial support from Key Projects of Philosophy and Social Sciences Research of Ministry of Education (09JZD0038)
文摘Assuming that oil price follows the stochastic processes of Geometric Brownian Motion （GBM） or the Mean-Reverting Process （MRP）, this paper takes the net present value （NPV） as an economic index and models the PSC in 11 different scenarios by changing the value of each contract element （i.e. royalty, cost oil, profit oil as well as income tax）. Then the NPVs are shown in probability density graphs to investigate the effect of different elements on contract economics. The results show that under oil price uncertainty the influence of profit oil and income tax on NPV are more significant than those of royalty and cost oil, while a tax holiday could improve the contractor＇s financial status remarkably. Results also show that MRP is more appropriate for cases with low future oil price volatility, and GBM is best for high future oil price volatility.
文摘In this work we investigate the pricing of swing options in a model where the underlying asset follows a jump diffusion process.We focus on the derivation of the partial integro-differential equation(PIDE)which will be applied to swing contracts and construct a novel pay-off function from a tree-based pay-off matrix that can be used as initial condition in the PIDE formulation.For valuing swing type derivatives we develop a theta implicit-explicit finite difference scheme to discretize the PIDE using a Gaussian quadrature method for the integral part.Based on known results for the classical theta-method the existence and uniqueness of solution to the new implicit-explicit finite difference method is proven.Various numerical examples illustrate the usability of the proposed method and allow us to analyse the sensitivity of swing options with respect to model parameters.In particular the effects of number of exercise rights,jump intensities and dividend yields will be investigated in depth.
