【作者】 林建伟；

【导师】 卢国富；

【作者基本信息】 华侨大学 ， 基础数学， 2005， 硕士

【摘要】 本文研究永久百慕大期权的定价问题.采用二叉树方法和偏微分方程方法分别对离散情形下和连续情形下的永久百慕大期权进行定价,构造出它们相应的离散数学模型(二叉树算法)和连续数学模型(抛物型偏微分方程的定解问题),运用压缩映射原理证明永久百慕大期权(离散和连续)作为周期解的存在唯一性,以及利用永久百慕大期权(离散和连续)对原生资产的性质证明在实施日最佳实施边界点的存在唯一性,进而通过迭代法得到在实施日永久百慕大期权(离散和连续)含有级数形式的定价公式,以及相应的最佳实施边界位置所满足的非线性方程.同时考虑到Black-Scholes模型的价格偏差,本文也对带跳跃-扩散项的永久百慕大期权进行定价,采用偏微分方程方法构造出带跳跃-扩散项的永久百慕大期权的数学模型(它是一个周期解问题),以及给出其相应的定价公式和最佳实施边界位置所满足的非线性方程。更多还原

【Abstract】 We consider pricing problem of the perpetual Bermudan option. We make use of the Binomial Tree Method(BTM) and partial differential equation method(PDE) to value the price of the perpetual Bermudan option in the discrete and continuous case respectively, constructing the corresponding the discrete model (the algorithm of BTM) and the continuous mathematical model (the value problem of the parabolic differential equations). The existence and uniqueness of the periodic solution of the perpetual Bermudan option (discrete and continuous) is proved by using the constraction mapping theorem. Furthermore the existence and uniqueness of the optimal exercised boundary is also proved by using the property of the perpetual Bermudan option (discrete and continuous) with respect to the underlying asset and the pricing formulas of the perpetual Bermudan option(discrete and continuous) in the form of series and the corresponding the nonlinear equation which the optimal exercise boundary in the exercise date satisfies are also given by iterative process. In the meanwhile, due to considering exhibiting some biases in Black-Scholes model, we also value the perpetual Bermudan option with jump-diffusion by PDE. The mathematical model of it is given. Furthermore the corresponding the pricing formula of it and the nonlinear equation which the optimal exercise boundary in the exercise date satisfies are present by iterative process.更多还原