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主要研究了当标的资产的价格遵循不连续的随机过程,即带跳的分数布朗运动时,欧式幂期权的定价问题.利用风险中性定价理论,引入了等价鞅测度,进而推导出新型期权———欧式幂期权的定价公式以及涨跌平价公式.接着,对定价公式展开数值分析和比较:一方面采用Monte Carlo的方法求得数值解,并进而分析模型参数对期权价格的影响.
We mainly study the pricing problem of the European power-law option when the price of the underlying asset follows the discontinuous stochastic process, that is, the fractional Brownian motion with jumps.Using the risk-neutral pricing theory, the equivalent martingale measure is introduced to derive the new option --- European power-options pricing formula and price-parity formula.Next, numerical analysis and comparison of the pricing formula: on the one hand using Monte Carlo method to obtain the numerical solution, and then analyze the impact of model parameters on the option price.