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扩散过程估计的参数化方法存在先入为主的不足,并且扩散项函数形式的设定十分困难,而非参数方法不需要数据产生过程的先验信息,直接从数据出发估计扩散函数,克服了以上不足。本文提出了一种基于连续时间过程的非参数股指期权定价模型。对于刻画基础资产动态行为特性的扩散函数不加任何函数形式限制,利用离散数据匹配密度函数构造它的非参数估计,进而计算股指期权的均衡价格。论文从理论上论证了扩散项估计的一致性和渐进正态性。实证研究表明,该方法对于实际市场价格具有较高的拟合效果,特别是在市场波动剧烈时期,非参数方法更优于经典B-S方法。
The parameterization method of diffusion process estimation is preconceived, and it is very difficult to set up the form of diffusion term function. Non-parametric method does not need prior information of data generation process and directly estimates the diffusion function from the data to overcome the above shortcomings. This paper presents a non-parametric stock index option pricing model based on continuous-time process. For the diffusion function which characterizes the dynamic behavior of the underlying assets without any functional form restriction, the non-parametric estimation is constructed by using the discrete data matching density function, and then the equilibrium price of the stock index options is calculated. The dissertation proves the consistency and the asymptotic normality of the estimates of diffusion terms theoretically. Empirical studies show that this method has a higher fitting effect on the actual market price, especially in the period of market volatility, the non-parametric method is superior to the classical B-S method.