股指期权定价的非参数数值方法研究

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。

Nonparametric Methods Based Stock Index Option Pricing

The parametric estimation of the diffusion process has naturally born deficiency,with the first impression firmly entrenched.Besides,it’s a pretty tough job to set the diffusion function.However,by the nonparametric,prior information of the data generating process is not a must anymore,instead,it estimates the diffusion function based on discrete data directly,through which irons out the shortcomings mentioned above.Upon the continuous time process,this paper develops a nonparametric stock option model.It lifts all the restrictions for the diffusion function of the underlying process,constructs its nonparametric estimator helped by discrete data to match the density function,and further calculates its equilibrium price.This essay theoretically demonstrates the consistency and asymptotic normality of diffusion estimation.The empirical studies deliver a very clear message: compared with the actual market price,this presented method has a high accuracy of simulation,especially in the market turbulence,under which it estimates much better than the classic B-S model.