不完全信息下二叉树期权价格上下界

由于信息不完全和市场冲击,经典期权定价理论的股票波动率不能准确得到,从而导致期权的理论价格和实际价格出现偏差。本文假设可以通过相关的有限信息信号对波动率进行推断,基于二叉树框架对欧式看涨期权进行定价,得到了不完全信息下期权价格的定价区间,并研究了影响期权价格上下界的因素。通过对单期模型和多期模型、单信号和多信号模型的分析表明,信息质量的提高使得定价区间变小,从而提高定价的准确性。本文的模型也能包容波动率为随机变量的期权模型,是经典二叉树模型的推广。

Upper and Lower Bounds of Binomial Option Pricing Model under Incomplete Information

Because of incomplete information and the impact of market,the volatility of classical option pricing theories can not be obtained accurately,which leads to the price bias.This paper supposes that the volatility can not been observed directly,but have to be inferred by some limited information signal.Based on this hypothesis we establish our models with binominal option pricing frame,and draw the conclusion that the price of European call option is not unique but falls within an interval.Through the analysis of single-period and multi-period models,single-signal and multi-signal models,we find that improvement of the quality of information makes the price interval narrower and improves the accuracy of option pricing.Our model can contain the situation with random volatility,and it is the generalization of CRR model.