上证指数的正态性研究

Research on Normality of Shanghai Composite Index

摘要: 期权定价等金融研究常以股价的对数收益服从正态分布为基础，而上证指数是A股股指的代表，因此本文研究上证指数的正态性。通过研究发现，对于同一组上证指数，它的收益率与对数收益是同时服从或同时不服从正态分布；并且上证指数的收益率服从正态分布比上证指数的对数收益服从正态分布更吻合实际指数。本文的研究结果扩充了已有文献的结论，为金融市场研究提供理论基础。

Abstract: This paper studies the normality of Shanghai composite index because options pricing and other financial studies are often based on the normal distribution of the logarithm return of stock price. It is found that for the same group of Shanghai index, its return and logarithm return have the same results about normal distribution, and the rate of return obeys the normal distribution, which is more consistent with the actual index than the logarithmic return. The research results of this paper expand the conclusions of the existing literature, and provide the theoretical basis for the research of financial market.