随机游走行情期权复制的研究并推导出若干公式

Research on the Replication of the Option of Random Walk Market and Deducing Some Formulas

摘要: 首先，本文推导出随机游走行情的期权定价公式，然后提出三个命题并分别证明。命题一从新的角度阐述期权复制原理。命题二发现两个不等式，给出了标准正态分布累积函数的上下界。结合命题二和命题三发现了四个逼近标准正态分布累积函数的初等函数，第二个函数的精度最高：最大绝对误差是0.0000406。

Abstract: First, this paper deduces the option pricing formula of random walks, and then proposes three propositions and proves them separately. Proposition 1 explains the principle of option replication from a new perspective. Proposition 2 finds two inequalities and gives the upper and lower bounds of the cumulative function of the standard normal distribution. Combining Proposition 2 and Proposition 3, four elementary functions that approximate the cumulative function of the standard normal distribution are found. The second function has the highest precision: the maximum absolute error is 0.0000406.