基于涨跌幅限制的双边截断正态分布期权定价模型

Doubly Truncated Log-Normal Distributions are Used in the Pricing of Options

标准Black Scholes期权定价公式假设股票价格服从对数正态分布,没有考虑股票价格涨跌幅的限制带来的影响.放松该假设条件,假设股票价格服从双边截断对数正态分布,考虑中国股票市场的涨跌幅限制,得到一个新的B-S期权定价公式来表达股价行为.双边截断正态分布假设下收益率的波动率要要比正态分布下的波动率小,所以新B-S公式计算出的期权价格就会比标准B-S公式计算出的价格低.

Standard Black-Scholes option pricing model suppose the stock prices follow the log-normal distribution, without consider the effect of price limits. In this paper, relax the conditions, suppose the stock prices follow doubly truncated log-normal distribution in China＇s stock market, we obtain a new Black-Scholes＇ of European option pricing formula, explain the effect of stock price behavioral. Because the volatility of stock return under the doubly truncated log-normal distribution is small than the log-normal distribution, use new B-S formula calculate the option price is small than standard B-S formula.