股价波动源模型下欧式下出局期权的鞅定价  

The Martingale Pricing of the European Down-and-Out Calls under the Models of Stock Price Fluctuation

作　　者：朱丹[1] 

机构地区：[1]湖南财政经济学院,长沙410205

出　　处：《价值工程》2013年第14期188-189,共2页Value Engineering

基　　金：湖南省科技厅软科学基金(No:2011ZK3101)

摘　　要：机游走模型(Random Walk)和对数正态分布模型是两种最常见的描述股票价格的模型,但是这两种都存在着一定的缺陷,距离实际上的波动还具有较大的差距。波动源模型更全面的考虑了大量散户交易者对股票价格的影响,以及其他的一些因素,能够更加接近实际的描述出股票的价格变动以及波动现象.在股票价格波动源模型下,利用Martingale Pricing方法推导出欧式下出局期权(买权)的定价公式.作为特例,同时得到了传统的对数正态分布模型下欧式下出局期权的定价公式。Random Walk and the lognormal distribution model are the two most common description of stock price model, but the two have some flaws, also have a big gap distance actually fluctuations. The wave source model is more comprehensive account of influence of a large number of retail traders on stock prices, and other factors, can be more close to the actual description of stock price movements and vdatility. Under the models of stock price fluctuation we get the pricing formula of the European Down-and-Out Calls by means of Martingale approach （risk-neutral valuation）, especially,we get the pricing formula under the models of lognormal distribution.

关 键 词：障碍期权 鞅测度 价格波动源模型 风险中性定价 GIRSANOV定理 

分 类 号：F830.9[经济管理—金融学]