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中文摘要：
通常情况下,期权定价研究都假定股票价格的波动率为常数.该文假定波动率为股票价格的一般函数.将该模型下障碍期权所满足的偏微分方程做近似化处理,使得偏微分方程变为可解模型.通过求解偏微分方程获得下降敲出看涨期权和上升敲出看涨期权显式解.为了数学表述的严谨性,文章最后给出了定价公式的误差估计.
英文摘要：
Previous option pricing research typically assumes that the stock volatility is constant during the life of the option.In this study,we assume the stock volatility in our option valuation model is function of stock.By approximate method,the partial differential equation satisfied the down-and-out option and up-and-out option are changed to another partial differential equation which can be solved.Finally,the pricing formula for down-and-out option and up-and-out option are obtained.In order to the mathematically rigorous,we supply the error estimation.
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