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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和期望收益率为常数,基于此,假定波动率和期望收益率为股票价格的一般函数,利用体积有限元方法研究了上述假定模型下的Black-Scholes偏微分方程,获得了永久美式期权所满足的较高精度的隐式差分格式以及显示差分格式,最后,给出了该方法的误差估计。
英文摘要：
Previous option pricing research typically assumes that the stock volatility and ex- pectation return rate are constants during the life of the option. Therefore, it is assumed that the stock volatility and expectation return rate in the option valuation model are functions of stock. By the finite volume element method, the implicit procedures and explicit calculation for the perpetual American option are obtained. Finally, the error estimate is obtained.
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