论文部分内容阅读
通常情况下,期权定价的理论研究均假定股票价格的波动率和期望收益率为常数.本文假定波动率和期望收益率为股票价格的一般函数,并在此基础之上研究了障碍期权定价问题.首先,利用偏微分方程的摄动理论将障碍期权的Black-.Scholes方程分解成一系列常系数抛物方程.其次,通过求解这些常系数抛物方程得到了障碍期权定价问题的一个近似解.最后,通过Feymann-Kac公式给出了近似结论的误差估计,结果表明近似解一致收敛于相应期权价格的精确解.
Under normal circumstances, the theoretical research of option pricing assumes that the stock price volatility and expected return rate are constant.This paper assumes the volatility and expected return rate as the general function of stock prices, and on this basis, studies the barrier pricing problem First of all, the Black-Scholes equation of barrier option is decomposed into a series of constant coefficient parabolic equations by using the perturbation theory of partial differential equations.Secondly, by solving these constant coefficient parabolic equations, an approximate solution of the barrier option pricing problem is obtained.Finally, The error estimate of the approximate conclusion is given by Feymann-Kac formula. The result shows that the approximate solution converges uniformly to the exact solution of the corresponding option price.