美式巴黎期权的定价模型与数值方法

The Pricing Model of American Parisian Option and Numerical Methods

给出了连续时间框架下美式巴黎期权的自由边界问题的表达式并运用有限差分进行计算,此外还运用前向打靶网格方法和最小二乘蒙特卡罗两种数值方法研究美式巴黎期权的定价问题。计算结果表明向上敲出看涨美式巴黎期权价格与障碍价格、窗口期和期权价格成正向关系,和波动率成反向关系。对于向上敲入看涨美式巴黎期权,结论正好相反。研究结果还表明,向上敲出看涨美式巴黎期权和向上敲入看涨美式巴黎期权的价格之和要远大于相同参数下的经典美式期权价格,三种数值方法的计算结果都比较接近,验证了各个数值方法的合理性,为美式巴黎期权的进一步应用奠定了基础。

American Parisian option pricing is explored by Finite Difference method,Forward Shooting Grid method,Least-Square Monte Carlo method.About the Up-Out Call American Parisian Option,Option price has positive relationship with barrier price and duration and negative relationship with volatility.About the Up-In Call American Parisian Option,we have the opposite conclusions.The numerical results show that the sum of option price of Up-Out Call American Parisian Option and Up-Out Call American Parisian Option is strict higher than the vanilla American option.Three numerical methods all obtain the similar numerical results,which verify the reasonability of these approaches.These conclusions lay a foundation for its wide applications.