基于停时模拟的移动窗口巴黎期权的定价

Pricing moving window Parisian options by hitting time simulation

移动窗口巴黎期权是更高层次的极为复杂的巴黎期权,在可转换债券等领域均有广泛应用.在连续时间框架下,扩展了Anderluh的方法,通过模拟具有移动窗口巴黎期权特征的停时,给出了移动窗口巴黎期权的定价表达式、算法及算法实现,并且对比了累计巴黎期权、连续巴黎期权和移动窗口巴黎期权在不同参数条件下计算出来的价格,验证了所提出方法的有效性.最后,为了验证停时模拟方法的计算精度,将障碍期权(退化的巴黎期权)的解析解作为基准,比较了停时模拟和标准蒙特卡罗这两种算法,结果显示停时模拟算法具有较高的精度.该方法的应用将有利于提高可转债定价的精确度,为我国可转债的发行和投资决策提供有价值的依据.

Moving window Parisian options are higher level of complicated Parisian options, they are widely used in the convertible bonds and so on. In the continuous time framework, this paper expands the Anderluh＇s method, presents the pricing formula, the algorithm and algorithm realized based on the hitting time simulation of moving window Parisian options. According this method, we compare the prices of cumulative Parisian options, consecutive Parisian options and moving window Parisian options with different parameters. Results show that the method is efficient. Finally, in order to verify the precision of the simulation, we compare the hitting time simulation algorithm and standard Monte Carlo algorithm employing barrier options （degenerate Parisian option） as a benchmark, which shows the hitting time simulation algorithm has higher precision. This method will improve the accuracy of the valuation of the convertible bonds, and provide a valuable basis for convertible bonds issuance and investment decisions in China.