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障碍期权定价的一种高效蒙特卡罗方法
发表时间：2021-12-31 浏览量：1219 下载量：226
| 全部作者： | 黄慧敏，杨雪斌，杨晓忠 |
| 作者单位： | 华北电力大学数理学院信息与计算研究所；中央财经大学中国公共财政与政策研究院 |
| 摘 要： | 针对障碍期权的定价问题，给出了一种高效的蒙特卡罗（Monte Carlo，MC）模拟方法——基于布朗桥构造路径的随机化拟蒙特卡罗（Brownian bridge path randomization quasi Monte Carlo，BBPR-QMC）方法。首先，用Faure序列代替MC方法中的随机序列，得到了Faure序列的拟蒙特卡罗（quasi Monte Carlo，QMC）模拟方法；其次，应用Moro算法得到了随机化拟蒙特卡罗（randomization quasi Monte Carlo，R-QMC）模拟方法；最后，将QMC方法和R-QMC方法结合，利用布朗桥技术来降低有效维，得到障碍期权定价的BBPR-QMC方法。数值试验表明，与MC方法和R-QMC方法相比较，BBPR-QMC方法模拟的价格与真实价格更接近、收敛速度更快。数值试验证实，BBPR-QMC方法是一种高效求解障碍期权定价的数值方法。 |
| 关 键 词： | 应用数学；障碍期权定价方法；布朗桥构造路径的随机化拟蒙特卡罗（BBPR-QMC）方法；Black-Scholes方程；计算实例 |
| Title： | Efficient Monte Carlo method for pricing barrier options |
| Author： | HUANG Huimin, YANG Xuebin, YANG Xiaozhong |
| Organization： | Institute of Information and Computing, School of Mathematics and Physics, North China Electric Power University; China Academy of Public Finance and Public Policy, Central University of Finance and Economics |
| Abstract： | Aiming at the pricing problem of barrier options, an efficient Monte Carlo (MC) simulation method-Brownian bridge path randomization quasi Monte Carlo (BBPR-QMC) was presented in this paper. Firstly, Faure sequence was used to replace the random sequence in MC method, and the quasi Monte Carlo (QMC) simulation method of Faure sequence was obtained. Secondly, the randomization quasi Monte Carlo (R-QMC) Simulation method was obtained by using Moro algorithm. Finally, combining the QMC method with the R-QMC method, the BBPR-QMC method for barrier option pricing was given by using the Brownian bridge technology to reduce the effective dimension. Numerical experiments indicated that compared with MC method and R-QMC method, the price simulated by BBPR-QMC method was closer to the real price and converged faster. Numerical experiments show that BBPR-QMC is an efficient numerical method to solve the pricing of barrier options. |
| Key words： | applied mathematics; barrier option pricing method; Brownian bridge path randomization quasi Monte Carlo (BBPR-QMC) method; Black-Scholes equation; calculation example |
| 发表期数： | 2021年12月第4期 |
| 引用格式： | 黄慧敏，杨雪斌，杨晓忠. 障碍期权定价的一种高效蒙特卡罗方法[J]. 中国科技论文在线精品论文，2021，14（4）：440-446. |
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