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非线性Leland方程交替三点组显式差分的并行计算方法
发表时间：2017-04-14 浏览量：2148 下载量：413
| 全部作者： | 傅宇明，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 |
| 摘 要： | 非线性Leland方程是考虑支付交易费用的非线性Black-Scholes（B-S）期权定价模型之一，对其数值方法的研究具有非常重要的理论意义和实际价值。针对Leland模型，构造一种具有并行本性的差分数值方法——交替三点组显式（alternating three points group explicit，AGE-3）方法，给出AGE-3格式的稳定性及解的误差估计。理论分析表明AGE-3格式是绝对稳定的，数值试验显示AGE-3格式较已有的隐式格式和交替分段Crank-Nicolson（alternating segment Crank-Nicolson，ASC-N）格式大幅度提高了计算速度，节省了99%的时间，表明AGE-3格式对求解非线性Leland方程是高效的。 |
| 关 键 词： | 金融数学；非线性Leland模型；交替三点组显式方法；并行计算；数值试验 |
| Title： | Parallel computation method by alternating three points group explicit difference for nonlinear Leland equation |
| Author： | FU Yuming, YANG Xiaozhong |
| Organization： | Institute of Information and Computation, Mathematics and Physics Department, North China Electric Power University |
| Abstract： | Nonlinear Leland equation is one of Black-Scholes (B-S) option pricing model with transaction costs. The study of the numerical method is of important theoretical significance and practical value. In view of Leland model, we constructed a kind of difference numerical method with intrinsic parallelism: alternating three points group explicit (AGE-3) method. Theoretical analysis demonstrates that AGE-3 difference method of the model is unconditionally stable. The stability of the AGE-3 scheme and the error estimate of the solution are given. The numerical experiment shows that AGE-3 scheme can improve the calculation speed rapidly in contrast with implicit scheme and alternating segment Crank Nicolson (ASC-N) scheme, where 99% time was saved, thus the AGE-3 method can be used to solve the nonlinear Leland equation effectively. |
| Key words： | financial mathematics; nonlinear Leland equation; alternating three poiats explicit method; parallel computing; numerical experiments |
| 发表期数： | 2017年4月第7期 |
| 引用格式： | 傅宇明，杨晓忠. 非线性Leland方程交替三点组显式差分的并行计算方法[J]. 中国科技论文在线精品论文，2017，10（7）：718-732. |
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