非线性Leland方程交替三点组显式差分的并行计算方法
Parallel computation method by alternating three points group explicit difference for nonlinear Leland equation
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(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。
Nonlinear Leland equation is one of Black-Scholes option pricing model with transaction costs. The study of the numerical method has a very important theoretical significance and practical value. In view of Leland model, this paper constructs a kind of difference numerical method with intrinsic parallelism-Alternating Three Points Group Explicit (AGE-3) method and gives the stability of AGE-3 scheme and the error estimate of the solution. Theoretical analysis demonstrates that AGE-3 difference method of the model is unconditional stable. 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, thus the AGE-3 method can be used to solve the nonlinear Leland equation effectively.?????
杨晓忠、傅宇明
数学计算技术、计算机技术财政、金融
金融数学非线性Leland模型GE-3方法并行计算数值试验
financial mathematicsnonlinear Leland equationAGE-3 methodparallel computingnumerical experiments
杨晓忠,傅宇明.非线性Leland方程交替三点组显式差分的并行计算方法[EB/OL].(2016-07-08)[2025-08-03].http://www.paper.edu.cn/releasepaper/content/201607-100.点此复制
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