赵卫娟， 杨晓忠^*

（  华北电力大学数理学院信息与计算研究所，北京 102206；  ）

摘要： 含有支付交易费用的非线性Black-Scoles期权定价模型（非线性Leland模型）在期权权定价中占有重要地位，其数值解法的研究具有非常重要的理论意义和实际价值。本文首先给出一类高精度并行差分方法：改进的交替分段Crank-Nicolson (Improved Alternating Segment Crank-Nicolson, IASC-N) 方法；其次理论分析该类方法具有存在唯一解、无条件稳定、计算精度为二阶的特性。最后通过数值试验比较几类高精度并行差分方法：IASC-N方法、交替分段Crank-Nicolson(Alternating segment Crank-Nicolson, ASC-N) 方法、交替分段显-隐 (Alternating segment explicit-implicit, ASE-I) 方法。数值试验表明：IASC-N方法的计算精度为二阶、计算效率比ASC-N高，ASE-I方法的计算效率最好。综合比较，本文给出的IASC-N并行差分方法是求解非线性Leland模型的最实用方法。
关键词： 非线性Leland模型；改进的交替分段Crank-Nicolson (IASC-N) 方法；交替分段Crank-Nicolson (ASC-N) 方法；交替分段显-隐 (ASE-I) 方法；并行计算；数值计算

ZHAO Weijuan， YANG Xiaozhong^*

（  Institute of Information and Computation, Mathematics and Physics Department,North China Electric Power University,Beijing 102206,China；  ）

Abstract： The nonlinear Black-Scoles option pricing model with transaction costs (nonlinear Leland model) occupies an important position in the option pricing and the study of numerical methods is of very important theoretical significance and practical significance. This paper proposes a kind of high precision parallel difference method: the improved alternating segment Crank- Nicolson (IASC-N) method. Theoretical analysis demonstrates that IASC-N method has characteristics with unique solution, unconditional stable and second order calculation precision. Finally, through numerical experiment we compare IASC-N method, alternating segment Crank- Nicolson (ASC-N) method, and alternating segment explicit-implicit (ASE-I) method. Nnumerical experiments show that the calculation precision of IASC-N method is second order, the computing efficiency of IASC-N method is taller than ASC-N method, and the computing efficiency of ASE-I method is best. By comprehensivly comparing, IASC-N parallel difference method given by this paper is most practical for solving nonlinear Leland model.
Keywords： nonlinear Leland model；IASC-N method；ASC-N method；ASE-I method；parallel computing；numerical experiments