支付红利下Black-Scholes方程的交替分段C-N格式解法

Alternating Segment C-N Algorithm for Black-Scholes Equation with Dividend Paying

摘要: Black-Scholes方程是金融数学中期权定价的重要模型，研究它的数值解法具有非常重要的理论意义和实际应用价值。本文对支付红利下Black-Scholes方程构造了一种具有并行本性的交替分段Crank-Nicolson格式(ASC-N格式)，给出格式解的存在唯一性、稳定性和收敛性分析；理论分析和数值试验表明ASC-N格式与经典格式C-N计算精度相当，但是其计算效率(计算时间)要比经典C-N节省近40%；数值试验验证了理论分析，表明本文ASC-N格式对求解支付红利下Black-Scholes方程是有效的。

Abstract: Black-Scholes equation is an important model in option pricing theory of financial mathematics, which is very practical in the application of numerical computation. This paper constructs a kind of parallel alternating segment Crank-Nicolson (ASC-N) scheme for solving the payment of dividend Black-Scholes equation. Secondly, it gives the existence and uniqueness of solution, stability and convergence analysis of the scheme. The theoretical analysis and numerical examples demonstrate that ASC-N scheme has same computational accuracy with C-N scheme’s, but its computational efficiency (computational time) can save nearly 40% compared with C-N scheme. Numerical experiment verifies the theoretical analysis, and it shows that ASC-N scheme is effective for solving Black-Scholes equation with dividend paying.