Black-Scholes期权定价模型的五点式混合差分方法
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引用本文:蹇明,宜娜,张春晓.Black-Scholes期权定价模型的五点式混合差分方法[J].经济数学,2011,(4):66-70
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作者单位
蹇明,宜娜,张春晓 (华中科技大学 数学与统计学院,湖北 武汉430074) 
中文摘要:研究了欧式看涨期权定价问题的差分方法,将Black-Scholes方程等价代换为标准抛物型偏微分方程,在时间方向上采用前、后差商,空间方向上采用五点差分格式,再引入参数θ建立一个稳定的混合差分格式.根据Von Neumann条件证明了该格式的稳定性及收敛性,并通过数值计算的实际应用,结果表明该算法适用于到期日较长的期权定价.
中文关键词:期权定价  数值方法  Black-Scholes模型
 
Five-Point Form Hybrid Difference Method for Black-Scholes Option Pricing Model
Abstract:We studied the difference method for the European Call option pricing problem. Firstly we equivalently transformed the Black-Scholes equation into a standard parabolic partial differential equation. We adopted forward difference and backward difference with respect to the direction of time. Meanwhile, we adopted five-point difference scheme with respect to the direction of space. Next, we used the parameter θ to establish a hybrid difference scheme which is stable. Moreover, according to Von Neumann condition we proved the stability and convergence of this scheme. Finally, we show that the method is applicable to long term option pricing problem through the result of numerical experiments.
keywords:option pricing  numerical method  Black-Scholes equation
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