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| A kind of efficient difference method for time-fractional option pricing model |
| YANG Xiao-zhong, ZHANG Xue, WU Li-fei |
| School of Mathematis and Physics, North China Electric Power University, Beijing 102206, China |
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Abstract It is important in the application to study the numerical computation for timefractional option pricing model (time-fractional Black-Scholes equation). Explicit-Implicit (E-I) scheme and Implicit-Explicit (I-E) scheme are constructed for solving time-fractional Black-Scholes equation. The stable, convergent, existence and uniqueness of solutions given by these schemes are discussed. Theoretical analysis demonstrates that E-I and I-E schemes are unconditional stability and convergent. They have the same calculation. Numerical experiments show that computational accuracy of E-I and I-E schemes is similar to the classic Crank-Nicolson (C-N) scheme, and their computational efficiency (computing time) is 30% higher than C-N scheme. Theoretical analysis and numerical experiments demonstrate the superiority of E-I and I-E schemes for solving time-fractional option pricing model, and affirm that time-fractional Black-Scholes equation is more in line with the actual financial market.
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Received: 23 October 2014
Published: 05 June 2018
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时间分数阶期权定价模型的一类有效差分方法
时间分数阶期权定价模型(时间分数阶Black-Scholes方程)数值解法的研究具有重要的理论意义和实际应用价值. 对时间分数阶Black-Scholes方程构造了显-隐格式和隐-显差分格式, 讨论了两类格式解的存在唯一性, 稳定性和收敛性. 理论分析证实, 显-隐格式和隐-显格式均为无条件稳定和收敛的, 两种格式具有相同的计算量. 数值试验表明：显-隐和隐-显格式的计算精度与经典Crank-Nicolson(C-N)格式的计算精度相当, 其计算效率(计算时间) 比C-N格式提高30%. 数值试验验证了理论分析, 表明本文的显-隐和隐-显差分方法对求解时间分数阶期权定价模型是高效的, 证实了时间分数阶Black-Scholes方程更符合实际金融市场.
关键词：
时间分数阶期权定价模型,
显-隐格式,
稳定性,
收敛性,
数值试验
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