A class of intrinsic parallel difference methods for time-space fractional Black-Scholes equation

作者：Li, Yue; Yang, Xiaozhong^*; Sun, Shuzhen

来源：Advances in Difference Equations, 2018, 2018(1): 280.

DOI：10.1186/s13662-018-1736-2

• Time-space fractional Black-Scholes (B-S) equation
• Intrinsic parallel difference methods
• Unconditional stability
• Convergence
• Parallel computing

To quickly solve the fractional Black-Scholes (B-S) equation in the option pricing problems, in this paper, we construct pure alternative segment explicit-implicit (PASE-I) and pure alternative segment implicit-explicit (PASI-E) difference schemes for time-space fractional B-S equation. It is a kind of intrinsic parallel difference schemes constructed on the basis of classic explicit scheme and classic implicit scheme combined with alternate segmentation technique. PASE-I and PASI-E schemes are analyzed to be unconditionally stable, convergent with second-order spatial accuracy and (2 - alpha) th-order time accuracy, and they have a unique solution. The numerical experiments show that the two schemes have obvious parallel computing properties, and the computation time is greatly improved compared to Crank-Nicolson (C-N) scheme. The PASE-I and PASI-E intrinsic parallel difference methods are efficient to solve the time-space fractional B-S equation.

• 出版日期2018-8-13
• 单位华北电力大学（保定）; 华北电力大学