Numerically Pricing Nonlinear Time-Fractional Black–Scholes Equation with Time-Dependent Parameters Under Transaction Costs

M. Rezaei (), A. R. Yazdanian (), A. Ashrafi and S. M. Mahmoudi
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M. Rezaei: Semnan University
A. R. Yazdanian: Kharazmi University
A. Ashrafi: Semnan University
S. M. Mahmoudi: Semnan University

Computational Economics, 2022, vol. 60, issue 1, No 10, 243-280

Abstract: Abstract One of the assumptions of the classical Black–Scholes (B–S) is that the market is frictionless. Also, the classical B–S model cannot show the memory effect of the stock price in the financial markets. Previously, Ankudinova and Ehrhardt (Comput Math Appl 56:799–812, 2008) priced a European option under the classical B–S model with transaction costs when dividends are paid on assets during that period. But due to the importance of the trend memory effect in financial pricing, we extend Ankudinova’s and Ehrhardt’s study under the fractional B–S model when the price change of the underlying asset with time follows a fractal transmission system. The option price is governed by a time-fractional B–S equation of order $$ 0

Keywords: Time-fractional Black–Scholes equation; Nonlinear equation; Transaction cost; Implicit difference scheme; Stability and convergence (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10614-021-10148-z

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