Abstract
The fractional Black-Scholes (B-S) equation is an important mathematical model in finance engineering, and the study of its numerical methods has very significant practical applications. This paper constructs a new kind of universal difference method to solve the time-space fractional B-S equation. The universal difference method is analyzed to be stable, convergent, and uniquely solvable. Furthermore, it is proved that with numerical experiments the universal difference method is valid and efficient for solving the time-space fractional B-S equation. At the same time, numerical experiments indicate that the time-space fractional B-S equation is more consistent with the actual financial market.
Highlights
The Black-Scholes (B-S) equation is an important mathematical model in option pricing theory of finance engineering
The extensive application of B-S option pricing model has been driven by the rapid development of the financial derivatives market [, ]
Based on the existing problems, this paper mainly studies the numerical methods of the time-space fractional B-S option pricing model in the actual financial market
Summary
The Black-Scholes (B-S) equation is an important mathematical model in option pricing theory of finance engineering. Based on the existing problems, this paper mainly studies the numerical methods of the time-space fractional B-S option pricing model in the actual financial market. We combine the call options to construct the universal difference scheme for solving the time-space fractional B-S equation. Numerical experiments demonstrate the effectiveness of the universal difference scheme for solving the time-space fractional B-S equation.
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