THE FRACTIONAL BLACK-SCHOLES EQUATION

By W. Wyss. 2000

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Numerical solution of the space fractional Fokker-Planck equation (2004, background): “Wyss [41] considered a fractional BlackScholes equation and gave a complete solution of this equation.”
Analytically pricing European-style options under the modified Black-Scholes equation with a spatial-fractional derivative (2014, unknown): “Regarding a fractional derivative in time, Wyss [19] considered the pricing of option derivatives under the modiﬁed BS equation with a time-fractional derivative and derived a closed-form solution for European vanilla options.”
On History of Mathematical Economics: Application of Fractional Calculus (2019, methodology): “) For the first time a fractional generalization of the Black–Scholes equation was proposed in [48] by Walter Wyss in 2000.”
Solution of the Fractional Black-Scholes Option Pricing Model by Finite Difference Method (2013, background): “Wyss [10] gave the fractional Black-Scholes equation with a time-fractional derivative to price European call option.”
Derivation and solutions of some fractional Black-Scholes equations in coarse-grained space and time. Application to Merton's optimal portfolio (2010, methodology): “23)) Comparison with previous modeling As we mentioned it, Wyss [22] proposed a B–S equation in the form P (α) t (x, t) = rP − rxPx − (1/2)σ (2)x(2)Pxx, (5.”