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GENERALISED CLASS OF TIME FRACTIONAL BLACK SCHOLES EQUATION AND NUMERICAL ANALYSIS

机译：广义时代分数黑学学学等式和数值分析

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摘要

It is well known now, that a Time Fractional Black Scholes Equa-tion (TFBSE) with a time derivative of real order α can be obtained to describe the price of an option, when for example the change in the underlying asset is assumed to follow a fractal transmission system. Fractional derivatives as they are called were introduced in option pricing in a bid to take advantage of their memory properties to capture both major jumps over small time periods and long range dependencies in markets. Recently new derivatives of Fractional Calculus with non local and/or non singular Kernel, have been introduced and have had substantial changes in modelling of some diffusion processes. Based on consistency and heuristic arguments , this work generalises previously ob-tained Time Fractional Black Scholes Equations to a new class of Time Frac-tional Black Scholes Equations. A numerical scheme solution is also derived. The stability of the numerical scheme is discussed, graphical simulations are produced to price a double barriers knock out call option.
机译：现在是众所周知的，可以获得具有实际顺序α的时间衍生的时间分数黑学学（TFBSE）来描述选项的价格，例如假设潜在资产的变化分形传动系统。呼叫的分数衍生物是在选项定价中引入的，以利用他们的记忆属性来捕获在小型时间段和市场中长距离依赖性的主要跳跃。最近介绍了具有非局部和/或非奇异内核的分数微积分的新衍生物，并在一些扩散过程的建模中具有大量变化。基于一致性和启发式争论，这项工作推出了以前的ob-table时间分数黑色学学学档程，以新的一类Frac-Tional Black Scholes方程式。还导出了数值方案解决方案。讨论了数值方案的稳定性，制作了图形模拟，以价格为双屏障敲除调用选项。

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