Lie symmetry analysis, and exact solutions to the time–fractional Black–Scholes equation of the Caputo–type

In this study, the Lie symmetry analysis, and exact solutions are investigated to the fractional Black–Scholes(B-S) equations of the Caputo–type modeling of the pricing options under the absence of arbitrage and self-financing portfolio assumptions. A class of exact invariant and solitary solutions are given to B-S equations. Some examples are presented in which we use the obtained reductions to find their exact solutions.

Keywords:

Lie symmetry analysis , Time–fractional Black–Scholes equation , Caputo fractional derivative , Invariant solutions