On numerical pricing of put-call parities for Asian options driven by new time-fractional Black-Scholes evolution equation

The objective of this paper is twofold. Firstly, to derive time-fractional evolution equation modeling the No-Arbitrage premium Asian option (with arithmetic and geometric averages ) contingent upon an underlying asset that satisfies fractional stochastic differential equation, in a setting when strike price fixed floating. Secondly, we have computed four versions put-call parities for options, by solving Black-Scholes difference premiums put call through Fractional Reduced Differential Transform (FRDT) algorithm. We also established convergence error estimates FRDT Algorithm two independent variables.