Open AccessOn numerical pricing of put-call parities for Asian options driven by new time-fractional Black-Scholes evolution equation
Author(s) -
Javed Hussain,
Shoaib Khan
Publication year - 2021
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil2113427h
Subject(s) - mathematics , asian option , black–scholes model , valuation of options , arbitrage , convergence (economics) , stochastic differential equation , econometrics , finance , economics , volatility (finance) , economic growth
The objective of this paper is twofold. Firstly, to derive time-fractional evolution equation modeling the No-Arbitrage premium of Asian option (with arithmetic and geometric averages ) contingent upon an underlying asset that satisfies the fractional stochastic differential equation, in a setting when the strike price is fixed and floating. Secondly, we have computed the four versions of the put-call parities for Asian options, by solving the time-fractional Black-Scholes evolution modeling the difference of the premiums of put and call Asian options, through Fractional Reduced Differential Transform (FRDT) algorithm. We have also established the convergence and the error estimates for the FRDT Algorithm for the two independent variables.