Pricing Options with Modified Time-Fractional BS. Equation and with Samudu Transform

  • Kamran Zakaria Faculty of Information Sciences and Humanities, NED University, Karachi, Pakistan
  • Saeed Hafeez Faculty of Information Sciences and Humanities, NED University, Karachi, Pakistan
  • Saad Nadeem Faculty of Chemical and Process Engineering, NED University, Karachi, Pakistan
  • Abdullah Ishtiaq Faculty of Mechanical and Manufacturing Engineering, NED University, Karachi, Pakistan
  • Shifa Huma Faculty of Electrical and Computer Engineering, NED University, Karachi, Pakistan
Keywords: Options, pricing, call option, put options, Black Sholes equation, risk free rates, series solution, Samudu Transformation.


Background: The maximum payoff is always the wish of a successful business person, and it is possible only when the risk is minimized and they maximize their gain. Even now, it is a big challenge for financial managers of different investors to predict the minimized risk values in a random environment. Specifically, the stock exchange is a good example of option pricing. Option pricing theory is very important to companies and companies because it estimates the fair value of options that will be used to design various future pricing strategies.

Purpose of the Study: The purpose of the study is to predict risk-free prices for two stocks by using modified Black-Scholes partial differential equations in the fractional time sequence for two stocks that have been worked on very little or not at all before.

Finding: The present study finds out that the Samudu Transformation methodĀ have a significant role to get theĀ better solution of two dimensional time fractional modified Black-Scholes partial differential equation to make better predication of company shares selling and purchasing.

Value/Implications: This paper provides a new solution for research scholars, bankers, practitioners, and government policy-making departments on how the risk free rates for two-dimensional stocks may be obtained. Finance managers play a critical role in the advancement of the country.