Option is an agreement between two parties on financial markets. Option gives rights to its buyer to buy or sell a financial asset at a specified price and specified time. Buyer of the option pays the price of the option to its seller.  Seller of the option needs to trade on the financial market, using a replicating hedging strategy. A fair price of the option can be obtained by using value function of the corresponding option and replicating hedging strategy requires the knowledge of the partial derivative of the option value function.

Project titled “Control of open channel water flow and detecting leaks and dumps”,

sponsored by National Research Program for Universities, Higher Education Commission, Government of Pakistan (2017-2019).

Research grant number 5398/Federal/NRPU /R&D/HEC/2016 (1.93 Million PKR)

Project titled “Convergence of Iterative Algorithms of Nonlinear Operators with Applications”,

Sponsored by National Research Program for Universities, Higher Education Commission, Government of Pakistan (2019-2021).

Research grant number 9340/Federal/NRPU /R&D/HEC/2019 (2.27 Million PKR).

Project titled “Iterated Function Systems of Generalized Rational Contractive Mappings in Semi Metric Spaces”,

sponsored by Deanship of Scientific Research, King Abdulaziz University, Ministry of Higher Education, Kingdom Of Saudi Arabia (2019-2020).