Financial derivatives pricing is used to help investors raise potential returns and to minimize the risk of an investment. In particular, options offer advantages such as limited risk and leverage, and for this reason, much research has been devoted to the development of models that price options accurately. The Black-Scholes model is the most popular model for option pricing, however, when reduced to the heat equation, the simplistic assumptions contribute to the mispricing of options. Therefore, extensions of this model have been developed that take into account a shift in volatility. We study the classical method in this work using finite difference schemes for the heat equation, and then apply computational schemes for stochastic differential equations using Euler-Maruyama method. We begin by considering asset models where time-dependent coefficients are volatility and interest rate, and then expand these models to coefficients that also depend on the price of the underlying asset. We see that the numerical conditions are met as long as appropriate conditions on the coefficients are satisfied. It is also noted that approximations would converge on the price of European call options poorly and powerfully. Option pricing in Pakistan has not been launched yet, but there is a good possibility that it will be introduced in several years to come. Our main goal is to incorporate all these numerical methods to see how useful these techniques are in the Pakistan stock market.