This research article aims to describe how the confluence of financial economics, mathematics and computational technologies can prove to be so effective in the practice of financial engineering. As per modern demands, financial derivatives constitute a vast and rapidly growing portion of the global financial markets. The tool is being used exponentially in portfolio management and for hedging purposes and thus, strong efforts have been projected on modelling of derivative products. In addition, this research article also addresses one of the major problems of pricing European plain vanilla options namely the constant volatility assumption of the Black-Scholes model concentrating the volatility of the underlying assets. Since pricing bias emerges as the most dominant feature of Black-Scholes whenever applied with options and this is the main cause why Black-Scholes model is not widely operated upon in pricing of complex non-vanilla options. However, despite the pricing bias problem, amid its simplicity the Black-Scholes framework dominates the pricing of European style options traded on exchanges, since its inception. The issue of eliminating the price bias has already occupied a huge space in previous published literature of this stream, thus instead of focusing on the price bias of Black-Scholes this work is an attempt to resolve and suggest some of the finest solutions of the financial mathematics to overcome this complex problem of option pricing.
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