The Black-Scholes formula, explained

Introduction to the most famous equation in finance

The Black–Scholes model is a mathematical model simulating the dynamics of a financial market containing derivative financial instruments. Since its introduction in 1973 and refinement in the 1970s and 80s, the model has become the de-facto standard for estimating the price of European-style stock options. The key idea behind the model is to hedge the options in an investment portfolio by buying and selling the underlying asset (such as a stock) in just the right way and as a consequence, eliminate risk. The method has later become known within finance as “continuously revised delta hedging”, and been adopted by many of the world’s foremost investment banks and hedge funds.

The goal of this article is to explain the Black-Scholes equation’s mathematical foundation, underlying assumptions and implications. Continue reading

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