# Online Black-Scholes Pricing

The Black–Scholes model or Black–Scholes–Merton is a mathematical model of a financial market containing certain derivative investment instruments. From the model, one can deduce the Black–Scholes formula, which gives the price of European-style options. The formula led to a boom in options trading and legitimised scientifically the activities of the Chicago Board Options Exchange and other options markets around the world.lt is widely used by options market participants. Many empirical tests have shown the Black–Scholes price is “fairly close” to the observed prices, although there are well-known discrepancies such as the “option smile”.

The model was first articulated by Fischer Black and Myron Scholes in their 1973 paper, “The Pricing of Options and Corporate Liabilities”, published in the Journal of Political Economy. They derived a partial differential equation, now called the Black–Scholes equation, which governs the price of the option over time. The key idea behind the derivation was to hedge perfectly the option by buying and selling the underlying asset in just the right way and consequently “eliminate risk”.This hedge is called delta hedging and is the basis of more complicated hedging strategies such as those engaged in by Wall Street investment banks. The hedge implies there is only one right price for the option and it is given by the Black–Scholes formula.Robert C. Merton was the first to publish a paper expanding the mathematical understanding of the options pricing model and coined the term Black–Scholes options pricing model.

Merton and Scholes received the 1997 Nobel Prize in Economics (The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel) for their work. Though ineligible for the prize because of his death in 1995, Black was mentioned as a contributor by the Swedish academy.

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