Black–Scholes

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Simulated geometric Brownian motions with parameters from market data

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”.

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