The
Black–Scholes or
Black–Scholes–Merton model is a
mathematical model of a
financial market containing
derivative investment instruments. From the model, one can deduce the
Black–Scholes formula, which gives a theoretical estimate of 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, although often with adjustments and corrections, by options market participants. Many empirical tests have shown that the Black–Scholes price is "fairly close" to the observed prices, although there are well-known discrepancies such as the "
option smile".