In finance, Black's approximation is an approximate method for computing the value of an American call option on a stock paying a single dividend. It was described by Fischer Black in 1975.[1]
The Black–Scholes formula (hereinafter, "BS Formula") provides an explicit equation for the value of a call option on a non-dividend paying stock. In case the stock pays one or more discrete dividend(s) no closed formula is known, but several approximations can be used, or else the Black–Scholes PDE will have to be solved numerically. One such approximation is described here. See also Black–Scholes model#American options.
The method essentially entails using the BS formula to compute the value of two European call options:
(1) A European call with the same maturity as the American call being valued, but with the stock price reduced by the present value of the dividend, and
(2) A European call that expires on the day before the dividend is to be paid.
The largest of (1) and (2) is taken as the approximate value for the American call. See example aside. The resulting value is sometimes called the "pseudo American" value of the call.