Why is the Binomial method so popular for pricing derivatives in practice?

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The Black-Scholes model only works for options written on stocks that do not pay dividends.

For many exotic options, analytic formulae do not exist therefore the Binomial approach is a convenient approximation.

The Binomial approach makes assumptions about share price movements that are more realistic than the assumptions underlying the Black Scholes model.

Since risk-neutral pricing is state of the art, older techniques such as the Black-Scholes analytic formula are obsolete.