As regards derivative pricing, the binomial options pricing model provides a discretized version of Black–Scholes, useful for the valuation of American styled options. Discretized models of this type are built—at least implicitly—using state-prices (as above); relatedly, a large number of researchers have used options to extract state-prices for a variety of other applications in financial economics.[1][2][14] For path dependent derivatives, Monte Carlo methods for option pricing are employed; here the modelling is in continuous time, but similarly uses risk neutral expected value.