The least squares method for option pricing revisited

It is shown that the the popular least squares method of option pricing converges even if the underlying is non-Markovian, the pay-offs are path dependent and with a very flexible setup for approximation of conditional expectations. The main benefit is the increase of freedom in creating specific implementations of the method, but depending on the extent of adopted generality and complexity, the method may become very demanding computationally. It is argued, however, that in many practical applications even modest but computationally viable extensions of standard linear regression may produce satisfactory results from the empirical point of view. This claim is illustrated with several empirical examples.