Pricing of American style options with an adjoint process correction method

Pricing of American options is a more complicated problem than pricing of European options. In this work a formula is derived that allows the computation of the early exercise premium, i.e. the price difference between these two option types in terms of an adjoint process evolving in the reversed time direction of the original process determining the evolution of the European price. We show how this equation can be utilised to improve option price estimates from numerical schemes like finite difference or Monte Carlo methods.