We give a new way to price American options by using Samuelson’s formula. We first obtain the option price corresponding to a European option at time <i>t</i>, weighing it by the probability that the underlying asset takes the value <i>S</i> at time <i>t</i>. We then use Samuelson’s formula with this factor which is given by the solution of the Fokker-Planck (Kolmogorov) equation for the transition probability density. The main advantage of this approach is that we can systematically introduce the effect of macroeconomic factors. If a macroeconomic framework is given by a dynamical system in the form of a set of ordinary differential equations we only have to solve a partial differential equation for the transition probability density. In this context, we verify, for the sake of consistency, that this formula coincides with the Black-Scholes model and compare several numerical implementations.
KeywordsAmerican OptionsFokker-PlanckBlack-ScholesSamuelsonProbability Density Function
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