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Elizondo, Rocio
Padilla, Pablo
Bladt, Mogens
Year of Publication: 
Series/Report no.: 
Working Papers, Banco de México 2009-06
Abstract (Translated): 
We give a new way to price American options, using Samuelson's formula. We first obtain the option price corresponding to a European option at time t, weighting it by the probability that the underlying asset takes the value S at time t. This factor 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 introduce systematically the effect of macroeconomic factors. If a macroeconomic framework is given by a dynamic 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 is consistent with the Black-Scholes model.
american options
density probability function
Document Type: 
Working Paper
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