Una fórmula alternativa de valuar opciones americanas - Rocio Elizondo; Pablo Padilla; Mogens Bladt (Banco de México, 2009)
– 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.
Keywords: 330; american options; Fokker-Planck; Black-Scholes; Samuelson; density probability function