An Alternative Formula to Price American Options

Rocio Elizondo, Padilla Pablo and Bladt Mogens

No 2009-06, Working Papers from Banco de México

Abstract: 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 completeness, that this formula is consistent with the Black-Scholes model.

JEL-codes: C00 C02 G10 G13 (search for similar items in EconPapers)
Date: 2009-08
New Economics Papers: this item is included in nep-cfn and nep-rmg
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