Pricing American Options Using Transition Probabilities: A Dynamical Systems Approach

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 t, weighing it by the probability that the underlying asset takes the value S at time t. 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.

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The authors declare no conflicts of interest.

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Elizondo, R. , Padilla, P. and Bladt, M. (2015) Pricing American Options Using Transition Probabilities: A Dynamical Systems Approach. Open Journal of Statistics, 5, 525-542. doi: 10.4236/ojs.2015.56056.

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