Padilla, P. and Bladt, M. (2001) Nonlinear Financial Models: Finite Markov Modulation and Its Limits. In: Avellaneda, M., Ed., Quantitative Analysis in Financial Markets, Collected Papers of the New York University Mathematical Finance Seminar, Vol. III, World Scientific Publishing, Singapore, 159-171.

has been cited by the following article:

• TITLE: Pricing American Options Using Transition Probabilities: A Dynamical Systems Approach

  AUTHORS: Rocio Elizondo, Pablo Padilla, Mogens Bladt

  KEYWORDS: American Options, Fokker-Planck, Black-Scholes, Samuelson, Probability Density Function

  JOURNAL NAME: Open Journal of Statistics, Vol.5 No.6, October 20, 2015

  ABSTRACT: 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.