Pricing American Options Using Transition Probabilities: A Dynamical Systems Approach

• 作者: Mogens Bladt Pablo Padilla Rocio Elizondo
• 来源期刊: 统计学期刊(英文)
• 学科: 数学
• 关键词: American OPTIONS FOKKER-PLANCK BLACK-SCHOLES Samuelson PROBABILITY Density Function
• 年，卷（期）: 2015,（6）
• 页码范围: 525-542
• 页数: 18页
• 分类号: O1

摘要

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.