Distributional Approximation of Asset Returns with Nonparametric Markovian Trees

Abstract

Summary The paper proposes the use a Markov chain to model and predict the distributional behaviour of a portfolio of returns. In particular, it describes an algorithm to compute the distribution of returns that follow a markovian tree. This approach reduces the computational complexity as compared to the classic markovian approach, since the tree recombines at each temporal step. Furthermore, the paper compares ex-post the assumption that returns follow either a geometric Brownian motion or a Markov chain. Finally, it discusses some possible financial applications of the proposed approach.