Modelling financial data through Lévy processes

Abstract

Early in the 20th Century the use of Brownian Motion for modelling movements of stock prices became trendy. Later, it became apparent that another kind of stochastic process, the now called Lévy processes, were better suited to model the log returns of stock prices than Brownian Motion. Theory on this topic is vast, and there have been many contributions to this area of study in the last decade. In chapter 3 we explore some of this vast theory. For the purpose of this dissertation we focus on high-frequency, non-parametric estimation methods. We discuss some methods in chronological order, fi rst the Rubin and Tucker estimation method, after we analyze the Gegler and Stadtmüller [15] estimation method, and finally the Sant and Caruana estimation method. The latter being the most recent one, released in 2018. In chapter 5 we apply the estimators discussed in the forth chapter to a local financial data set, furthermore, a simulation study is conducted, and some of the estimation methods are compared.