Statistics for Finance

Chapter 13

Parameter estimation in discretely observed SDEs

13.1 Introduction

This chapter describes methods for estimating parameters in stochastic differential equations (SDEs). A brief introduction to the GMM method is given, but a major part of the presentation is devoted to a class of maximum likelihood methods which can be used for estimation parameters in both linear and non-linear SDEs.

It is clear that a method for estimating parameters of non-linear stochastic differential equations can also be used for estimating the parameters of a linear stochastic differential equation. If a linear model is considered, it is, however, advantageous to take the linearity into account at the estimation procedure. Likewise it is beneficial to simplify ...