Quantitative Finance

16Factor and Copulas Models

16.1 Introduction

In this chapter we will discuss factor and copulas models. Factor models are very useful for analyzing high‐dimensional response data with dependence coming from unobservable variables or factors. There are several types of factor models, but they all are constructed using factor analysis techniques and can be divided into three basic categories: statistical, macroeconomic, and fundamental. In the first part of this chapter, we will discuss all three categories. The second half of this chapter will focus on copulas models. A copula is a cumulative distribution function connecting multivariate marginal distributions in a specified form. Copulas are popular in high‐dimensional statistical applications since they allow one to easily model and estimate the distribution of random vectors by estimating marginals and copula separately. An advantage of the copula approach is the fact that it helps achieve the goal of data reduction by locating the common factor variables affecting the selected data series. The copulas can better assist in identifying the dependence relationships and model the chosen financial data.

16.2 Factor Models

A factor model relates the return on an asset (be it a stock, bond, or mutual fund) to the values of a limited number of factors, with the relationship described by a linear equation. In a general form, such a model can be written as:

(16.1)

where,

The variables , and are generally not known in advance. ...