Introduction to Bayesian Estimation and Copula Models of Dependence

CHAPTER 8 International Markets

8.1 Introduction

One of the important fields of research in modern financial mathematics and risk management deals with stock indexes. Global, regional, and national stock indexes and index futures contracts serve as instruments for hedging and diversification in the international markets. Statistical modeling of the joint behavior of stock indexes has been of special interest recently because such models can be used directly to hedge complex multinational investment portfolios, see Sharma and Seth [34].

Portfolio diversification can be attained through taking positions in futures, which are indexed through geographically or economically remote markets. In the classical Markowitz model this remoteness is modeled using an insignificant or even negative correlation between the national indexes. However, considering modern financial data, correlation analysis often proves to be insufficient because linear correlation, which fits perfectly dependence in multivariate normal models, poorly describes nonnormal joint distributions, since they allow for such deviations as asymmetry, heavy tails, and nonlinear dependence of distribution components, see [9], [10], or [30]. That is why we are especially interested in the analysis of tails of joint distributions, see Fortin and Kuzmics [12], as it helps us to assess the probabilities of several stock indexes plummeting simultaneously, which could cause global markets to collapse and inflict great losses on ...