Extreme Events in Finance

Chapter 9Statistics of Extremes: Challenges and Opportunities

M. de Carvalho^*

Faculty of Mathematics, Pontificia Universidad Católica de Chile, Santiago, Chile

9.1 Introduction

My experience on discussing concepts of risk and statistics of extremes with practitioners started in 2009 while I was a visiting researcher at the Portuguese Central Bank (Banco de Portugal). At the beginning, colleague practitioners were intrigued about the methods I was applying; the questions were recurrent: “What is the difference between statistics of extremes and survival analysis (or duration analysis)?¹ And why don't you apply empirical estimators?” The short answer is that when modeling rare catastrophic events, we need to extrapolate beyond observed data—into the tails of a distribution—and standard inference methods often fail to deal with this properly. To see this, suppose that we observe a random sample of losses and that we estimate the survivor function , using the empirical survivor function, , for . Now, suppose that we want to assess what is the probability of observing a loss just larger ...