Extreme Events in Finance

Chapter 6Bootstrap Methods in Statistics of Extremes

M. Ivette Gomes¹, Frederico Caeiro², Lígia Henriques-Rodrigues³ and B.G. Manjunath⁴

¹Universidade de Lisboa, FCUL, DEIO and CEAUL, Portugal

²Universidade Nova de Lisboa, FCT and CMA, Portugal

³Universidade de São Paulo, IME and CEAUL, Brazil

⁴Universidade de Lisboa, CEAUL, Portugal

AMS 2010 subject classification. Primary 62G32, 62E20; Secondary 65C05.

AMS 2000 subject classification. Primary 62G32, 62E20; Secondary 62G09, 62G30.

6.1 Introduction

Let be a random sample from an underlying cumulative distribution function (CDF) . If we assume that is known, we can easily estimate the sampling distribution of any estimator of an unknown parameter through the use of a Monte Carlo simulation, described in the following algorithm:

1. S1.  For ,
   1. S1.1  generate random samples ,
   2. S1.2  and compute .
2. S2.  On the basis of the output , after ...