7. Extreme Values, Quantiles, and Value at Risk

  1. Ruey S. Tsay

Published Online: 2 AUG 2010

DOI: 10.1002/9780470644560.ch7

Analysis of Financial Time Series, Third Edition, Third Edition

Analysis of Financial Time Series, Third Edition, Third Edition

How to Cite

Tsay, R. S. (2010) Extreme Values, Quantiles, and Value at Risk, in Analysis of Financial Time Series, Third Edition, Third Edition, John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/9780470644560.ch7

Author Information

  1. The University of Chicago Booth School of Business, Chicago, IL, USA

Publication History

  1. Published Online: 2 AUG 2010
  2. Published Print: 13 AUG 2010

Book Series:

  1. Wiley Series in Probability and Statistics

Book Series Editors:

  1. Walter A. Shewhart and
  2. Samuel S. Wilks

ISBN Information

Print ISBN: 9780470414354

Online ISBN: 9780470644560

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Keywords:

  • extremal index;
  • extreme value theory;
  • quantile estimation;
  • value at risk (VaR)

Summary

This chapter discusses various methods for calculating value at risk (VaR) and the statistical theories behind these methods. In particular, it considers the extreme value theory developed in the statistical literature for studying rare events and its application to VaR. Both unconditional and conditional concepts of extreme values are discussed. The unconditional approach to VaR calculation for a financial position uses the historical returns of the instruments involved to compute VaR. On the other hand, a conditional approach uses the historical data and explanatory variables to calculate VaR. The explanatory variables may include macroeconomic variables of an economy and accounting variables of companies involved. Quantile estimation provides a nonparametric approach to VaR calculation. It makes no specific distributional assumption on the return of a portfolio except that the distribution continues to hold within the prediction period. The chapter discusses extremal index for a strictly stationary time series.

Controlled Vocabulary Terms

expected value; quantile function; value at risk (VaR)