Estimation of Short- and Long-Term VaR for Long-Memory Stochastic Volatility Models

Abstract

The phenomenon of long-memory stochastic volatility (LMSV) has been extensively documented for speculative returns. This research investigates the effect of LMSV for estimating the value at risk (VaR) or the quantile of returns. The proposed model allows the return’s volatility component to be short- or long-memory. We derive various types of limit theorems that can be used to construct confidence intervals of VaR for both short-term and long-term returns. For the latter case, the results are in particular of interest to financial institutions with exposure of long-term liabilities, such as pension funds and life insurance companies, which need a quantitative methodology to control market risk over longer horizons.

Keywords

Long-memory stochastic volatility model Stochastic volatility model Value-at-risk Quantile 

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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Institute of Statistical Science, Academia SinicaTaipeiROC
  2. 2.Department of FinanceNational Taiwan UniversityTaipeiROC

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