A value-at-risk approach with kernel estimator

Abstract

This article proposes an alternative approach of Value-at-Risk (VaR) estimation. Financial assets are known to have irregular return patterns; not only the volatility but also the distribution functions themselves may vary with time. Therefore, traditional time-series models of VaR estimation assuming constant and specific distribution are often unreliable. The study addresses the issue and employs the nonparametric kernel estimator technique directly on the tail distributions of financial assets to produce VaR estimates. Various key methodologies of VaR estimation are briefly discussed and compared. The empirical study utilizing a sample of stocks and stock indices for almost 14 years data shows that the proposed approach outperforms other existing methods.

Notes

¹ See McNeil (1997), Danielsson and de Vries (2000) and McNeil and Frey (2000).

² For detailed methods, see Embrechts et al. (1999), Neftci (2000) and Cotter (2004).

³ The Center for Research in Security Prices database located at the University of Chicago.

⁴ The composite list of stocks of Dow Jones during the sample period has been modified twice in 1999 and 2004. The sample used in the study is based on the composite list for the last day of sample, 31 August 2007.