MaxVaR for non-normal and heteroskedastic returnsFootnote¶

^¶This work was carried out when Nityanand Misra and Bharat Kodase were graduate students at the Indian Institute of Management Bangalore.

References

• Alexander , C and Lazar , E . 2006 . Normal mixture GARCH(1, 1): applications to exchange rate modelling . J. Appl. Econometr. , 21 ( 3 ) : 307 – 336 .
   Web of Science ®Google Scholar
• Angelidis , T , Benos , A and Degiannakis , S . 2004 . The use of GARCH models in VaR estimation . Statist. Methodol. , 1 ( 1/2 ) : 105 – 128 .
   Google Scholar
• Bai , J and Ng , S . 2004 . Tests for skewness, kurtosis, and normality for time series data . J. Bus. Econ. Statist. , 23 : 49 – 60 .
   Web of Science ®Google Scholar
• Boudoukh , J , Richardson , M , Stanton , R and Whitelaw , RF . 2004 . MaxVaR: long horizon value at risk in a mark-to-market environment . J. Invest. Mmgt , 2 ( 3 ) : 14 – 19 .
   Google Scholar
• Burckhardt , N . 2005 . “ Time dependency of risk measures ” . In International Finance Seminar , University of St. Gallen . Available online at: http://www.sbf.unisg.ch/org/sbf/web.nsf/c2d5250e0954edd3c12568e40027f306/c838918233f320a7c125703c005da569/$FILE/Burckhardt%20Nicolas_paper.pdf
   Google Scholar
• Engle , R . 2001 . GARCH 101: the use of ARCH/GARCH models in applied econometrics . J. Econ. Perspect. , 15 ( 4 ) : 157 – 168 .
   Web of Science ®Google Scholar
• Gouriéroux , C . 1997 . ARCH-Models and Financial Applications , Berlin : Springer .
   Google Scholar
• Grigoletto , M and Lisi , F . 2006 . “ Looking for skewness in financial time series ” . Working Paper 7-2006 Italy : Department of Statistical Sciences, University of Padua .
   Google Scholar
• Grigoletto , M and Lisi , F . 2005 . “ A GARCH-type model with dynamic skewness and kurtosis ” . In in Proceedings of the Meeting on Modelli Complessi e Metodi Computazionali Intensivi per la Stima e la Previsione , Italy : Department of Statistical Sciences, University of Padua .
   Google Scholar
• Heinrich , J . 2004 . “ A guide to the Pearson type IV distribution ” . University of Pennsylvania . Available online at: http://www-cdf.fnal.gov/publications/cdf6820_pearson4.pdf (accessed 17 October 2008)
   Google Scholar
• Hull , JC . 2006 . Options, Futures and Other Derivatives , 6th , Prentice-Hall of India .
   Google Scholar
• Johnson , NL and Kotz , S . 1970 . Distributions in Statistics: Continuous Univariate Distributions-1 , New York : Wiley .
   Google Scholar
• McNeil , AJ and Frey , R . 2000 . Estimation of tail-related risk measures for heteroscedastic financial time series: an extreme value approach . J. Empir. Finan. , 7 ( 3/4 ) : 271 – 300 .
   Google Scholar
• Nagahara , Y . 1999 . The PDF and CF of Pearson type IV distributions and the ML estimation of the parameters . Statist. Probab. Lett. , 43 ( 3 ) : 251 – 264 .
   Web of Science ®Google Scholar
• Newey , WK and Steigerwald , DG . 1997 . Asymptotic bias for quasi-maximum-likelihood estimators in conditional heteroskedasticity models . Econometrica , 65 ( 3 ) : 587 – 599 .
   Web of Science ®Google Scholar
• Premaratne , G and Bera , AK . “ Modeling asymmetry and excess kurtosis in stock return data ” . Illinois Research & Reference Working Paper No. 00-123, 2001 Available online at: http://ssrn.com/abstract=259009 (accessed 17 October 2008)
   Google Scholar
• Press , WH , Teukolsky , SA , Vetterling , WT and Flannery , BP . 1992 . Numerical Recipes in C: The Art of Scientific Computing , 2nd , Cambridge : Cambridge University Press .
   Google Scholar
• Verhoeven , P and McAleer , M . 2004 . Fat tails and asymmetry in financial volatility models . Math. Comput. Simul. , 64 ( 3/4 ) : 351 – 361 .
   Web of Science ®Google Scholar
• Yan , J . 2005 . “ Asymmetry, Fat-tail, and Autoregressive Conditional Density in Financial Return Data with Systems of Frequency Curves ” . Department of Statistics and Actuarial Science, University of Iowa . Available online at: http://www.stat.uiowa.edu/techrep/tr355.pdf (accessed 17 October 2008)
   Google Scholar