Expansion methods applied to asset return distributions

Semi-nonparametric VaR forecasts for hedge funds during the recent crisis

“…The EVT, however, is very sensitive to the threshold selection [59] and thus our study particularly focuses on and recommends the SNP approach. Within the SNP framework we analyze the performance of distributions based on GC series, unlike other related contributions that implement the Cornish-Fisher [15], Laguerre [60] or Positive Edgeworth-Sargan expansions [47]. Furthermore, the article compares the VaR forecasting performance of the GC series traditionally expanded to the fourth term for option prices purposes [44,45] to larger expansions proposed to quantify portfolio risk [34].…”

On optimal smoothing of density estimators obtained from orthogonal polynomial expansion methods

“…In such cases, the approximation quality is sensitive to the order of the expansion. Marumo and Wolff (2007) and Jaschke (2002) study the relationship between the order and the approximation quality; however, general criteria for determining an optimal order of expansions have not been proposed, as far as we can determine.…”

“…As noted in the Introduction, besides using the Hermite expansion, the Laguerre expansion is sometimes applied to densities with non-negative support. See Marumo and Wolff (2007) and Marumo (2007).…”

“…Due to these kinds of difficulties, application of expansion methods has been rather limited. For instance, Marumo and Wolff (2007) apply univariate expansion methods to approximating the pdfs of asset return distributions.…”