Rearranging Edgeworth-Cornish-Fisher expansions

This paper applies a regularization procedure called increasing rearrangement to monotonize Edgeworth and Cornish-Fisher expansions and any other related approximations of distribution and quantile functions of sample statistics. Besides satisfying the logical monotonicity, required of distribution and quantile functions, the procedure often delivers strikingly better approximations to the distribution and quantile functions of the sample mean than the original Edgeworth-Cornish-Fisher expansions.

Rearranging Edgeworth-Cornish-Fisher Expansions

This paper applies a regularization procedure called increasing rearrangement to monotonize Edgeworth and Cornish-Fisher expansions and any other related approximations of distribution and quantile functions of sample statistics. Besides satisfying the logical monotonicity, required of distribution and quantile functions, the procedure often delivers strikingly better approximations to the distribution and quantile functions of the sample mean than the original Edgeworth-Cornish-Fisher expansions.Comment: 17 pages, 3 figure

Rearranging Edgeworth-Cornish-Fisher expansions

August 13, 200

Edgeworth Expansions for Realized Volatility and Related Estimators

This paper shows that the asymptotic normal approximation is often insufficiently accurate for volatility estimators based on high frequency data. To remedy this, we compute Edgeworth expansions for such estimators. Unlike the usual expansions, we have found that in order to obtain meaningful terms, one needs to let the size of the noise to go zero asymptotically. The results have application to Cornish-Fisher inversion and bootstrapping.

Estimation and decomposition of downside risk for portfolios with non-normal returns.

We propose a new estimator for Expected Shortfall that uses asymptotic expansions to account for the asymmetry and heavy tails in financial returns. We provide all the necessary formulas for decomposing estimators of Value at Risk and Expected Shortfall based on asymptotic expansions and show that this new methodology is very useful for analyzing and predicting the risk properties of portfolios of alternative investments.Alternative investments; Component expected shortfall; Cornish-Fisher expansion; Downside risk; Expected shortfall; Portfolio; Risk contribution; Value at risk;

Estimating Value-at-Risk and Expected Shortfall: Do Polynomial Expansions Outperform Parametric Densities?

We assess Value-at-Risk (VaR) and Expected Shortfall (ES) estimates assuming different models for the standardized returns: distributions based on polynomial expansions such as Cornish-Fisher and Gram-Charlier, and well-known parametric densities such as normal, skewed-t and Johnson. This paper aims to analyze whether models based on polynomial expansions outperform the parametric ones. We carry out the model performance comparison in two stages: first, with a backtesting analysis of VaR and ES; and second, using loss functions. Our backtesting results show that all distributions, except for normal ones, perform quite well in VaR and ES estimations. Regarding the loss function analysis, we conclude that polynomial expansions (specifically, the Cornish-Fisher one) usually outperform parametric densities in VaR estimation, but the latter (specifically, the Johnson density) slightly outperform the former in ES estimation; however, the gains of using one approach or the other are modest.This paper has been supported by Spanish Government under project PID2021-124860NB-I00 and Generalitat Valenciana under project CIPROM/2021/060