4.3 Article

Gram-Charlier densities: a multivariate approach

Journal

QUANTITATIVE FINANCE
Volume 9, Issue 7, Pages 855-868

Publisher

ROUTLEDGE JOURNALS, TAYLOR & FRANCIS LTD
DOI: 10.1080/14697680902773611

Keywords

Empirical finance; Econometrics of financial markets; Financial assets; VaR

Funding

  1. Spanish Ministry of Education [SEJ2006-06104/ECON]

Ask authors/readers for more resources

This paper introduces a new family of multivariate distributions based on Gram-Charlier and Edgeworth expansions. This family encompasses many of the univariate semi-non-parametric densities proposed in financial econometrics as marginal of its different formulations. Within this family, we focus on the analysis of the specifications that guarantee positivity to obtain well-defined multivariate semi-non-parametric densities. We compare two different multivariate distributions of the family with the multivariate Edgeworth-Sargan, Normal, Student's t and skewed Student's t in an in-and out-of-sample framework for financial returns data. Our results show that the proposed specifications provide a reasonably good performance, and would therefore be of interest for applications involving the modelling and forecasting of heavy-tailed distributions.

Authors

I am an author on this paper
Click your name to claim this paper and add it to your profile.

Reviews

Primary Rating

4.3
Not enough ratings

Secondary Ratings

Novelty
-
Significance
-
Scientific rigor
-
Rate this paper

Recommended

Article Energy & Fuels

Modeling Electricity Price and Quantity Uncertainty: An Application for Hedging with Forward Contracts

Alfredo Trespalacios, Lina M. Cortes, Javier Perote

Summary: This paper proposes a static hedging strategy based on a bivariate semi-nonparametric distribution to help electricity generators in liberalized markets mitigate price and quantity uncertainty. The model suggests that the hedge ratio is influenced by skewness, kurtosis, correlation, and forward risk premium.

ENERGIES (2021)

Article Multidisciplinary Sciences

Firm size and economic concentration: An analysis from a lognormal expansion

Lina M. Cortes, Juan M. Lozada, Javier Perote

Summary: This study examines the distribution of firm size in the Colombian economy, revealing evidence against Gibrat's law and proposing a lognormal expansion model to better fit the distribution, while also showing that firm growth depends heavily on firm characteristics.

PLOS ONE (2021)

Article Business, Finance

Monetary policy and corporate investment: A panel-data analysis of transmission mechanisms in contexts of high uncertainty

Luis P. de la Horra, Javier Perote, Gabriel de la Fuente

Summary: The study shows that uncertainty spikes can undermine the policy-rate-based transmission mechanisms, and asymmetries exist at the firm level where factors such as investment irreversibility, market power, and cash flows influence firms' responsiveness to monetary policy changes. The effectiveness of monetary policy depends on authorities' ability to reduce uncertainty and target sectors more likely to be affected by policy shifts.

INTERNATIONAL REVIEW OF ECONOMICS & FINANCE (2021)

Article Business, Finance

The transformed Gram Charlier distribution: Parametric properties and financial risk applications

Angel Leon, Trino-Manuel Niguez

Summary: This paper extends the GC density and ensures positivity through a transformation. It investigates the parametric properties of the density and conditional properties under the TGARCH model. In an empirical application, it estimates tail index, reestimates density, VaR and ES, and conducts a comparative analysis.

JOURNAL OF EMPIRICAL FINANCE (2021)

Article Business, Finance

Semi-nonparametric risk assessment with cryptocurrencies

Ines Jimenez, Andres Mora-Valencia, Javier Perote

Summary: This paper establishes a brand-new perspective of analyzing the risk of crypto assets through a semi-nonparametric approach and suggests Median Shortfall as a robust and reliable risk measure for cryptocurrencies. The evidence supports Median Shortfall at 98.31% and 98.51% confidence levels as accurate alternatives to Value-at-Risk at 99% and Expected Shortfall at 97.5%.

RESEARCH IN INTERNATIONAL BUSINESS AND FINANCE (2022)

Article Business, Finance

Polynomial adjusted Student-t densities for modeling asset returns

Angel Leon, Trino-Manuel Niguez

Summary: This paper presents a polynomial expansion method for the standardized Student-t distribution, deriving closed-form expressions for moments and distribution functions, suitable for modeling skewed and heavy-tailed distributions of asset returns. Empirical applications and analyses demonstrate that this new density could be a promising candidate for risk management.

EUROPEAN JOURNAL OF FINANCE (2022)

Article Social Sciences, Interdisciplinary

Dynamic selection of Gram-Charlier expansions with risk targets: an application to cryptocurrencies

Ines Jimenez, Andres Mora-Valencia, Javier Perote

Summary: This study implements a procedure for dynamically selecting the Gram-Charlier approximation that best fits the empirical distribution of cryptocurrency returns and tests it using backtesting techniques. The results demonstrate that dynamic selection of the Gram-Charlier expansion order can significantly improve conditional coverage compared to fixed-order Gram-Charlier expansions.

RISK MANAGEMENT-AN INTERNATIONAL JOURNAL (2022)

Article Business

Technical note: Modified variance incorporating high-order moments in risk measure with Gram-Charlier returns

Bernardo Leon-Camacho, Andres Mora-Valencia, Javier Perote

Summary: This paper introduces a new risk measure for portfolio choice and compares its performance with two related metrics. By taking into account investor attitudes towards skewness and kurtosis-related risks, the proposed methodology provides a more accurate description of portfolio risk. The results show the superiority of this approach under different risk tolerance parameters based on the minimum variance and Sharpe ratio criteria.

ENGINEERING ECONOMIST (2022)

Article Economics

The impact of economic policy uncertainty and monetary policy on R&D investment: An option pricing approach

Luis P. de la Horra, Javier Perote, Gabriel de la Fuente

Summary: This paper adopts a real options approach to investigate the effects of economic policy uncertainty (EPU) and monetary policy on R&D investment. The findings show that higher EPU and contractionary monetary policy have a positive influence on R&D investment, while lower EPU and expansionary monetary policy have a negative influence. These findings shed light on the counter-intuitive behavior of R&D investments and can help policymakers anticipate such effects.

ECONOMICS LETTERS (2022)

Article Business, Finance

Has the interaction between skewness and kurtosis of asset returns information content for risk forecasting?

Ines Jimenez, Andres Mora-Valencia, Javier Perote

Summary: This paper introduces the effect of crossed products of Hermite polynomials on Gram-Charlier densities and proposes an improved density function to accurately capture the distribution tails. It evaluates risk quantification for S&P500 losses using backtesting procedures for Value-at-Risk and Median Shortfall.

FINANCE RESEARCH LETTERS (2022)

Article Energy & Fuels

The impact of the El Nino phenomenon on electricity prices in hydrologic-based production systems: A switching regime semi-nonparametric approach

Alfredo Trespalacios, Lina M. Cortes, Javier Perote

Summary: Electricity production in hydrological-dependent systems is influenced by weather phenomena, impacting spot prices. We propose a stochastic process with mean reversion and switching regime component to represent spot price dynamics. Our study on the Colombian electricity market shows that scarcity seasons increase spot price mean, variance, and risk level. The switching regime model with semi-nonparametric distributions outperforms traditional models, making it a valuable tool for resource planning and risk management in electricity markets with high climatic dependency.

ENERGY SCIENCE & ENGINEERING (2023)

Article Economics

Financial contagion drivers during recent global crises

Julian Pineda, Lina M. Cortes, Javier Perote

Summary: Financial contagion, known as the simultaneous spread of crisis among stock markets due to their interconnection, has a long-lasting effect and is manifested in herd behavior. This study examines the presence of contagion, its transmission channels, and potential herd behavior using worldwide MSCI indices covering the subprime, European, and COVID-19 crises. Results show evidence of contagion during all three crises, driven mainly by investor expectations and their impact on volatility. In addition, during the COVID-19 crisis, the dissemination of information measured through text-based indices played a significant role in market contagion and led to herd behavior.

ECONOMIC MODELLING (2022)

Article Business, Finance

How reactive is investment in US green bonds and ESG-eligible stocks in times of crisis? Exploring the COVID-19 crisis

Javier Perote, Jose D. Vicente-Lorente, Jose Angel Zuniga-Vicente

Summary: This study investigates the response of green bonds and ESG stock markets to the COVID-19 crisis in the US. Unlike the S&P 500 index, the impact of pandemic progress on green bonds and ESG markets is nonlinear: a low (large) level of confirmed new cases of COVID-19 has a positive (negative) effect. Additionally, the implementation of containment policies, such as stringency measures and vaccination campaigns, is viewed positively, but their simultaneous usage is perceived negatively by investors. Overall, this research raises questions about the resilience of investments in green bonds and ESG markets.

FINANCE RESEARCH LETTERS (2023)

Article Economics

Skewness in energy returns: Estimation, testing and implications for tail risk

M. Angeles Carnero, Angel Leon, Trino-Manuel Niguez

Summary: In this study, we estimate the skewness of energy returns and test its statistical significance. Traditional and robust tests for skewness are compared with tests based on the implied skewness in a TGARCH-GC model. The study also examines the impact of skewness on tail risk through the evaluation of VaR and ES accuracy. The results suggest that crude oil and gasoline returns have negative skewness, indicating higher tail risk compared to other energy returns.

QUARTERLY REVIEW OF ECONOMICS AND FINANCE (2023)

Article Business, Finance

Backtesting expected shortfall for world stock indexETFswith extreme value theory andGram-Charliermixtures

Enrique Molina-Munoz, Andres Mora-Valencia, Javier Perote

Summary: The paper analyzes risk quantification for three main stock market index exchange-traded funds in world financial markets, comparing parametric and semi-nonparametric models. The study shows that peaks-over-threshold and flexible Gram-Charlier approximations are suitable for quantifying market risk.

INTERNATIONAL JOURNAL OF FINANCE & ECONOMICS (2021)

No Data Available