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Assimetrias na volatilidade e nas perturbações nos modelos de volatilidade; Leverage effect and asymmetry of the error distribution in volatility models

Daniel de Almeida
Fonte: Biblioteca Digital da Unicamp Publicador: Biblioteca Digital da Unicamp
Tipo: Dissertação de Mestrado Formato: application/pdf
Publicado em 31/07/2013 Português
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56.33%
O objetivo da dissertação é estudar modelos de volatilidade que consideram dois tipos de assimetria usualmente encontradas em séries de finanças, a assimetria das perturbações e o efeito de alavancagem. Perturbações assimétricas são utilizadas devido ao fato estilizado de que perdas têm distribuição com cauda mais pesada do que ganhos. Já o efeito de alavancagem leva em consideração que perdas têm maior influência na volatilidade do que os ganhos. São estudados os modelos GARCH univariados que contemplam os dois tipos de assimetria separadamente e conjuntamente e modelos GARCH multivariados que permitem o efeito de alavancagem. Os resultados são apresentados em dois artigos. O primeiro descreve os principais modelos univariados que possam explicar estes dois fatos estilizados e analisa, com detalhes, oito séries: os índices Ibovespa, Merval e S&P 500, e as ações Itaú-Unibanco, Vale, Petrobras, Banco do Brasil e do Bradesco. A conclusão é que os dois tipos de assimetria estão presentes nas séries, na maioria das vezes simultaneamente. O segundo artigo faz uma revisão dos principais modelos multivariados da família GARCH, incluindo modelos com efeitos assimétricos nas variâncias e nas covariâncias condicionais. Alguns destes modelos são analisados com mais detalhes através de simulações. Considerou-se as perdas de eficiência na estimativa da matriz de volatilidade ao se ter erros de especificação...

THE LEVERAGE EFFECT AND THE ASYMMETRY OF THE ERROR DISTRIBUTION IN GARCH-BASED MODELS: THE CASE OF BRAZILIAN MARKET RELATED SERIES

Almeida,Daniel de; Hotta,Luiz K.
Fonte: Sociedade Brasileira de Pesquisa Operacional Publicador: Sociedade Brasileira de Pesquisa Operacional
Tipo: Artigo de Revista Científica Formato: text/html
Publicado em 01/08/2014 Português
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46.25%
Traditional GARCH models fail to explain at least two of the stylized facts found in financial series: the asymmetry of the distribution of errors and the leverage effect. The leverage effect stems from the fact that losses have a greater influence on future volatilities than do gains. Asymmetry means that the distribution of losses has a heavier tail than the distribution of gains. We test whether these features are present in some series related to the Brazilian market. To test for the presence of these features, the series were fitted by GARCH(1,1), TGARCH(1,1), EGARCH(1,1), and GJR-GARCH(1,1) models with standardized Student t distribution errors with and without asymmetry. Information criteria and statistical tests of the significance of the symmetry and leverage parameters are used to compare the models. The estimates of the VaR (value-at-risk) are also used in the comparison. The conclusion is that both stylized facts are present in some series, mostly simultaneously.

The Leverage Effect on Wealth Distribution in a Controllable Laboratory Stock Market

Zhu, Chenge; Yang, Guang; An, Kenan; Huang, Jiping
Fonte: Public Library of Science Publicador: Public Library of Science
Tipo: Artigo de Revista Científica
Publicado em 26/06/2014 Português
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46.29%
Wealth distribution has always been an important issue in our economic and social life, since it affects the harmony and stabilization of the society. Under the background of widely used financial tools to raise leverage these years, we studied the leverage effect on wealth distribution of a population in a controllable laboratory market in which we have conducted several human experiments, and drawn the conclusion that higher leverage leads to a higher Gini coefficient in the market. A higher Gini coefficient means the wealth distribution among a population becomes more unequal. This is a result of the ascending risk with growing leverage level in the market plus the diversified trading abilities and risk preference of the participants. This work sheds light on the effects of leverage and its related regulations, especially its impact on wealth distribution. It also shows the capability of the method of controllable laboratory markets which could be helpful in several fields of study such as economics, econophysics and sociology.

A Theoretical Comparison Between Integrated and Realized Volatilies

MEDDAHI, Nour
Fonte: Université de Montréal Publicador: Université de Montréal
Tipo: Artigo de Revista Científica Formato: 1631096 bytes; application/pdf
Português
Relevância na Pesquisa
46.03%
In this paper, we provide both qualitative and quantitative measures of the cost of measuring the integrated volatility by the realized volatility when the frequency of observation is fixed. We start by characterizing for a general diffusion the difference between the realized and the integrated volatilities for a given frequency of observations. Then, we compute the mean and variance of this noise and the correlation between the noise and the integrated volatility in the Eigenfunction Stochastic Volatility model of Meddahi (2001a). This model has, as special examples, log-normal, affine, and GARCH diffusion models. Using some previous empirical works, we show that the standard deviation of the noise is not negligible with respect to the mean and the standard deviation of the integrated volatility, even if one considers returns at five minutes. We also propose a simple approach to capture the information about the integrated volatility contained in the returns through the leverage effect.; Dans cet article, nous quantifions qualitativement et quantitativement la précision de la mesure de la volatilité intégrée par la volatilité réalisée quand la fréquence d’observations est fixée. Nous commençons par caractériser pour une diffusion générale la différence entre les volatilités réalisée et intégrée pour une fréquence d’observations donnée. Ensuite...

Modelling long-memory volatilities with leverage effect: ALMSV versus FIEGARCH

Ruiz, Esther; Veiga, Helena
Fonte: Universidade Carlos III de Madrid Publicador: Universidade Carlos III de Madrid
Tipo: Trabalho em Andamento Formato: application/pdf
Publicado em /10/2006 Português
Relevância na Pesquisa
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In this paper, we propose a new stochastic volatility model, called A-LMSV, to cope simultaneously with the leverage effect and long-memory. We derive its statistical properties and compare them with the properties of the FIEGARCH model. We show that the dependence of the autocorrelations of squares on the parameters measuring the asymmetry and the persistence is different in both models. The kurtosis and autocorrelations of squares do not depend on the asymmetry in the A-LMSV model while they increase with the asymmetry in the FIEGARCH model. Furthermore, the autocorrelations of squares increase with the persistence in the A-LMSV model and decrease in the FIEGARCH model. On the other hand, the autocorrelations of absolute returns increase with the magnitude of the asymmetry in the FIEGARCH model while they can increase or decrease depending on the sign of the asymmetry in the L-MSV model. Finally, the cross-correlations between squares and original observations are, in general, larger in the FIEGARCH model than in the ALMSV model. The results are illustrated by fitting both models to represent the dynamic evolution of volatilities of daily returns of the S and P500 and DAX indexes.

Measuring causality between volatility and returns with high-frequency data

Dufour, Jean-Marie; García, René; Taamouti, Abderrahim
Fonte: Universidade Carlos III de Madrid Publicador: Universidade Carlos III de Madrid
Tipo: info:eu-repo/semantics/workingPaper; info:eu-repo/semantics/workingPaper Formato: application/pdf
Publicado em /09/2008 Português
Relevância na Pesquisa
46.4%
We use high-frequency data to study the dynamic relationship between volatility and equity returns. We provide evidence on two alternative mechanisms of interaction between returns and volatilities: the leverage effect and the volatility feedback effect. The leverage hypothesis asserts that return shocks lead to changes in conditional volatility, while the volatility feedback effect theory assumes that return shocks can be caused by changes in conditional volatility through a time-varying risk premium. On observing that a central difference between these alternative explanations lies in the direction of causality, we consider vector autoregressive models of returns and realized volatility and we measure these effects along with the time lags involved through short-run and long-run causality measures proposed in Dufour and Taamouti (2008), as opposed to simple correlations. We analyze 5-minute observations on S&P 500 Index futures contracts, the associated realized volatilities (before and after filtering jumps through the bispectrum) and implied volatilities. Using only returns and realized volatility, we find a weak dynamic leverage effect for the first four hours at the hourly frequency and a strong dynamic leverage effect for the first three days at the daily frequency. The volatility feedback effect appears to be negligible at all horizons. By contrast...

Modelling long-memory volatilities with leverage effect: A-LMSV versus FIEGARCH

Ruiz, Esther; Veiga, Helena
Fonte: Elsevier Publicador: Elsevier
Tipo: Artigo de Revista Científica Formato: application/pdf
Publicado em 20/02/2008 Português
Relevância na Pesquisa
46.03%
A new stochastic volatility model, called A-LMSV, is proposed to cope simultaneously with leverage effect and long-memory in volatility. Its statistical properties are derived and compared with the properties of the FIEGARCH model. It is shown that the dependence of the autocorrelations of squares on the parameters measuring the asymmetry and the persistence is different in both models. The kurtosis and autocorrelations of squares do not depend on the asymmetry in the A-LMSV model while they increase with the asymmetry in the FIEGARCH model. Furthermore, the autocorrelations of squares increase with the persistence in the A-LMSV model and decrease in the FIEGARCH model. On the other hand, if the correlation between returns and future volatilities is negative, the autocorrelations of absolute returns increase with the magnitude of the asymmetry in the FIEGARCH model while they decrease in the A-LMSV model. Finally, the cross-correlations between squares and original observations are, in general, larger in absolute value in the FIEGARCH model than in the A-LMSV model. The results are illustrated by fitting both models to represent the dynamic evolution of volatilities of daily returns of the S&P500 and DAX indexes.

Volatility models with Leverage effect

Rodríguez Villar, Mª José
Fonte: Universidade Carlos III de Madrid Publicador: Universidade Carlos III de Madrid
Tipo: Tese de Doutorado Formato: application/octet-stream; application/octet-stream; application/pdf
Português
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El objetivo de esta tesis es analizar y comparar la capacidad de algunos de los modelos habituales de series temporales para representar la volatilidad de las series financieras y sus características más importantes. En concreto, una de las principales consiste en que las series suelen presentan mayor número de observaciones extremas que las esperadas bajo Gausianidad. Además, las observaciones se agrupan de tal manera que tras movimientos grandes siguen movimientos grandes, mientras que por el contrario, cuando los movimientos comienzan a ser pequeños siguen siéndolo durante cierto tiempo. Este agrupamiento de volatilidad se refleja a través de la autocorrelación de cuadrados que suele ser significativa, positiva y presenta decaimiento exponencial. Finalmente, otra característica extensamente observada y propuesta por Black (1976) es la respuesta asimétrica de la volatilidad ante rendimientos positivos o negativos y conocida como leverage effect. En concreto, el incremento en la volatilidad es mayor cuando los retornos anteriores son negativos que cuando éstos son de la misma magnitud pero positivos. La presencia de este tipo de comportamiento se detecta en las correlaciones cruzadas entre rendimientos y rendimientos futuros al cuadrado...

A note on the properties of power-transformed returns in long-memory stochastic volatility models with leverage effect

Pérez, Ana; Ruiz, Esther; Veiga, Helena
Fonte: Elsevier Publicador: Elsevier
Tipo: info:eu-repo/semantics/acceptedVersion; info:eu-repo/semantics/article Formato: application/pdf
Publicado em //2009 Português
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The autocorrelation function (acf) of powered absolute returns and their cross-correlations with original returns are derived, for any value of the power parameter, in the context of long-memory stochastic volatility models with leverage effect and Gaussian noises. These autocorrelations and cross-correlations generalize and correct recent results on the acf of squared and absolute returns.; We acknowledge financial support from the Spanish Government, project SEJ2006-03919. The research of A. Pérez was also supported by Junta de Castilla y León, projects VA092A08 and VA027A08. We are very grateful to the editor E. Kontoghiorghes and two anonymous referees for their comments

One for all : nesting asymmetric stochastic volatility models

Mao, Xiuping; Ruiz, Esther; Veiga, Helena
Fonte: Universidade Carlos III de Madrid Publicador: Universidade Carlos III de Madrid
Tipo: info:eu-repo/semantics/draft; info:eu-repo/semantics/workingPaper Formato: application/pdf; text/plain
Publicado em /05/2013 Português
Relevância na Pesquisa
46.03%
This paper proposes a new stochastic volatility model to represent the dynamic evolution of conditionally heteroscedastic time series with leverage effect. Although there are already several models proposed in the literature with the same purpose, our main justification for a further new model is that it nests some of the most popular stochastic volatility specifications usually implemented to real time series of financial returns. We derive closed-form expressions of its statistical properties and, consequently, of those of the nested specifications. Some of these properties were previously unknown in the literature although the restricted models are often fitted by empirical researchers. By comparing the properties of the restricted models, we are able to establish the advantages and limitations of each of them. Finally, we analyze the performance of a MCMC estimator of the parameters and volatilities of the new proposed model and show that, if the error distribution is known, it has appropriate finite sample properties. Furthermore, estimating the new model using the MCMC estimator, one can correctly identify the restricted true specifications. All the results are illustrated by estimating the parameters and volatilities of simulated time series and of a series of daily S&P500 returns; Financial support from the Spanish Ministry of Education and Science...

Identification of asymmetric conditional heteroscedasticity in the presence of outliers

Carnero Fernández, María Ángeles; Pérez, Ana; Ruiz, Esther
Fonte: Universidade Carlos III de Madrid Publicador: Universidade Carlos III de Madrid
Tipo: info:eu-repo/semantics/draft; info:eu-repo/semantics/workingPaper
Publicado em /07/2014 Português
Relevância na Pesquisa
46.03%
The identification of asymmetric conditional heteroscedasticity is often based on samplecross-correlations between past and squared observations. In this paper we analyse theeffects of outliers on these cross-correlations and, consequently, on the identification ofasymmetric volatilities. We show that, as expected, one isolated big outlier biases thesample cross-correlations towards zero and hence could hide true leverage effect.Unlike, the presence of two or more big consecutive outliers could lead to detectingspurious asymmetries or asymmetries of the wrong sign. We also address the problemof robust estimation of the cross-correlations by extending some popular robustestimators of pairwise correlations and autocorrelations. Their finite sample resistanceagainst outliers is compared through Monte Carlo experiments. Situations with isolatedand patchy outliers of different sizes are examined. It is shown that a modified Ramsayweightedestimator of the cross-correlations outperforms other estimators in identifyingasymmetric conditionally heteroscedastic models. Finally, the results are illustrated withan empirical application

Asymmetric Smiles, Leverage Effects and Structural Parameters.

GARCIA, René; LUGER, Richard; RENAULT, Éric
Fonte: Université de Montréal Publicador: Université de Montréal
Tipo: Artigo de Revista Científica Formato: 9569067 bytes; application/pdf
Português
Relevância na Pesquisa
46.18%
In this paper, we characterize the asymmetries of the smile through multiple leverage effects in a stochastic dynamic asset pricing framework. The dependence between price movements and future volatility is introduced through a set of latent state variables. These latent variables can capture not only the volatility risk and the interest rate risk which potentially affect option prices, but also any kind of correlation risk and jump risk. The standard financial leverage effect is produced by a cross-correlation effect between the state variables which enter into the stochastic volatility process of the stock price and the stock price process itself. However, we provide a more general framework where asymmetric implied volatility curves result from any source of instantaneous correlation between the state variables and either the return on the stock or the stochastic discount factor. In order to draw the shapes of the implied volatility curves generated by a model with latent variables, we specify an equilibrium-based stochastic discount factor with time non-separable preferences. When we calibrate this model to empirically reasonable values of the parameters, we are able to reproduce the various types of implied volatility curves inferred from option market data.; Dans cet article...

Erratum for: Smile dynamics -- a theory of the implied leverage effect

Ciliberti, Stefano; Bouchaud, Jean-Philippe; Potters, Marc
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
46.18%
We correct a mistake in the published version of our paper. Our new conclusion is that the "implied leverage effect" for single stocks is underestimated by option markets for short maturities and overestimated for long maturities, while it is always overestimated for OEX options, except for the shortest maturities where the revised theory and data match perfectly.; Comment: Erratum to "Smile dynamics -- a theory of the implied leverage effect", Wilmott Journal Volume 1, Issue 2, pages 87-94, April 2009

Gain/loss asymmetry in time series of individual stock prices and its relationship to the leverage effect

Siven, Johannes Vitalis; Lins, Jeffrey Todd
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
46.18%
Previous research has shown that for stock indices, the most likely time until a return of a particular size has been observed is longer for gains than for losses. We establish that this so-called gain/loss asymmetry is present also for individual stocks and show that the phenomenon is closely linked to the well-known leverage effect -- in the EGARCH model and a modified retarded volatility model, the same parameter that governs the magnitude of the leverage effect also governs the gain/loss asymmetry.

Principal Regression Analysis and the index leverage effect

Reigneron, Pierre-Alain; Allez, Romain; Bouchaud, Jean-Philippe
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
46.22%
We revisit the index leverage effect, that can be decomposed into a volatility effect and a correlation effect. We investigate the latter using a matrix regression analysis, that we call `Principal Regression Analysis' (PRA) and for which we provide some analytical (using Random Matrix Theory) and numerical benchmarks. We find that downward index trends increase the average correlation between stocks (as measured by the most negative eigenvalue of the conditional correlation matrix), and makes the market mode more uniform. Upward trends, on the other hand, also increase the average correlation between stocks but rotates the corresponding market mode {\it away} from uniformity. There are two time scales associated to these effects, a short one on the order of a month (20 trading days), and a longer time scale on the order of a year. We also find indications of a leverage effect for sectorial correlations as well, which reveals itself in the second and third mode of the PRA.; Comment: 10 pages, 7 figures

The leverage effect in financial markets: retarded volatility and market panic

Bouchaud, Jean-Philippe; Matacz, Andrew; Potters, Marc
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
46.07%
We investigate quantitatively the so-called leverage effect, which corresponds to a negative correlation between past returns and future volatility. For individual stocks, this correlation is moderate and decays exponentially over 50 days, while for stock indices, it is much stronger but decays faster. For individual stocks, the magnitude of this correlation has a universal value that can be rationalized in terms of a new `retarded' model which interpolates between a purely additive and a purely multiplicative stochastic process. For stock indices a specific market panic phenomenon seems to be necessary to account for the observed amplitude of the effect.; Comment: Corrected word inversion in abstract (should read: past returns and future volatility). LaTeX, 12 pp, 2 figures

Smile dynamics -- a theory of the implied leverage effect

Ciliberti, Stefano; Bouchaud, Jean-Philippe; Potters, Marc
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 19/09/2008 Português
Relevância na Pesquisa
46.32%
We study in details the skew of stock option smiles, which is induced by the so-called leverage effect on the underlying -- i.e. the correlation between past returns and future square returns. This naturally explains the anomalous dependence of the skew as a function of maturity of the option. The market cap dependence of the leverage effect is analyzed using a one-factor model. We show how this leverage correlation gives rise to a non-trivial smile dynamics, which turns out to be intermediate between the "sticky strike" and the "sticky delta" rules. Finally, we compare our result with stock option data, and find that option markets overestimate the leverage effect by a large factor, in particular for long dated options.; Comment: Submitted to Wilmott

Leverage effect in energy futures

Kristoufek, Ladislav
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 01/03/2014 Português
Relevância na Pesquisa
46.29%
We propose a comprehensive treatment of the leverage effect, i.e. the relationship between returns and volatility of a specific asset, focusing on energy commodities futures, namely Brent and WTI crude oils, natural gas and heating oil. After estimating the volatility process without assuming any specific form of its behavior, we find the volatility to be long-term dependent with the Hurst exponent on a verge of stationarity and non-stationarity. Bypassing this using by using the detrended cross-correlation and the detrending moving-average cross-correlation coefficients, we find the standard leverage effect for both crude oil. For heating oil, the effect is not statistically significant, and for natural gas, we find the inverse leverage effect. Finally, we also show that none of the effects between returns and volatility is detected as the long-term cross-correlated one. These findings can be further utilized to enhance forecasting models and mainly in the risk management and portfolio diversification.; Comment: 19 pages, 2 figures, 5 tables

Executive Compensation and Firm Leverage

Albert, Michael Joseph
Fonte: Universidade Duke Publicador: Universidade Duke
Tipo: Dissertação
Publicado em //2013 Português
Relevância na Pesquisa
36.31%

This dissertation explores the role of executive compensation in determining the capital structure decisions of a firm. CEOs experience a large personal cost of default that interacts through the risk adjusted probability of default with their compensation contract. Since default happens in a particularly costly state of the world for a CEO whose compensation contract consists primarily of pay for performance elements, i.e. a CEO who has a large personal equity stake in the firm, a large pay performance sensitivity is negatively and significantly associated with firm leverage choice. I document this effect in detail for the first time, and I show that it is both statistically robust and significant in magnitude, approximately 1\% of firm value. I show that this effect is driven by the stock holdings of the CEO, not the option holdings. I provide a simple principal agent model that explains the observed negative relationship and makes additional predictions on the relationship of other firm characteristics to pay performance sensitivity and leverage. I then test and confirm these predictions empirically using a standard OLS framework and an instrumental variable approach to control for endogeneity in the compensation contract. I also look at leverage adjustment speeds and show that CEOs with higher pay performance sensitivity adjust leverage upwards towards target values more slowly and downwards more quickly than their peers...

An analysis of leverage ratios and default probabilities

Piffer, Michele
Fonte: London School of Economics and Political Science Thesis Publicador: London School of Economics and Political Science Thesis
Tipo: Thesis; NonPeerReviewed Formato: application/pdf
Publicado em /05/2014 Português
Relevância na Pesquisa
36.29%
The thesis consists of three independent chapters. In Chapter 1 (page 7) - Counter-cyclical defaults in “costly state verification” models - I argue that a pro-cyclical risk-free rate can solve the problem of pro-cyclical defaults in “costly state verification” models. Using a partial equilibrium framework, I compute numerically the coefficient of a Taylor rule that delivers pro-cyclical output, pro-cyclical capital and counter-cyclical defaults. This parametrization is consistent with the empirical evidence on Taylor rules. In Chapter 2 (page 67) - Monetary Policy, Leverage, and Default - I use the Bernanke, Gertler and Gilchrist (1999) model to study the effect of monetary policy on the probability that firms default on loans. I argue that a monetary expansion affects defaults through two opposing partial equilibrium effects. It increases defaults because it leads firms to take on more debt and leverage up net worth, and it decreases defaults because the cost of borrowing decreases and aggregate demand shifts out, increasing firms’ profits and net worth. I argue that the leverage effect could explain the empirical partial equilibrium finding by Jimenez et al. (2008) that defaults on new loans increase after a monetary expansion. I then argue that this effect does not hold in general equilibrium due to an increase in firms’ profits. In the full model...