This paper evaluates the application of two well-known asymmetric stochastic volatility (ASV) mod... more This paper evaluates the application of two well-known asymmetric stochastic volatility (ASV) models to option price forecasting and dynamic delta hedging. They are specified in discrete time in contrast to the classical stochastic volatility (SV) models used in option pricing. There is some related literature, but little is known about the empirical implications of volatility asymmetry on option pricing. The objectives of this paper are to estimate ASV option pricing models using a Bayesian approach unknown in this type of literature, and to investigate the effect of volatility asymmetry on option pricing for different size equity sectors and periods of volatility. Using the S&P MidCap 400 and S&P 500 European call option quotes, results show that volatility asymmetry benefits the accuracy of option price forecasting and hedging cost effectiveness in the large-cap equity sector. However, asymmetric SV models do not improve the option price forecasting and dynamic hedging in the mid-cap equity sector.
We analyze the stock market return predictability for three different periods. We evaluate the co... more We analyze the stock market return predictability for three different periods. We evaluate the conditional variance (CV) and the variance risk premium (VRP) as predictors of stock market returns for which we are using well-established versions of the heterogeneous auto-regressive (HAR) model and propose two new semi-parametric extensions. Results show that the CV and VRP are predictors of future stock market returns in the period before the global financial crisis (GFC). However, these variables lose predictive power after the Dodd-Frank Act (DFA) and change sign, indicating that investors are willing to pay a risk premium for "good uncertainty".
This paper evaluates the application of two well-known asymmetric stochastic volatility (ASV) mod... more This paper evaluates the application of two well-known asymmetric stochastic volatility (ASV) models to option price forecasting and dynamic delta hedging. They are specified in discrete time in contrast to the classical stochastic volatility (SV) models used in option pricing. There is some related literature, but little is known about the empirical implications of volatility asymmetry on option pricing. The objectives of this paper are to estimate ASV option pricing models using a Bayesian approach unknown in this type of literature, and to investigate the effect of volatility asymmetry on option pricing for different size equity sectors and periods of volatility. Using the S&P MidCap 400 and S&P 500 European call option quotes, results show that volatility asymmetry benefits the accuracy of option price forecasting and hedging cost effectiveness in the large-cap equity sector. However, asymmetric SV models do not improve the option price forecasting and dynamic hedging in the mid-cap equity sector.
The statistical properties of a general family of asymmetric stochastic volatility (A-SV) models ... more The statistical properties of a general family of asymmetric stochastic volatility (A-SV) models which capture the leverage effect in financial returns are derived providing analytical expressions of moments and autocorrelations of power-transformed absolute returns. The parameters of the A-SV model are estimated by a particle filter-based simulated maximum likelihood estimator and Monte Carlo simulations are carried out to validate it. It is shown empirically that standard SV models may significantly underestimate the valueat-risk of weekly S&P 500 returns at dates following negative returns and overestimate it after positive returns. By contrast, the general specification proposed provide reliable forecasts at all dates. Furthermore, based on daily S&P 500 returns, it is shown that the most adequate specification of the asymmetry can change over time.
We analyze the stock market return predictability for three different periods. We evaluate the co... more We analyze the stock market return predictability for three different periods. We evaluate the conditional variance (CV) and the variance risk premium (VRP) as predictors of stock market returns for which we are using well-established versions of the heterogeneous auto-regressive (HAR) model and propose two new semi-parametric extensions. Results show that the CV and VRP are predictors of future stock market returns in the period before the global financial crisis (GFC). However, these variables lose predictive power after the Dodd-Frank Act (DFA) and change sign, indicating that investors are willing to pay a risk premium for "good uncertainty".
We analyze the ability of Threshold Stochastic Volatility (TSV) models to represent and forecast ... more We analyze the ability of Threshold Stochastic Volatility (TSV) models to represent and forecast asymmetric volatilities. First, we derive the statistical properties of TSV models. Second, we demonstrate the good finite sample properties of a MCMC estimator, implemented in the software package WinBUGS, when estimating the parameters of a general specification, denoted CTSV, that nests the TSV and asymmetric autoregressive stochastic volatility (A-ARSV) models. The MCMC estimator also discriminates between the two specifications and allows us to obtain volatility forecasts. Third, we analyze daily S&P 500 and FTSE 100 returns and show that the estimated CTSV model implies plug-in moments that are slightly closer to the observed sample moments than those implied by other nested specifications. Furthermore, different asymmetric specifications generate rather different European options prices. Finally, although none of the models clearly emerge as best outof-sample, it seems that including both threshold variables and correlated errors may be a good compromise.
It is well known that outliers can affect both the estimation of parameters and volatilities when... more It is well known that outliers can affect both the estimation of parameters and volatilities when fitting a univariate GARCH-type model. Similar biases and impacts are expected to be found on correlation dynamics in the context of multivariate time series. We study the impact of outliers on the estimation of correlations when fitting multivariate GARCH models and propose a general detection algorithm based on wavelets, that can be applied to a large class of multivariate volatility models. Its effectiveness is evaluated through a Monte Carlo study before it is applied to real data. The method is both effective and reliable, since it detects very few false outliers.
In this paper we estimate, for several investment horizons, minimum capital risk requirements for... more In this paper we estimate, for several investment horizons, minimum capital risk requirements for short and long positions, using the unconditional distribution of three daily indexes futures returns and a set of GARCH-type and stochastic volatility models. We consider the possibility that errors follow a t-Student distribution in order to capture the kurtosis of the returns distributions. The results suggest that an accurate modeling of extreme returns obtained for long and short trading investment positions is possible with a simple autoregressive stochastic volatility model. Moreover, modeling volatility as a fractional integrated process produces, in general, excessive volatility persistence and consequently leads to large minimum capital risk requirement estimates. The performance of models is assessed with the help of out-of-sample tests and p-values of them are reported.
The paper proposes the use of data cloning (DC) to the estimation of general asymmetric stochasti... more The paper proposes the use of data cloning (DC) to the estimation of general asymmetric stochastic volatility (ASV) models with flexible distributions for the standardized returns. These models are able to capture the asymmetric volatility, the leptokurtosis and the skewness of the distribution of returns. Data cloning is a general technique to compute maximum likelihood estimators, along with their asymptotic variances, by means of a Markov chain Monte Carlo (MCMC) methodology. The main aim of this paper is to illustrate how easily general ASV models can be estimated and consequently studied via data cloning. Changes of specifications, priors and sampling error distributions are done with minor modifications of the code. Using an intensive simulation study, the finite sample properties of the estimators of the parameters are evaluated and compared to those of a benchmark estimator that is also user-friendly. The results show that the proposed estimator is computationally efficient and robust, and can be an effective alternative to the exiting estimation methods applied to ASV models. Finally, we use data cloning to estimate the parameters of general ASV models and forecast the one-step-ahead volatility of S&P 500 and FTSE-100 daily returns.
This paper models and forecasts the crude oil ETF volatility index (OVX). The motivation lies on ... more This paper models and forecasts the crude oil ETF volatility index (OVX). The motivation lies on the evidence that the OVX has been used in the last years as an important alternative measure to track and analyze the volatility of future oil prices. The analysis of the OVX suggests that it presents similar features to those of the daily market volatility index. The main characteristic is the long range dependence that is modeled either by autoregressive fractional integrated moving averaging (ARFIMA) models or by heterogeneous autoregressive (HAR) specifications. Regarding the latter family of models, we first propose extensions of the HAR model that are based on the net and scale measures of oil prices changes. The aim is to improve the HAR model by including predictors that better capture the impact of oil price changes on the economy. Second, we test the forecasting performance of the new proposals and benchmarks with the model confidence set (MCS) and the Generalized-AutoContouR (G-ACR) tests in terms of point forecasts and density forecasting, respectively. Our main findings are as follows: the new asymmetric proposals have superior predictive ability than the heterogeneous autoregressive leverage (HARL) model under two known loss functions. Regarding density forecasting, the best model is the one that includes the scale measure as a proxy of oil price changes and considers a flexible distribution for the errors.
In a global economy shocks occurring in one market can spillover to other markets. This paper inv... more In a global economy shocks occurring in one market can spillover to other markets. This paper investigates the impact of oil shocks and stock markets crashes on correlations between stock and oil markets. We test changes in correlations with non-overlapping confidence intervals based on estimated wavelets correlations that account for the correlations at different scales. This allows us to distinguish contagion from co-movements. Our method, contrary to others existing in the literature does not need adjustment for heteroskedasticity biases on the correlation coefficients. Our results show that oil shocks spread to stock markets affecting the correlation between both markets. During the shock, correlations between oil and stock markets become negative, while in non-shock periods, correlations are around zero or slightly positive. The test confirms that most of the correlations between oil and stock markets are statistically different from those in the shock period. The evidence on the change of correlation between stock markets after an oil shock is weaker, the co-movements are stronger but the test does not reject the equality of correlations, except in some specific cases during the Kuwait war and the OPEC cutback period. Conversely, we only find weak evidence that stock market crashes change the correlation between oil and stock markets. Overall, the evidence shows a decrease on correlations between stock and oil markets in oil shock periods, giving support to include oil as an asset class in asset allocation strategies.
In this paper we propose a new class of asymmetric stochastic volatility (SV) models, which speci... more In this paper we propose a new class of asymmetric stochastic volatility (SV) models, which specifies the volatility as a function of the score of the distribution of returns conditional on volatilities based on the Generalized Autoregressive Score (GAS) model. Different specifications of the log-volatility are obtained by assuming different return error distributions. In particular, we consider three of the most popular distributions, namely, the Normal, Student-t and Generalized Error Distribution and derive the statistical properties of each of the corresponding score driven SV models. We show that some of the parameters cannot be property identified by the moments usually considered as to describe the stylized facts of financial returns, namely, excess kurtosis, autocorrelations of squares and cross-correlations between returns and future squared returns. The parameters of some restricted score driven SV models can be estimated adequately using a MCMC procedure. Finally, the new proposed models are fitted to financial returns and evaluated in terms of their in-sample and out-of-sample performance.
This paper proposes a new stochastic volatility model to represent the dynamic evolution of condi... more 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
The statistical properties of a general family of asymmetric stochastic volatility (A-SV) models ... more The statistical properties of a general family of asymmetric stochastic volatility (A-SV) models which capture the leverage effect in financial returns are derived providing analytical expressions of moments and autocorrelations of power-transformed absolute returns. The parameters of the A-SV model are estimated by a particle filter-based simulated maximum likelihood estimator and Monte Carlo simulations are carried out to validate it. It is shown empirically that standard SV models may significantly underestimate the valueat-risk of weekly S&P 500 returns at dates following negative returns and overestimate it after positive returns. By contrast, the general specification proposed provide reliable forecasts at all dates. Furthermore, based on daily S&P 500 returns, it is shown that the most adequate specification of the asymmetry can change over time.
In this paper we estimate minimum capital risk requirements for short and long positions with thr... more In this paper we estimate minimum capital risk requirements for short and long positions with three investment horizons, using the traditional GARCH model and two other GARCH-type models that incorporate the possibility of asymmetric responses of volatility to price changes. We also address the problem of the extremely high estimated persistence of the GARCH model to generate observed volatility patterns by including realised volatility as an explanatory variable into the model's variance equation. The results suggest that the inclusion of realised volatility improves the GARCH forecastability as well as its ability to calculate accurate minimum capital risk requirements and makes it quite competitive when compared with asymmetric conditional heteroscedastic models such as the GJR and the EGARCH.
In this paper we focus on the impact of additive outliers (level and volatility) on the calculati... more In this paper we focus on the impact of additive outliers (level and volatility) on the calculation of risk measures, such as minimum capital risk requirements. Through simulation and empirical studies, we compare six alternative proposals that are used in the literature to reduce the effects of outliers in the estimation of risk measures when using GARCH type models. The methods are based on [1] correcting for significant outliers, [2] accommodating outliers using complex (e.g. fat tail) distributions and [3] accounting for outlier effects by robust estimation. The main conclusions of the simulation study are that the presence of outliers bias these risk measures, being the proposal by Grané and Veiga (2010) that providing the highest bias reduction. From the out of sample results for four international stock market indexes we found weak evidence that more complex models (specification and error distribution) perform better in estimating the minimum capital risk requirements during the last global financial crisis.
Computational Statistics & Data Analysis, 2010
Outliers in financial data can lead to model parameter estimation biases, invalid inferences and ... more Outliers in financial data can lead to model parameter estimation biases, invalid inferences and poor volatility forecasts. Therefore, their detection and correction should be taken seriously when modeling financial data. The present paper focuses on these issues and ...
According to the Taylor-Effect the autocorrelations of absolute financial returns are higher than... more According to the Taylor-Effect the autocorrelations of absolute financial returns are higher than the ones of squared returns. In this work, we analyze this empirical property for three different asymmetric stochastic volatility models, with short and/or long memory. Specially, we ...
Outliers in financial data can lead to model parameter estimation biases, invalid inferences and ... more Outliers in financial data can lead to model parameter estimation biases, invalid inferences and poor volatility forecasts. Therefore, their detection and correction should be taken seriously when modeling financial data. This paper focuses on these issues and proposes ...
In this paper we estimate, for several investment horizons, minimum capital risk requirements for... more In this paper we estimate, for several investment horizons, minimum capital risk requirements for short and long positions, using the unconditional distribution of three daily indexes futures returns and a set of GARCH-type and stochastic volatility models. We consider the ...
This paper evaluates the application of two well-known asymmetric stochastic volatility (ASV) mod... more This paper evaluates the application of two well-known asymmetric stochastic volatility (ASV) models to option price forecasting and dynamic delta hedging. They are specified in discrete time in contrast to the classical stochastic volatility (SV) models used in option pricing. There is some related literature, but little is known about the empirical implications of volatility asymmetry on option pricing. The objectives of this paper are to estimate ASV option pricing models using a Bayesian approach unknown in this type of literature, and to investigate the effect of volatility asymmetry on option pricing for different size equity sectors and periods of volatility. Using the S&P MidCap 400 and S&P 500 European call option quotes, results show that volatility asymmetry benefits the accuracy of option price forecasting and hedging cost effectiveness in the large-cap equity sector. However, asymmetric SV models do not improve the option price forecasting and dynamic hedging in the mid-cap equity sector.
We analyze the stock market return predictability for three different periods. We evaluate the co... more We analyze the stock market return predictability for three different periods. We evaluate the conditional variance (CV) and the variance risk premium (VRP) as predictors of stock market returns for which we are using well-established versions of the heterogeneous auto-regressive (HAR) model and propose two new semi-parametric extensions. Results show that the CV and VRP are predictors of future stock market returns in the period before the global financial crisis (GFC). However, these variables lose predictive power after the Dodd-Frank Act (DFA) and change sign, indicating that investors are willing to pay a risk premium for "good uncertainty".
This paper evaluates the application of two well-known asymmetric stochastic volatility (ASV) mod... more This paper evaluates the application of two well-known asymmetric stochastic volatility (ASV) models to option price forecasting and dynamic delta hedging. They are specified in discrete time in contrast to the classical stochastic volatility (SV) models used in option pricing. There is some related literature, but little is known about the empirical implications of volatility asymmetry on option pricing. The objectives of this paper are to estimate ASV option pricing models using a Bayesian approach unknown in this type of literature, and to investigate the effect of volatility asymmetry on option pricing for different size equity sectors and periods of volatility. Using the S&P MidCap 400 and S&P 500 European call option quotes, results show that volatility asymmetry benefits the accuracy of option price forecasting and hedging cost effectiveness in the large-cap equity sector. However, asymmetric SV models do not improve the option price forecasting and dynamic hedging in the mid-cap equity sector.
The statistical properties of a general family of asymmetric stochastic volatility (A-SV) models ... more The statistical properties of a general family of asymmetric stochastic volatility (A-SV) models which capture the leverage effect in financial returns are derived providing analytical expressions of moments and autocorrelations of power-transformed absolute returns. The parameters of the A-SV model are estimated by a particle filter-based simulated maximum likelihood estimator and Monte Carlo simulations are carried out to validate it. It is shown empirically that standard SV models may significantly underestimate the valueat-risk of weekly S&P 500 returns at dates following negative returns and overestimate it after positive returns. By contrast, the general specification proposed provide reliable forecasts at all dates. Furthermore, based on daily S&P 500 returns, it is shown that the most adequate specification of the asymmetry can change over time.
We analyze the stock market return predictability for three different periods. We evaluate the co... more We analyze the stock market return predictability for three different periods. We evaluate the conditional variance (CV) and the variance risk premium (VRP) as predictors of stock market returns for which we are using well-established versions of the heterogeneous auto-regressive (HAR) model and propose two new semi-parametric extensions. Results show that the CV and VRP are predictors of future stock market returns in the period before the global financial crisis (GFC). However, these variables lose predictive power after the Dodd-Frank Act (DFA) and change sign, indicating that investors are willing to pay a risk premium for "good uncertainty".
We analyze the ability of Threshold Stochastic Volatility (TSV) models to represent and forecast ... more We analyze the ability of Threshold Stochastic Volatility (TSV) models to represent and forecast asymmetric volatilities. First, we derive the statistical properties of TSV models. Second, we demonstrate the good finite sample properties of a MCMC estimator, implemented in the software package WinBUGS, when estimating the parameters of a general specification, denoted CTSV, that nests the TSV and asymmetric autoregressive stochastic volatility (A-ARSV) models. The MCMC estimator also discriminates between the two specifications and allows us to obtain volatility forecasts. Third, we analyze daily S&P 500 and FTSE 100 returns and show that the estimated CTSV model implies plug-in moments that are slightly closer to the observed sample moments than those implied by other nested specifications. Furthermore, different asymmetric specifications generate rather different European options prices. Finally, although none of the models clearly emerge as best outof-sample, it seems that including both threshold variables and correlated errors may be a good compromise.
It is well known that outliers can affect both the estimation of parameters and volatilities when... more It is well known that outliers can affect both the estimation of parameters and volatilities when fitting a univariate GARCH-type model. Similar biases and impacts are expected to be found on correlation dynamics in the context of multivariate time series. We study the impact of outliers on the estimation of correlations when fitting multivariate GARCH models and propose a general detection algorithm based on wavelets, that can be applied to a large class of multivariate volatility models. Its effectiveness is evaluated through a Monte Carlo study before it is applied to real data. The method is both effective and reliable, since it detects very few false outliers.
In this paper we estimate, for several investment horizons, minimum capital risk requirements for... more In this paper we estimate, for several investment horizons, minimum capital risk requirements for short and long positions, using the unconditional distribution of three daily indexes futures returns and a set of GARCH-type and stochastic volatility models. We consider the possibility that errors follow a t-Student distribution in order to capture the kurtosis of the returns distributions. The results suggest that an accurate modeling of extreme returns obtained for long and short trading investment positions is possible with a simple autoregressive stochastic volatility model. Moreover, modeling volatility as a fractional integrated process produces, in general, excessive volatility persistence and consequently leads to large minimum capital risk requirement estimates. The performance of models is assessed with the help of out-of-sample tests and p-values of them are reported.
The paper proposes the use of data cloning (DC) to the estimation of general asymmetric stochasti... more The paper proposes the use of data cloning (DC) to the estimation of general asymmetric stochastic volatility (ASV) models with flexible distributions for the standardized returns. These models are able to capture the asymmetric volatility, the leptokurtosis and the skewness of the distribution of returns. Data cloning is a general technique to compute maximum likelihood estimators, along with their asymptotic variances, by means of a Markov chain Monte Carlo (MCMC) methodology. The main aim of this paper is to illustrate how easily general ASV models can be estimated and consequently studied via data cloning. Changes of specifications, priors and sampling error distributions are done with minor modifications of the code. Using an intensive simulation study, the finite sample properties of the estimators of the parameters are evaluated and compared to those of a benchmark estimator that is also user-friendly. The results show that the proposed estimator is computationally efficient and robust, and can be an effective alternative to the exiting estimation methods applied to ASV models. Finally, we use data cloning to estimate the parameters of general ASV models and forecast the one-step-ahead volatility of S&P 500 and FTSE-100 daily returns.
This paper models and forecasts the crude oil ETF volatility index (OVX). The motivation lies on ... more This paper models and forecasts the crude oil ETF volatility index (OVX). The motivation lies on the evidence that the OVX has been used in the last years as an important alternative measure to track and analyze the volatility of future oil prices. The analysis of the OVX suggests that it presents similar features to those of the daily market volatility index. The main characteristic is the long range dependence that is modeled either by autoregressive fractional integrated moving averaging (ARFIMA) models or by heterogeneous autoregressive (HAR) specifications. Regarding the latter family of models, we first propose extensions of the HAR model that are based on the net and scale measures of oil prices changes. The aim is to improve the HAR model by including predictors that better capture the impact of oil price changes on the economy. Second, we test the forecasting performance of the new proposals and benchmarks with the model confidence set (MCS) and the Generalized-AutoContouR (G-ACR) tests in terms of point forecasts and density forecasting, respectively. Our main findings are as follows: the new asymmetric proposals have superior predictive ability than the heterogeneous autoregressive leverage (HARL) model under two known loss functions. Regarding density forecasting, the best model is the one that includes the scale measure as a proxy of oil price changes and considers a flexible distribution for the errors.
In a global economy shocks occurring in one market can spillover to other markets. This paper inv... more In a global economy shocks occurring in one market can spillover to other markets. This paper investigates the impact of oil shocks and stock markets crashes on correlations between stock and oil markets. We test changes in correlations with non-overlapping confidence intervals based on estimated wavelets correlations that account for the correlations at different scales. This allows us to distinguish contagion from co-movements. Our method, contrary to others existing in the literature does not need adjustment for heteroskedasticity biases on the correlation coefficients. Our results show that oil shocks spread to stock markets affecting the correlation between both markets. During the shock, correlations between oil and stock markets become negative, while in non-shock periods, correlations are around zero or slightly positive. The test confirms that most of the correlations between oil and stock markets are statistically different from those in the shock period. The evidence on the change of correlation between stock markets after an oil shock is weaker, the co-movements are stronger but the test does not reject the equality of correlations, except in some specific cases during the Kuwait war and the OPEC cutback period. Conversely, we only find weak evidence that stock market crashes change the correlation between oil and stock markets. Overall, the evidence shows a decrease on correlations between stock and oil markets in oil shock periods, giving support to include oil as an asset class in asset allocation strategies.
In this paper we propose a new class of asymmetric stochastic volatility (SV) models, which speci... more In this paper we propose a new class of asymmetric stochastic volatility (SV) models, which specifies the volatility as a function of the score of the distribution of returns conditional on volatilities based on the Generalized Autoregressive Score (GAS) model. Different specifications of the log-volatility are obtained by assuming different return error distributions. In particular, we consider three of the most popular distributions, namely, the Normal, Student-t and Generalized Error Distribution and derive the statistical properties of each of the corresponding score driven SV models. We show that some of the parameters cannot be property identified by the moments usually considered as to describe the stylized facts of financial returns, namely, excess kurtosis, autocorrelations of squares and cross-correlations between returns and future squared returns. The parameters of some restricted score driven SV models can be estimated adequately using a MCMC procedure. Finally, the new proposed models are fitted to financial returns and evaluated in terms of their in-sample and out-of-sample performance.
This paper proposes a new stochastic volatility model to represent the dynamic evolution of condi... more 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
The statistical properties of a general family of asymmetric stochastic volatility (A-SV) models ... more The statistical properties of a general family of asymmetric stochastic volatility (A-SV) models which capture the leverage effect in financial returns are derived providing analytical expressions of moments and autocorrelations of power-transformed absolute returns. The parameters of the A-SV model are estimated by a particle filter-based simulated maximum likelihood estimator and Monte Carlo simulations are carried out to validate it. It is shown empirically that standard SV models may significantly underestimate the valueat-risk of weekly S&P 500 returns at dates following negative returns and overestimate it after positive returns. By contrast, the general specification proposed provide reliable forecasts at all dates. Furthermore, based on daily S&P 500 returns, it is shown that the most adequate specification of the asymmetry can change over time.
In this paper we estimate minimum capital risk requirements for short and long positions with thr... more In this paper we estimate minimum capital risk requirements for short and long positions with three investment horizons, using the traditional GARCH model and two other GARCH-type models that incorporate the possibility of asymmetric responses of volatility to price changes. We also address the problem of the extremely high estimated persistence of the GARCH model to generate observed volatility patterns by including realised volatility as an explanatory variable into the model's variance equation. The results suggest that the inclusion of realised volatility improves the GARCH forecastability as well as its ability to calculate accurate minimum capital risk requirements and makes it quite competitive when compared with asymmetric conditional heteroscedastic models such as the GJR and the EGARCH.
In this paper we focus on the impact of additive outliers (level and volatility) on the calculati... more In this paper we focus on the impact of additive outliers (level and volatility) on the calculation of risk measures, such as minimum capital risk requirements. Through simulation and empirical studies, we compare six alternative proposals that are used in the literature to reduce the effects of outliers in the estimation of risk measures when using GARCH type models. The methods are based on [1] correcting for significant outliers, [2] accommodating outliers using complex (e.g. fat tail) distributions and [3] accounting for outlier effects by robust estimation. The main conclusions of the simulation study are that the presence of outliers bias these risk measures, being the proposal by Grané and Veiga (2010) that providing the highest bias reduction. From the out of sample results for four international stock market indexes we found weak evidence that more complex models (specification and error distribution) perform better in estimating the minimum capital risk requirements during the last global financial crisis.
Computational Statistics & Data Analysis, 2010
Outliers in financial data can lead to model parameter estimation biases, invalid inferences and ... more Outliers in financial data can lead to model parameter estimation biases, invalid inferences and poor volatility forecasts. Therefore, their detection and correction should be taken seriously when modeling financial data. The present paper focuses on these issues and ...
According to the Taylor-Effect the autocorrelations of absolute financial returns are higher than... more According to the Taylor-Effect the autocorrelations of absolute financial returns are higher than the ones of squared returns. In this work, we analyze this empirical property for three different asymmetric stochastic volatility models, with short and/or long memory. Specially, we ...
Outliers in financial data can lead to model parameter estimation biases, invalid inferences and ... more Outliers in financial data can lead to model parameter estimation biases, invalid inferences and poor volatility forecasts. Therefore, their detection and correction should be taken seriously when modeling financial data. This paper focuses on these issues and proposes ...
In this paper we estimate, for several investment horizons, minimum capital risk requirements for... more In this paper we estimate, for several investment horizons, minimum capital risk requirements for short and long positions, using the unconditional distribution of three daily indexes futures returns and a set of GARCH-type and stochastic volatility models. We consider the ...
In this paper we estimate, for several investment horizons, minimum capital risk requirements for... more In this paper we estimate, for several investment horizons, minimum capital risk requirements for short and long positions, using the unconditional distribution of three daily indexes futures returns and a set of GARCH-type and stochastic volatility models. We consider the possibility that errors follow a t-Student distribution in order to capture the kurtosis of the returns distributions. The results suggest
In this paper, we estimate minimum capital risk requirements for short, long positions and three ... more In this paper, we estimate minimum capital risk requirements for short, long positions and three investment horizons, using the traditional GARCH model and two other GARCH-type models that incorporate the possibility of asymmetric responses of volatility to price changes; and, ...
Outliers in financial data can lead to model parameter estimation biases, invalid inferences and ... more Outliers in financial data can lead to model parameter estimation biases, invalid inferences and poor volatility forecasts. Therefore, their detection and correction should be taken seriously when modeling financial data. This paper focuses on these issues and proposes a general detection and correction method based on wavelets that can be applied to a large class of volatility models. The effectiveness
In this paper we focus on the impact of additive level outliers on the calculation of risk measur... more In this paper we focus on the impact of additive level outliers on the calculation of risk measures, such as minimum capital risk requirements, and compare four alternatives of reducing these measures' estimation biases. The first three proposals proceed by detecting and correcting outliers before estimating these risk measures with the GARCH(1,1) model, while the fourth procedure fits a Student’s
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Papers by Helena Veiga