QUANTILE FORECASTS OF FINANCIAL RETURNS USING REALIZED GARCH MODELS*

This article applies the realized generalized autoregressive conditional heteroskedasticity (GARCH) model, which incorporates the GARCH model with realized volatility, to quantile forecasts of financial returns, such as Value‐at‐Risk and expected shortfall. Student's t‐ and skewed Student's t‐distributions as well as normal distribution are used for the return distribution. The main results for the S&P 500 stock index are: (i) the realized GARCH model with the skewed Student's t‐distribution performs better than that with the normal and Student's t‐distributions and the exponential GARCH model using the daily returns only; and (ii) using the realized kernel to take account of microstructure noise does not improve the performance.     

Modelling conditional heteroskedasticity: Application to the “IBEX-35” stock-return index

This paper compares alternative time-varying volatility models for daily stock-returns using data from Spanish equity index IBEX-35. Specifically, we estimate a parametric family of models of generalized autoregressive heteroskedasticity (which nests the most popular symmetric and asymmetric GARCH models), a semiparametric GARCH model, the generalized quadratic ARCH model, the stochastic volatility model, the Poisson Jump Diffusion model and, finally, a nonparametric model. Those models which use conditional standard deviation (specifically, TGARCH and AGARCH models) produce better fits than all other GARCH models. We also compare the within sample predictive power of all models using a standard efficiency test. Our results show that the asymmetric behaviour of responses is a statistically significant characteristic of these data. Moreover, we observe that specifications with a distribution which allows for fatter tails than a normal distribution do not necessarily outperform specifications with a normal distribution.     

TESTING THE STRUCTURE OF CONDITIONAL CORRELATIONS IN MULTIVARIATE GARCH MODELS: A GENERALIZED CROSS‐SPECTRUM APPROACH*

We introduce a class of generally applicable specification tests for constant and dynamic structures of conditional correlations in multivariate GARCH models. The tests are robust to the presence of time‐varying higher‐order conditional moments of unknown form and are pure significance tests. The tests can identify linear and nonlinear misspecifications in conditional correlations. Our approach does not necessitate a particular parameter estimation method and distributional assumption on the error process. The asymptotic distribution of the tests is invariant to the uncertainty in parameter estimation. We assess the finite sample performance of our tests using simulated and real data.     

A COMPARISON OF CONDITIONAL AND UNCONDITIONAL APPROACHES IN VALUE‐AT‐RISK ESTIMATION*

In this paper, we attempt to find the most important factor causing the differences in the performance of Value‐at‐Risk (VaR) estimation by comparing the performances of conditional and unconditional approaches. For each approach, we use various methods and models with different degrees of flexibility in their distributions including S_U‐normal distribution, which is one of the most flexible distribution functions. Our empirical results underscore the importance of the flexibility‐of‐distribution function in VaR estimation models. Even though it seems to be unclear which approach is better between conditional and unconditional approaches, it seems to be clear that the more flexible distribution we use, the better the performance, regardless of which approach we use.     

German stock market dynamics

This article estimates generalized ARCH (GARCH) models for German stock market indices returns, using weekly and monthly data, various GARCH specifications and (non)normal error densities, and a variety of diagnostic checks. German stock return series exhibit significant levels of second-order dependence. Our results clearly demonstrate that for both weekly as well as monthly return series the Student-t distribution is superior to the standard normal distribution. In particular, the estimated GARCH-t models appear to be reasonably successful in accounting for both observed leptokurtosis and conditional heteroskedasticity from German stock return movements.     

BAYESIAN ANALYSIS OF GENERALIZED AUTOREGRESSIVE CONDITIONAL HETEROSKEDASTICITY AND STOCHASTIC VOLATILITY: MODELING LEVERAGE,JUMPS AND HEAVY‐TAILS FOR FINANCIAL TIME SERIES*

This paper develops a Bayesian model comparison of two broad major classes of varying volatility model, the generalized autoregressive conditional heteroskedasticity and stochastic volatility models, on financial time series. The leverage effect, jumps and heavy‐tailed errors are incorporated into the two models. For estimation, the efficient Markov chain Monte Carlo methods are developed and the model comparisons are examined based on the marginal likelihood. The empirical analyses are illustrated using the daily return data of US stock indices, individual securities and exchange rates of UK sterling and Japanese yen against the US dollar. The estimation results indicate that the stochastic volatility model with leverage and Student‐t errors yield the best performance among the competing models.     

Asymmetry, realised volatility and stock return risk estimates

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.     

基于FIGARCH模型的中国房地产指数的实证分析

在T分布和正态分布假设下采用GARCH模型和FIGARCH模型对上证地产股指数日收益率序列进行建模分析,结果表明,上证地产股指数日收益率序列的波动具有显著的长记忆性,表明外部冲击对波动有着长期的影响。因此,采用FIGARCH模型建模的效果优于采用GARCH模型建模的效果,并且在T分布假设下拟合模型,其效果优于在正态分布假设下拟合的模型。     

Modelling the dynamics of Bitcoin and Litecoin: GARCH versus stochastic volatility models

We examine and compare a large number of generalized autoregressive conditional heteroskedastic (GARCH) and stochastic volatility (SV) models using series of Bitcoin and Litecoin price returns to assess the model fit for dynamics of these cryptocurrency price returns series. The various models examined include the standard GARCH(1,1) and SV with an AR(1) log-volatility process, as well as more flexible models with jumps, volatility in mean, leverage effects, t-distributed and moving average innovations. We report that the best model for Bitcoin is SV-t while it is GARCH-t for Litecoin. Overall, the t-class of models performs better than other classes for both cryptocurrencies. For Bitcoin, the SV models consistently outperform the GARCH models and the same holds true for Litecoin in most cases. Finally, the comparison of GARCH models with GARCH-GJR models reveals that the leverage effect is not significant for cryptocurrencies, suggesting that these do not behave like stock prices.     

Early warning signals using AVaRs of infinitely divisible GARCH models — evidence from stock index markets

Classical time series models have failed to properly assess the risks that are associated with large adverse stock price behaviour. This article contributes to autoregressive moving average model–GARCH (ARMA–GARCH) models with standard infinitely divisible innovations and assesses the performance of these models by comparing them with other time series models that have normal innovation. We discuss the limitations of value at risk (VaR) and aim to develop early warning signal models using average value at risk (AVaRs) based on the ARMA–GARCH model with standard infinitely divisible innovations. Empirical results for the daily Dow Jones Industrial Average Index, the England Financial Times Stock Exchange 100 Index and the Japan Nikkei 225 Index reveal that estimating AVaRs for the ARMA–GARCH model with standard infinitely divisible innovations offers an improvement over prevailing models for evaluating stock market risk exposure during periods of distress in financial markets and provides a suitable early warning signal in both extreme events and highly volatile markets.     

On the Effect of Skewness and Kurtosis Misspecification on the Hedging Error

Using a result in Angelini and Herzel (2009a) , we measure, in terms of variance, the cost of hedging a contingent claim when the hedging portfolio is re‐balanced at a discrete set of dates. We analyse the dependence of the variance of the hedging error on the skewness and kurtosis as modeled by a Normal Inverse Gaussian model. We consider two types of strategies, the standard Black–Scholes Delta strategy and the locally variance‐optimal strategy, and we perform some robustness tests. In particular, we investigate the effect of different types of model misspecification on the performance of the hedging, like that of hedging without taking skewness into account. Computations are performed using a Fast Fourier Transform approach.     

Measuring and Optimizing Portfolio Credit Risk: A Copula‐based Approach*

In this work, we present a methodology for measuring and optimizing the credit risk of a loan portfolio taking into account the non‐normality of the credit loss distribution. In particular, we aim at modelling accurately joint default events for credit assets. In order to achieve this goal, we build the loss distribution of the loan portfolio by Monte Carlo simulation. The times until default of each obligor in portfolio are simulated following a copula‐based approach. In particular, we study four different types of dependence structure for the credit assets in portfolio: the Gaussian copula, the Student's t‐copula, the grouped t‐copula and the Clayton n‐copula (or Cook–Johnson copula). Our aim is to assess the impact of each type of copula on the value of different portfolio risk measures, such as expected loss, maximum loss, credit value at risk and expected shortfall. In addition, we want to verify whether and how the optimal portfolio composition may change utilizing various types of copula for describing the default dependence structure. In order to optimize portfolio credit risk, we minimize the conditional value at risk, a risk measure both relevant and tractable, by solving a simple linear programming problem subject to the traditional constraints of balance, portfolio expected return and trading. The outcomes, in terms of optimal portfolio compositions, obtained assuming different default dependence structures are compared with each other. The solution of the risk minimization problem may suggest us how to restructure the inefficient loan portfolios in order to obtain their best risk/return profile. In the absence of a developed secondary market for loans, we may follow the investment strategies indicated by the solution vector by utilizing credit default swaps.     

GARCH inadequacy for modelling exchange rates: empirical evidence from Latin America

This article checks for the adequacy of using GARCH models in exchange rate series. Using the Hinich portmanteau bicorrelation test, we find that a GARCH formulation or any of its variants fails to capture the data generating process of the main Latin American exchange rates. Our results highlight the potential of having misleading public policy when estimates are based in GARCH types of models. This article also complements recent similar findings encountered in European and Asian economies.     

Bayesian model comparison by Markov chain simulation: Illustration using stock market data

The paper illustrates the computation of marginal likelihoods and Bayes factors when Markov Chain Monte Carlo has been used to produce draws from a model’s posterior distribution. The method is based on Raftery (1996) and does not require that Gibbs sampling is used or conditional posterior distributions are available in closed form. Models used include a normal finite mixture, a GARCH and a Student t -model as alternative models for the Standard and Poor’s stock returns.     

Mapping the stocks in MICEX: Who is central in the Moscow Stock Exchange?

In this article, we use partial correlations to derive bi‐directional connections between major firms listed in the Moscow Stock Exchange. We obtain coefficients of partial correlation from the correlation estimates of the Constant Conditional Correlation GARCH (CCC‐GARCH) and the consistent Dynamic Conditional Correlation GARCH (cDCC‐GARCH) models. We map the graph of partial correlations using the Gaussian Graphical Model and apply network analysis to identify the most central firms in terms of both shock propagation and connectedness with others. Moreover we analyze some network characteristics over time and based on these we construct a measure of system vulnerability to external shocks. Our findings suggest that during the crisis interconnectedness between firms strengthens and becomes polarized and the system becomes more vulnerable to systemic shocks. In addition, we found that the most connected firms are the state‐owned firms Sberbank and Gazprom and the private oil company Lukoil, while in terms of the top most central systemic risk contributors, Sberbank gave its place to the NLMK Group.     

Modified Quasi‐Likelihood Ratio Test for Regime Switching

In this paper we propose a modified quasi‐likelihood ratio test of the null hypothesis of one regime against the alternative of two regimes in Markov regime‐switching models. The asymptotic distribution of the proposed test statistic is a simple function of Gaussian random variables, and the inference is no more complicated than in the standard case. Our simulations show that the proposed test has good finite sample size and power that are comparable to the quasi‐likelihood ratio test of Cho and White. We apply our test to stock returns and Japanese policy functions.     

House price dynamics,conditional higher-order moments,and density forecasts

Most studies on housing price dynamics are only concerned with the conditional mean and variance, but overlook other higher-order conditional moments and the structural change characteristics inherent in housing prices. In order to take into account these two important issues, this study utilizes the generalized Markov switching GARCH model to explore house price dynamics and conditional distribution for US market over 1975Q1–2007Q4. The housing return follows two distinct dynamics: the bust regime and the boom regime. The volatility pattern is different in the bust and boom regimes. In addition, the conditional densities derived by the regime-switching model change dramatically over time and are significantly different from normal distribution. More importantly, the regime-switching model can detect in advance a weak US housing market such as the one that occurred in the middle of 2007. The in-sample fitting ability of regime-switching model, which incorporates higher-order moments, has significant improvements compared to the single-regime AR and AR-GARCH models. For the out-of-sample Value-at-Risk forecasting performance, the ability of regime-switching AR-GARCH model to forecast one-step-ahead density is better compared to the single-regime AR-GARCH model.     

Tail dependence analysis of stock markets using extreme value theory

Financial risk modelling frequently uses the assumption of a normal distribution when considering the return series which is inefficient if the data is not normally distributed or if it exhibits extreme tails. Estimation of tail dependence between financial assets plays a vital role in various aspects of financial risk modelling including portfolio theory and hedging amongst applications. Extreme Value Theory (EVT) provides well established methods for considering univariate and multivariate tail distributions which are useful for forecasting financial risk or modelling the tail dependence of risky assets. The empirical analysis in this article uses nonparametric measures based on bivariate EVT to investigate asymptotic dependence and estimate the degree of tail dependence of the ASX-All Ordinaries daily returns with four other international markets, viz., the S&P-500, Nikkei-225, DAX-30 and Heng-Seng for both extreme right and left tails of the return distribution. It is investigated whether the asymptotic dependence between these markets is related to the heteroscedasticity present in the logarithmic return series using GARCH filters. The empirical evidence shows that the asymptotic extreme tail dependence between stock markets does not necessarily exist and rather can be associated with the heteroscedasticity present in the financial time series of the various stock markets.     

Optimal gasoline hedging strategies using futures contracts and exchange-traded funds

This article employs a variety of econometric models (including OLS, VEC/VAR, DCC GARCH and a class of copula-based GARCH models) to estimate optimal hedge ratios for gasoline spot prices using gasoline exchange-traded funds (ETFs) and gasoline futures contracts. We then compare their performance using four different measures from the perspective of both their hedging objectives and trading position using four different measures: variance reduction measure, utility-based measure and two tail-based measures (value at risk and expected shortfall). The impact of the 2008 financial market crisis on hedging performance is also investigated. Our findings indicate that, in terms of variance reduction, the static models (OLS and VEC/VAR) are found to be the best hedging strategies. However, more sophisticated time-varying hedging strategies could outperform the static hedging models when the other measures are used. In addition, ETF hedging is a more effective hedging strategy than futures hedging during the high-volatility (crisis) period, but this is not always the case during the normal time (post-crisis) period.     

Normality test for multivariate conditional heteroskedastic dynamic regression models

In this paper, we study the Jarque-Bera test for the normality of the innovations of multivariate GARCH models. It is shown that the test is distribution free and its limiting null distribution is a chi-square distribution.