Switching ARCH Research Articles

Risk of investing in volatility products: A regime-switching approach

ABSTRACT Volatility indexes provide a tool for investors to speculate and trade on market sentiment regarding future volatility. The risk of trading on volatility indexes can be measured by their second moments, namely, variance and correlation. This study considers the four representative volatility indexes published by the CBOE: stock market volatility index (VIX), crude oil volatility index (OVX), foreign exchange rate volatility index (EVZ), and gold price volatility index (GVZ). To examine their risk, we develop an extended multivariate Markov switching ARCH (MSARCH) model in which regime-switching variances, correlations, and variance-correlation relations are designed. Our empirical sample consists of the four volatility indexes from June 2008 to April 2020 for 612 weekly observations (Wednesday to Wednesday). For the conditional variances, we find evidence of regime-switching processes (switching between low and high volatility regimes) for the individual volatility index returns, with the exception of the GVZ. The estimated probability of the high volatility regime may be used to track economic distress and uncertainty shocks. These results provide evidence for volatility-of-volatility risk. For the conditional correlations, we find a regime-switching relation between variances and correlations. That is, the highest correlation appears when the paired volatility markets are simultaneously experiencing a state of high volatility. By contrast, when the paired volatility markets are encountering different volatility states, the correlation is weaker. These results indicate that the volatility-of-volatility risk is a factor affecting the dynamics of correlations between volatility indexes.

An integrated early warning system for stock market turbulence

This study constructs an integrated early warning system (EWS) that identifies and predicts stock market turbulence. Based on switching ARCH (SWARCH) filtering probabilities of the high volatility regime, the proposed EWS first classifies stock market crises according to an indicator function with thresholds dynamically selected by the two-peak method. An hybrid algorithm is then developed in the framework of a long short-term memory (LSTM) network to make daily predictions that alert turmoils. In the empirical evaluation based on ten-year Chinese stock data, the proposed EWS yields satisfying results with test-set accuracy of 96.4% and an average of 2.8 days forewarned period. The model’s stability and practical value in the real-time decision-making are also proven by the cross-validation, back-testing and reality check.

Asymptotic properties of the maximum likelihood estimator in regime switching econometric models

Markov regime switching models have been widely used in numerous empirical applications in economics and finance. However, the asymptotic distribution of the maximum likelihood estimator (MLE) has not been proven for some empirically popular Markov regime switching models. In particular, the asymptotic distribution of the MLE has been unknown for models in which some elements of the transition probability matrix have the value of zero, as is commonly assumed in empirical applications with models with more than two regimes. This also includes models in which the regime-specific density depends on both the current and the lagged regimes such as the seminal model of Hamilton (1989) and switching ARCH model of Hamilton and Susmel (1994). This paper shows the asymptotic normality of the MLE and consistency of the asymptotic covariance matrix estimate of these models.

Variations in energy use and output growth dynamics: An assessment for intertemporal and contemporaneous relationship

Departing from the prior literature on the energy consumption-economic growth linkages, this paper aims to quantify the asymmetric impact of unpredictable variations in energy use on GDP (gross domestic product) volatility across the high- and low-volatility regimes in the United Kingdom. For this purpose, the paper utilizes quarterly and monthly data on energy consumption and real GDP, covering the period from 1960 to 2013. To obtain the regime-dependent conditional volatility series, we estimate the two-state Markov regime switching ARCH model. We find significant evidence of the presence of regime shifting in behaviour of both underlying volatility series. By estimating the Markov regime switching model, we find that not only the current (contemporaneous) but also the past (intertemporal) volatility shocks in energy utilization are significant in explaining the output dynamics. Yet, we show that the impact of energy consumption volatility is quite asymmetric, depending on the intensiveness of volatility. Specifically, we show that although the effect of energy consumption volatility on GDP volatility is statistically insignificant in the low-volatility regime, in the high-volatility regime, it appears highly significant. From a policy perspective, our findings suggest that controlling unwanted variations in energy usage would be useful in stabilizing real sector of the economy.

The Regime Characteristics of Chinese Stock Market Industry Sectors

This article uses Markov regime Switching ARCH (SWARCH) model to research the volatility of Chinese stock market industry sectors, finding that all industry sectors were able to be significantly divided into two regimes, the high volatility regime and the low volatility regime. For different regime transfer, we can classify all sectors into three categories. Further the article analyzes the regime characteristics of industry sectors. The results show that the correlation coefficient in high volatility regime is higher than that in low volatility regime.

The Tunisian stock market index volatility: Long memory vs. switching regime

This paper investigates the dilemma of long memory versus a switching regime for the Tunisian stock market index volatility. Precisely, different specifications of the Fractionally Integrated GARCH (FIGARCH) model of Baillie et al. (1996) and Switching ARCH (SWARCH) model of Hamilton and Susmel (1994) have been estimated under both Gaussian and Student error distributions.The empirical results show that the Student FIGARCH(1,d,1) specification outperforms the Markov switching ARCH model. In addition, the empirical results indicate that the long memory behavior observed in the Tunisian stock price (TUNINDEX) volatility is a true behavior and is not spuriously created by changes in regimes.

Can VAR models capture regime shifts in asset returns? A long-horizon strategic asset allocation perspective

It is often suggested that through a judicious choice of predictors that track business cycles and market sentiment, simple vector autoregressive (VAR) models could produce optimal strategic portfolio allocations that hedge against the bull and bear dynamics typical of financial markets. However, a distinct literature exists that shows that nonlinear econometric frameworks, such as Markov switching (MS), are also natural tools to compute optimal portfolios in the presence of stochastic good and bad market states. In this paper we examine whether simple VARs can produce portfolio rules similar to those obtained under MS, by studying the effects of expanding both the order of the VAR and the number/selection of predictor variables included. In a typical stock–bond strategic asset allocation problem, we compute the out-of-sample certainty equivalent returns for a wide range of VARs and compare these measures of performance with those typical of nonlinear models for a long-horizon investor with constant relative risk aversion. We conclude that most VARs cannot produce portfolio rules, hedging demands, or (net of transaction costs) out-of-sample performances that approximate those obtained from equally simple nonlinear frameworks. We also compute the improvement in realized performance that may be achieved adopting more complex MS models and report this may be substantial in the case of regime switching ARCH.

The optimal value-at-risk hedging strategy under bivariate regime switching ARCH framework

Unlike the majority of other hedging literatures in which variance is taken as the risk indicator, this article uses the Value-at-Risk (VaR) as the risk management tool of the hedged portfolio. This article adopts a bivariate Markov regime Switching Autoregressive Conditional Heteroscedastic (SWARCH) model to formulate the optimal VaR hedging strategy and then compares it with the other dynamic futures hedging strategies mentioned in the literature in hedging performance. Using Taiwan Stock Exchange Capitalization Weighted Stock Index (TAIEX) futures data, the in-sample and out-of-sample results shows that when VaR is used as the criterion to measure the futures hedging effectiveness, the performance of the dynamic hedging strategy is superior to that of the static hedging strategy, and the performance of the optimal VaR hedging strategy is better than that of the minimum variance and mean-variance hedging strategies. Besides, from the standpoint that the volatility of hedge ratio and hedged portfolio variance decline, no matter what kind of hedging strategy is adopted, the regime switching model is better in in-sample and out-of-sample hedging effectiveness than the Generalized Autoregressive Conditional Heteroscedastic (GARCH) model.

Forecasting Volatility Switching Arch by treed gaussian process with Jumps to the Limiting Linear Model

In this paper, we propose a new hybrid model of asymmetric volatility by using treed Gaussian process with jumps to the limiting linear model (TGPLLM) of Gramacy and Lee combined with the volatility switching ARCH (VS-ARCH) developed by Fornari and Mele to model and predict stock market volatility. Nonparametric sensitivity analysis based on the TGPLLM is applied to check the relevance level of five input variables in the model. Meanwhile, support vector machine is also employed to obtain another new hybrid model for making a comparison with the former. Empirical analysis of NASDAQ index reveals that the five input variables are all significant; the hybrid model based on TGPLLM yields better predictive performance than the ones based on SVM, the parametric models of VS-ARCH, ARMA-GARCH and ARMA-GJR models.

Reply to “On some problems in the article Efficient Likelihood Estimation in State Space Models” by Cheng-Der Fuh [Ann. Statist. 34 (2006) 2026–2068

Motivated by studying asymptotic properties of the maximum likelihood estimator (MLE) in stochastic volatility (SV) models, in this paper we investigate likelihood estimation in state space models. We first prove, under some regularity conditions, there is a consistent sequence of roots of the likelihood equation that is asymptotically normal with the inverse of the Fisher information as its variance. With an extra assumption that the likelihood equation has a unique root for each $n$, then there is a consistent sequence of estimators of the unknown parameters. If, in addition, the supremum of the log likelihood function is integrable, the MLE exists and is strongly consistent. Edgeworth expansion of the approximate solution of likelihood equation is also established. Several examples, including Markov switching models, ARMA models, (G)ARCH models and stochastic volatility (SV) models, are given for illustration.

A Study on the Transmission of Money Market Tensions in EMEAP Economies during the Credit Crisis of 2007-2008

The recent tension in the interbank markets following the global financial crisis has raised concerns about the turbulence in interbank markets. This paper utilises two widely used indicators for measuring interbank stress (the interbank rate less the Overnight Index Swap rate and the interbank rate less the yield of government securities) to examine the transmission of interbank tension from the US dollar to nine interbank markets in the EMEAP economies. Using a vector autoregression model, we show that during the credit crisis of 2007-2008, the distress in the US dollar money market had a material impact with durations of seven to 13 days on the interbank markets for the Hong Kong dollar, Japanese yen, Australian dollar and New Zealand dollar. Moreover, based on a bivariate regime switching ARCH model, we also find evidence of volatility co-movement between the interbank stress indicator of the US dollar and that of the Hong Kong dollar, Japanese yen, Australian dollar, New Zealand dollar, Korean won and Singapore dollar during the crisis. The expected duration when two money markets are both in a high-volatility state is estimated to be as long as seven days. The short-lived impact on the EMEAP economies from a shock in the US dollar money market can be attributed to the policy actions taken by central banks and monetary authorities in the region and the coordinated efforts by policy makers worldwide to contain the credit crisis.

Value at risk and conditional extreme value theory via markov regime switching models

AbstractThis study develops a new conditional extreme value theory‐based (EVT) model that incorporates the Markov regime switching process to forecast extreme risks in the stock markets. The study combines the Markov switching ARCH (SWARCH) model (which uses different sets of parameters for various states to cope with the structural changes for measuring the time‐varying volatility of the return distribution) with the EVT to model the tail distribution of the SWARCH processed residuals. The model is compared with unconditional EVT and conditional EVT‐GARCH models to estimate the extreme losses in three leading stock indices: S&P 500 Index, Hang Seng Index and Hang Seng China Enterprise Index. The study found that the EVT‐SWARCH model outperformed both the GARCH and SWARCH models in capturing the non‐normality and in providing accurate value‐at‐risk forecasts in the in‐sample and out‐sample tests. The EVTSWARCH model, which exhibits the features of measuring the volatility of a heteroscedastic financial return series and coping with the non‐normality owing to structural changes, can be an alternative measure of the tail risk. © 2008 Wiley Periodicals, Inc. Jrl Fut Mark 28:155–181, 2008

A switching ARCH (SWARCH) model of stock market volatility: some evidence from Latin America

We use the Markov regime-switching ARCH (SWARCH) model of Hamilton and Susmel (J Econometrics 64:307–333, 1994) to document the presence of high volatility regimes in six Latin American countries (Argentina, Brazil, Chile, Mexico, Peru, and Venezuela). We found four high volatility episodes, each associated to either a local (the Mexican crisis of 1994, the Brazilian crisis of 1998–1999, the Argentinean crisis of 2001–2002) or a worldwide financial crisis (the Asian financial crisis of 1997). However, we found that the effects of each financial crisis are short-lived and that between 2 and 4 months after each crisis, all markets return to low volatility regimes.

Efficient likelihood estimation in state space models

Motivated by studying asymptotic properties of the maximum likelihood estimator (MLE) in stochastic volatility (SV) models, in this paper we investigate likelihood estimation in state space models. We first prove, under some regularity conditions, there is a consistent sequence of roots of the likelihood equation that is asymptotically normal with the inverse of the Fisher information as its variance. With an extra assumption that the likelihood equation has a unique root for each $n$, then there is a consistent sequence of estimators of the unknown parameters. If, in addition, the supremum of the log likelihood function is integrable, the MLE exists and is strongly consistent. Edgeworth expansion of the approximate solution of likelihood equation is also established. Several examples, including Markov switching models, ARMA models, (G)ARCH models and stochastic volatility (SV) models, are given for illustration.

Deviations from uncovered interest parity in Malaysia

This paper applies the Switching ARCH (SWARCH) model of Hamilton and Susmel (1994) to investigate the dynamics of deviations from Uncovered Interest Parity (UIP) for Malaysia for the sample period 1978–2002. In particular, the deviations (or the risk premium) are modelled as a time series subject to discrete regime shifts between two possible states, “high volatility” and “low volatility”. We find that the SWARCH model provides a better description of the data and implies a much lower degree of volatility persistence than conventional ARCH models. Overall, the SWARCH model provides a clearer picture of how the UIP deviations have evolved over time and how the changes in the volatility of the deviations have coincided with major changes in financial liberalisation in Malaysia. This adds credibility to the hypothesis that the shifts are not statistical artefacts but indeed reflect real economic changes.

A Switching ARCH Model for the German DAX Index

This paper estimates a switching autoregressive conditional heteroskedastic time series model for returns on the daily German stock market index. Volatility clustering is captured by persistent periods of different volatility levels and by the dependence on past innovations. We introduce a leverage term to model the asymmetric response of volatility to shocks. Model specification and estimation is performed within a Bayesian framework using Markov Chain Monte Carlo simulation methods. Model diagnostics document a good fit of the switching ARCH model. The persistence of shocks in volatility coming from the autoregressive conditional part of the variance is considerably lower than that obtained using a GARCH(1,1) model. Our volatility estimate closely follows market implied volatility. When we compare the forecasting performance, switching ARCH turns out to be an unbiased estimator of realized volatility. Nevertheless, over all forecast horizons, model-based volatility forecasts do not add information about future volatility. Up to a 7-day horizon, market implied volatility already contains nearly all information.

Estimating value-at-risk via Markov switching ARCH models – an empirical study on stock index returns

This paper estimates the Value-at-Risk (VaR) on returns of stock market indexes including Dow Jones, Nikkei, Frankfurt Commerzbank index, and FTSE via Markov Switching ARCH (SWARCH) models. It is conjectured that structural changes contribute to non-normality in stock return distributions. SWARCH models, which admit parameters based on various states to control structural changes in the estimating periods, may thus help mitigate kurtosis, tail-fatness and skewness problems in estimating VaR. Significant kurtosis and skewness in return distributions of Dow Jones, Nikkei, FCI and FTSE and significant tail-fatness (tail-thinness) in the 1% (5%) region critical probability are documented. Moreover, it is shown that the more generalized SWARCH outshines both ARCH and GARCH in capturing non-normalities with respect to both in- and out-sample VaR violation rate tests.

Bayesian analysis of switching ARCH models

We consider a time series model with autoregressive conditional heteroscedasticity that is subject to changes in regime. The regimes evolve according to a multistate latent Markov switching process with unknown transition probabilities, and it is the constant in the variance process of the innovations that is subject to regime shifts. The joint estimation of the latent process and all model parameters is performed within a Bayesian framework using the method of Markov chain Monte Carlo (MCMC) simulation. We perform model selection with respect to the number of states and the number of autoregressive parameters in the variance process using Bayes factors and model likelihoods. To this aim, the model likelihood is estimated by the method of bridge sampling. The usefulness of the sampler is demonstrated by applying it to the data set previously used by Hamilton and Susmel (1994) who investigated models with switching autoregressive conditional heteroscedasticity using maximum likelihood methods. The paper concludes with some issues related to maximum likelihood methods, to classical model selection, and to potential straightforward extensions of the model presented here.

Volatility and cross correlation across major stock markets

Several papers have documented the fact that correlations across major stock markets are higher when markets are more volatile—this is done by comparing unconditional correlations over sub-periods or by using conditional correlations that are time varying. In this paper we examine the relation between correlation and variance in a conditional time and state varying framework. We use a switching ARCH (SWARCH) technique that does two things. One, it enables us to model variance as state varying. Two, a bivariate SWARCH model allows us to go from conditional variance to state varying covariances and correlations and hence test for differences in correlations across variance regimes. We find that the correlations between the U.S. and other world markets are on average 2 to 3.5 times higher when the U.S. market is in a high variance state as compared to a low variance regime. We also find that, compared to a GARCH framework, the portfolio choices resulting from our SWARCH model lead to higher Sharpe ratios.

The dynamics of DM/£ exchange rate volatility: a SWARCH analysis

This paper applies the switching ARCH model introduced by Hamilton and Susmel (1994) to weekly DM/£ exchange rates for the period March 1987–December 1994. The sample period spans the UK's ERM tenure, which lasted until the currency crisis of September 1992. The SWARCH model generalizes standard ARCH models by allowing the conditional variance to experience jumps between discrete states or regimes. The SWARCH model is shown to provide a unified statistical framework for investigating two issues of interest in the literature: (i) the evolution of volatility and its implications for ERM credibility and (ii) the effects of regime shifts on the stochastic process governing conditional volatility. © 1998 John Wiley & Sons, Ltd.