The Markov switching asymmetric multiplicative error model (original) (raw)
Volatility Swings in the US Financial Markets
2012
Abstract Empirical evidence shows that the dynamics of high frequency–based measures of volatility exhibit persistence and occasional abrupt changes in the average level. By looking at volatility measures for major indices, we notice similar patterns (including jumps at about the same time), with stronger similarities, the higher the degree of company capitalization represented in the indices. We adopt the recent Markov Switching Asymmetric Multiplicative Error Model to model the dynamics of the conditional expectation of realized volatility.
Measuring and Trading Volatility on the US Stock Market: A Regime Switching Approach
SSRN Electronic Journal, 2018
The volatility premium is a well-documented phenomenon, which can be approximated by the difference between the previous month level of the VIX Index and the rolling 30-day close-to-close volatility. Along with the literature, we show evidence that VIX is generally above the 30-day rolling volatility giving rise to the volatility premium, so selling volatility can become a profitable trading strategy as long as proper risk management is under place. As a contribution, we introduced the implementation of a Hidden Markov Model (HMM), identifying two states of the nature and showing that the volatility premium undergoes temporal breaks in its behavior. Based on this, we formulate a trading strategy by selling volatility and switching to medium-term U.S. Treasury Bills when appropriated. We test the performance of the strategy using the conventional Carhart four-factor model showing a positive and statistically significant alpha.
Journal of Business Finance & Accounting, 2007
We propose generalised stochastic volatility models with Markov regime changing state equations (SVMRS) to investigate the important properties of volatility in stock returns, specifically high persistence and smoothness. The model suggests that volatility is far less persistent and smooth than the conventional GARCH or stochastic volatility. Persistent short regimes are more likely to occur when volatility is low, while far less persistence is likely to be observed in high volatility regimes. Comparison with different classes of volatility supports the SVMRS as an appropriate proxy volatility measure. Our results indicate that volatility could be far more difficult to estimate and forecast than is generally believed.
Journal of Empirical Finance, 2012
This paper proposes a two-state Markov-switching model for stock market returns in which the state-dependent expected returns, their variance and associated regime-switching dynamics are allowed to respond to market information. More specifically, we apply this model to examine the explanatory and predictive power of price range and trading volume for return volatility. Our findings indicate that a negative relation between equity market returns and volatility prevails even after having controlled for the time-varying determinants of conditional volatility within each regime. We also find an asymmetry in the effect of price range on intra-and inter-regime return volatility. While price range has a stronger effect in the high volatility state, it appears to significantly affect only the transition probabilities when the stock market is in the low volatility state but not in the high volatility state. Finally, we provide evidence consistent with the 'rebound' model of asset returns proposed by Samuelson (1991), suggesting that long-horizon investors are expected to invest more in risky assets than shorthorizon investors.
2016
A new model – the high-dimensional Markov (HDM) model – is proposed for financial returns and their latent variances. It is also applicable to model directly realized variances. Volatility is modeled as a product of three components: a Markov chain driving volatility persistence, an independent discrete process capable of generating jumps in the volatility, and a predictable (data-driven) process capturing the leverage effect. The Markov chain and jump components allow volatility to switch abruptly between thousands of states. The transition probability matrix of the Markov chain is structured in such a way that the multiplicity of the second largest eigenvalue can be greater than one. This distinctive feature generates a high degree of volatility persistence. The statistical properties of the HDM model are derived and an economic interpretation is attached to each component. In-sample results on six financial time series highlight that the HDM model compares favorably to the m...
A New Approach to Volatility Modeling: The High-Dimensional Markov Model
SSRN Electronic Journal, 2016
A new model-the high-dimensional Markov (HDM) model-is proposed for financial returns and their latent variances. It is also applicable to model directly realized variances. Volatility is modeled as a product of three components: a Markov chain driving volatility persistence, an independent discrete process capable of generating jumps in the volatility, and a predictable (data-driven) process capturing the leverage e↵ect. The Markov chain and jump components allow volatility to switch abruptly between thousands of states. The transition probability matrix of the Markov chain is structured in such a way that the multiplicity of the second largest eigenvalue can be greater than one. This distinctive feature generates a high degree of volatility persistence. The statistical properties of the HDM model are derived and an economic interpretation is attached to each component. In-sample results on six financial time series highlight that the HDM model compares favorably to the main Maciej Augustyniak gratefully acknowledges financial support from the Natural Sciences and Engineering Research Council of Canada (NSERC). Luc Bauwens acknowledges support of the "Communauté française de Belgique" through contract "Projet d'Actions de Recherche Concertées 12/17-045", granted by the "Académie universitaire Louvain". Arnaud Dufays gratefully acknowledges financial support from the Fonds de Recherche du Québec-Société et Culture.
This article makes an econometric analysis using the Markov Switching Autoregressive (MS-AR) model, with the objective of showing the dynamics presented by the main US stock market index, the S&P 500, because this index measures the performance of most capitalized companies in the United States market. The analysis covers the period from January 2005 to November 2020, when the subprime crisis occurred and the COVID-19 crisis began. In particular, two regimes (regime 1-low volatility and regime 2-high volatility) were used in the model so that the parameters of the S&P 500 index behave differently during economic crises with the representative regimes. The S&P 500 remained in regime 1 (low volatility) for five periods, totaling 110 months. In regime 2 (high volatility-2008 and 2020 crises), it remained for about 50 months, that is, 39 months in the 2008 crisis (including the global financial crisis-2009) and 11 months in the COVID-19 crisis. In addition, regime 1 is more persistent, that is, the probability of staying in that regime in a later period is 93,61% and a change to regime 2 of 6,39%. In regime 2, the probability of maintaining this regime in the period t + 1 is 92,52%, while the probability of changing to regime 1 is 7,42%.
Long memory and nonlinearities in realized volatility: A Markov switching approach
Computational Statistics & Data Analysis, 2012
Goal of this paper is to analyze and forecast realized volatility through nonlinear and highly persistent dynamics. In particular, we propose a model that simultaneously captures long memory and nonlinearities in which level and persistence shift through a Markov switching dynamics. We consider an efficient Markov chain Monte Carlo (MCMC) algorithm to estimate parameters, latent process and predictive densities. The insample results show that both long memory and nonlinearities are significant and improve the description of the data. The out-sample results at several forecast horizons, show that introducing these nonlinearities produces superior forecasts over those obtained from nested models.
2004
In this paper, the volatility of the return generating process of the market portfolio and the slope coefficient of the market model is assumed to follow a Markov switching process of order one. The results indicate very strong evidence of volatility switching behaviour in a sample of returns in the S&P500 index. In three of the thirty securities in the Dow Jones index, the estimated slope in the market model show strong switching behaviour. In these three securities the low risk state is more persistent than the high-risk state. For each security we estimate the conditional probabilities that the security is in the high (low) risk state given the market is in the high (low) volatility regime and show that this information can be used to classify securities into three distinct groups. There is no association between these groups and the securities' constant beta estimated in the market model and the Sharpe index. Some directions for further research are discussed.
Journal of Mathematics, 2014
We adopt aregime switchingapproach to study concrete financial time series with particular emphasis on their volatility characteristics considered in a space-time setting. In particular the volatility parameter is treated as an unobserved state variable whose value in time is given as the outcome of an unobserved, discrete-time and discrete-state, stochastic process represented by a suitable Markov chain. We will take into account two different approaches for inference on Markov switching models, namely, the classical approach based on the maximum likelihood techniques and the Bayesian inference method realized through a Gibbs sampling procedure. Then the classical approach shall be tested on data taken from theStandard & Poor’s 500and theDeutsche Aktien Indexseries of returns in different time periods. Computations are given for a four-state switching model and obtained numerical results are put beside by explanatory graphs which report the outcomes obtained exploiting both smoothi...
SSRN Electronic Journal, 2000
In this paper, the volatility of the return generating process of the market portfolio and the slope coefficient of the market model is assumed to follow a Markov switching process of order one. The results indicate very strong evidence of volatility switching behaviour in a sample of returns in the S&P500 index. In three of the thirty securities in the Dow Jones index, the estimated slope in the market model show strong switching behaviour. In these three securities the low risk state is more persistent than the high-risk state. For each security we estimate the conditional probabilities that the security is in the high (low) risk state given the market is in the high (low) volatility regime and show that this information can be used to classify securities into three distinct groups. There is no association between these groups and the securities' constant beta estimated in the market model and the Sharpe index. Some directions for further research are discussed.
A Markov Regime Switching Approach of Estimating Volatility Using Nigerian Stock Market
American Journal of Theoretical and Applied Statistics, 2020
Understanding and forecasting the behavior of volatility in stock market has received significant attention among researchers and analysts in the last few decades due to its crucial roles in financial markets. Portfolios managers, option traders, and market makers are all interested in the possibility of forecasting, with a reasonable level of accuracy. This study examined the volatility on the Nigeria stock market by comparing two Markov regime switching Autoregressive (MS-AR) Models estimated at different lagged values using the Nigeria stock exchange monthly All Share Index data from 1988 to 2018 in the Central Bank of Nigeria (CBN) Statistical Bulletin. It was found that factors like financial crisis, information flow, trading volume, economical aspects and investor's behavior are the causes of volatility in the stock market. The results and forecasts obtained from the statistical analysis in this research showed that the stock market will experience a steady growth in 2020 and beyond. Also, the stock market is experiencing fluctuations in the price indices which show that over the years, investors have been exposed to some certain risks in the time past. We therefore recommended that researchers should focus more attention in developing robust statistical model that will reflect and continue to monitor future trends and realities.
Secular Volatility Decline of the U.S. Composite Economic Indicator
2002
The paper treats the issue of decreasing volatility of the U.S. economy observed since the mid-1980s. As a measure of volatility the residual variance of a composite economic indicator with Markov switching is used which. Two additional regimes are included capturing the secular shift in volatility. The mixed frequency is allowed for permitting the use of both monthly and quarterly component series. The low-intercept regime probabilities comply to the NBER business cycle dating, while the low-variance regime probabilities indicate the beginning of 1984 as a possible date of the structural break in volatility.
A New Approach to Volatility Modeling: The Factorial Hidden Markov Volatility Model
Journal of Business & Economic Statistics
A new process-the factorial hidden Markov volatility (FHMV) model-is proposed to model financial returns or realized variances. Its dynamics are driven by a latent volatility process specified as a product of three components: a Markov chain controlling volatility persistence, an independent discrete process capable of generating jumps in the volatility, and a predictable (data-driven) process capturing the leverage effect. An economic interpretation is attached to each one of these components. Moreover, the Markov chain and jump components allow volatility to switch abruptly between thousands of states, and the transition matrix of the model is structured to generate a high degree of volatility persistence. An empirical study on six financial time series shows that the FHMV process compares favorably to state-of-the-art volatility models in terms of in-sample fit and out-of-sample forecasting performance over time horizons ranging from one to one hundred days.
Volatility transmission across markets: a Multichain Markov Switching model
2007
The integration of financial markets across countries has modified the way prices react to news. Innovations originating in one market diffuse to other markets following patterns which usually stress the presence of interdependence. In some cases, though, covariances across markets have an asymmetric component which reflects the dominance of one over the others. The volatility transmission mechanisms in such events may be more complex than what can be modelled as a multivariate GARCH model.
The Econometrics Journal, 2013
Empirical …ndings related to the time series properties of stock returns volatility indicate autocorrelations that decay slowly at long lags. In light of this, several longmemory models have been proposed. However, the possibility of level shifts has been advanced as a possible explanation for the appearance of long-memory and there is growing evidence suggesting that it may be an important feature of stock returns volatility. Nevertheless, it remains a conjecture that a model incorporating random level shifts in variance can explain the data well and produce reasonable forecasts. We show that a very simple stochastic volatility model incorporating both a random level shift and a short-memory component indeed provides a better in-sample …t of the data and produces forecasts that are no worse, and sometimes better, than standard stationary short and long-memory models. We use a Bayesian method for inference and develop algorithms to obtain the posterior distributions of the parameters and the smoothed estimates of the two latent components. We apply the model to daily S&P 500 and NASDAQ returns over the period 1980.1-2005.12. Although the occurrence of a level shift is rare, about once every two years, the level shift component clearly contributes most to the total variation in the volatility process. The half-life of a typical shock from the short-memory component is very short, on average between 8 and 14 days. We also show that, unlike common stationary short or long-memory models, our model is able to replicate keys features of the data. For the NASDAQ series, it forecasts better than a standard stochastic volatility model, and for the S&P 500 index, it performs equally well.
Switching Processes in Financial Markets
For an intriguing variety of switching processes in nature, the underlying complex system abruptly changes from one state to another in a highly discontinuous fashion. Financial market fluctuations are characterized by many abrupt switchings creating upward trends and downward trends, on time scales ranging from macroscopic trends persisting for hundreds of days to microscopic trends persisting for a few minutes. The question arises whether these ubiquitous switching processes have quantifiable features independent of the time horizon studied. We find striking scale-free behavior of the transaction volume after each switching. Our findings can be interpreted as being consistent with time-dependent collective behavior of financial market participants. We test the possible universality of our result by performing a parallel analysis of fluctuations in time intervals between transactions. We suggest that the well known catastrophic bubbles that occur on large time scales-such as the most recent financial crisis-may not be outliers but single dramatic representatives caused by the formation of increasing and decreasing trends on time scales varying over nine orders of magnitude from very large down to very small. complex systems | econometrics | switching phenomena | phase transitions | futurICT T he study of dramatic crash events is limited by the fortunately rare number of such events. However, there is a truly gargantuan amount of preexisting precise financial market data already collected, many orders of magnitude more than for other complex systems. Accordingly, financial markets are becoming a paradigm of complex systems (1, 2), and increasing numbers of scientists are analyzing market data (3-18) and modeling financial markets (19-29). The probability distribution function and the time autocorrelation function reveal interesting features, such as long-range power-law correlations in volatility (30) and fat tails in the price change probability distribution function (31, 32).