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I review the burgeoning literature on applications of Markov regime switching models in empirical finance. In particular, distinct attention is devoted to the ability of Markov Switching models to fit the data, filter unknown regimes and states on the basis of the data, to allow a powerful tool to test hypotheses formulated in light of financial theories, and to their forecasting performance with reference to both point and density predictions. The review covers papers concerning a multiplicity of sub-fields in financial economics, ranging from empirical analyses of stock returns, the term structure of default-free interest rates, the dynamics of exchange rates, as well as the joint process of stock and bond returns.

One important characteristic of cryptocurrencies has been their high and erratic volatility. To represent this complicated behavior, recent studies have emphasized the use of autoregressive models frequently concluding that generalized autoregressive conditional heteroskedasticity (GARCH) models are the most adequate to overcome the limitations of conventional standard deviation estimates. Some studies have expanded this approach including jumps into the modeling. Following this line of research, and extending previous research, our study analyzes the volatility of Bitcoin employing and comparing some symmetric and asymmetric GARCH model extensions (threshold ARCH (TARCH), exponential GARCH (EGARCH), asymmetric power ARCH (APARCH), component GARCH (CGARCH), and asymmetric component GARCH (ACGARCH)), under two distributions (normal and generalized error). Additionally, because linear GARCH models can produce biased results if the series exhibit structural changes, once the conditional volatility has been modeled, we identify the best fitting GARCH model applying a Markov switching model to test whether Bitcoin volatility evolves according to two different regimes: high volatility and low volatility. The period of study includes daily series from July 16, 2010 (the earliest date available) to January 24, 2019. Findings reveal that EGARCH model under generalized error distribution provides the best fit to model Bitcoin conditional volatility. According to the Markov switching autoregressive (MS-AR) Bitcoin’s conditional volatility displays two regimes: high volatility and low volatility.

In this chapter, we outline the statistical consequences of neglecting structural breaks and regime switches in autoregressive and GARCH models and propose two strategies to approach the problem. The first strategy is to identify regimes of constant unconditional volatility using a change point detector and estimate a separate GARCH model on the resulting segments. The second approach is to use a multiple-regime GARCH model, such as the Flexible Coefficient GARCH (FCGARCH) specification, where the regime-switches are governed by an observable variable. We apply both alternatives to an array of financial time series and compare their forecast performance.

We examine the role of structural breaks in forecasting stock return volatility. We begin by testing for structural breaks in the unconditional variance of daily returns for the S&P 500 market index and ten sectoral stock indices for 9/12/1989–1/19/2006 using an iterative cumulative sum of squares procedure. We find evidence of multiple variance breaks in almost all of the return series, indicating that structural breaks are an empirically relevant feature of return volatility. We then undertake an out-of-sample forecasting exercise to analyze how instabilities in unconditional variance affect the forecasting performance of asymmetric volatility models, focusing on procedures that employ a variety of estimation window sizes designed to accommodate potential structural breaks. The exercise demonstrates that structural breaks present important challenges to forecasting stock return volatility. We find that averaging across volatility forecasts generated by individual forecasting models estimated using different window sizes performs well in many cases and appears to offer a useful approach to forecasting stock return volatility in the presence of structural breaks.

This paper compares the out-of-sample forecasting performance of three long-memory volatility models (i.e., fractionally integrated (FI), break and regime switching) against three short-memory models (i.e., GARCH, GJR and volatility component). Using S&P 500 returns, we find that structural break models produced the best out-of-sample forecasts, if future volatility breaks are known. Without knowing the future breaks, GJR models produced the best short-horizon forecasts and FI models dominated for volatility forecasts of 10 days and beyond. The results suggest that S&P 500 volatility is non-stationary at least in some time periods. Controlling for extreme events (e.g., the 1987 crash) significantly improved forecasting performance.

Purpose – This chapter aimed to investigate hedge funds market risk. One aims to go further the traditional measures of risk that underestimates it by introducing a more appropriate method to hedge funds. One demonstrates that daily hedge fund return distributions are asymmetric and leptokurtic. Furthermore, volatility clustering phenomenon and the existence of ARCH effects demonstrate that hedge funds volatility varies through time. These features suggest the modelisation of their volatility using symmetric (GARCH) and asymmetric (EGARCH and TGARCH) models used to evaluate a 1-day-ahead value at risk (VaR).

Methodology/Approach – The conditional variances were estimated under the assumption that residuals t follow the normal and the student law. The knowledge of the conditional variance was used to forecast 1-day-ahead VaR. The estimations are compared with the Gaussian, the student and the modified VaR. To sum up, 12 VaRs are computed; those based on standard deviation and computed with normal, student and cornish fisher quantile and those based on conditional volatility models (GARCH, TGARCH and EGARCH) computed with the same quantiles.

Findings – The results demonstrate that VaR models based on normal quantile underestimate risk while those based on student and cornish fisher quantiles seem to be more relevant measurements. GARCH-type VaRs are very sensitive to changes in the return process. Back-testing results show that the choice of the model used to forecast volatility has an importance. Indeed, the VaR based on standard deviation is not relevant to measure hedge funds risks as it fails the appropriate tests. On the opposite side, GARCH-, TGARCH- and EGARCH-type VaRs are accurate as they pass most of the time successfully the back-testing tests. But, the quantile used has a more significant impact on the relevance of the VaR models considered. GARCH-type VaR computed with the student and especially cornish fisher quantiles lead to better results, which is consistent with Monteiro (2004) and Pochon and Teïletche (2006).

Originality/Value of chapter – A large set of GARCH-type models are considered to estimate hedge funds volatility leading to numerous evaluation of VaRs. These estimations are very helpful. Indeed, public savings under institutional investors management then delegate to hedge funds are concerned. Therefore, an adequate risk management is required. Another contribution of this chapter is the use of daily data to measure all hedge fund strategies risks.

This study is intended to investigate the volatility patterns in Bombay Stock Exchange Limited Sensitivity Index (BSE Sensex) based on time series data collected for 10 years period of time. To reach out the predefined objectives of the study, the authors have employed generalized autoregressive conditional heteroscedastic models. The study revealed that the presence of heteroscedasticiy is found in BSE Sensex. Further, the model produced highly accurate results when the researchers compared the estimated results from actual. Furthermore, the volatility of BSE Sensex has shown the features of clustering and significant time varying. Moreover, the model has indicated that there is a positive correlation between daily stock returns and the BSE Sensex volatility.

In this chapter, we investigate the effect of long memory in volatility on the accuracy of emerging stock markets risk estimation during the period of the recent global financial crisis. For this purpose, we use a short (GJR-GARCH) and long (FIAPARCH) memory volatility models to compute in-sample and out-of-sample one-day-ahead VaR. Using six emerging stock markets index, we show that taking into account the long memory property in volatility modelling generally provides a more accurate VaR estimation and prediction. Therefore, conservative risk managers may adopt long memory models using GARCH-type models to assess the emerging market risks, especially when incorporating crisis periods.