A Component Markov Regime-Switching Autoregressive Conditional Range Model

Regime-switching in volatility and correlation structure using range-based models with Markov-switching

A novel time-varying FIGARCH model for improving volatility predictions

Regime Switching GARCH Models and GARCH Models, in Stock Market of the Developing Countries'

Volatility plays an important role in the field of financial econometrics as one of the risk indicators. Many various models address the problem of modeling the volatilities of financial asset returns. This study provides a new empirical performance comparison of the four different GARCH-type models, namely GARCH, GARCH-M, GJR-GARCH, and log-GARCH models based on simulated data and real data such as the DJIA, S&P 500, and S&P CNX Nifty indices on a daily period from January 2000 to December 2017. We also investigate the estimation results obtained using Solver’Excel and verify those results against the results obtained using a Markov chain Monte Carlo method. The simulation study showed that the GARCH model is outperformed by other models. Meanwhile, the empirical study provides evidence that the GJR-GARCH model provides the best fitting, followed by the GARCH-M, GARCH, and log-GARCH models. Furthermore, this study recommends the use of Excel’s Solver in practice when the parameter estimates for GARCH-type model do not close to zero.

The 1997 Asian financial crisis and the 2008 global financial crisis had a significant impact on the economies of various countries, including Indonesia, Thailand, and South Korea. Therefore, this study aims to detect early financial crises in these three countries based on real exchange rate indicators. The early detection of financial crises, relevant institutions in applying appropriate policies. Thus, financial crises can be avoided. The real exchange rate indicator contains fluctuations, and changing conditions. As a solution, the volatility models, i.e. autoregressive conditional heteroscedasticity (ARCH) and generalized ARCH (GARCH) explains volatility or fluctuations, and Markov switching (MS) explains changing conditions. The combination of these models yields a smoothed probability value used for detecting financial crises. The real exchange rate of Indonesia, Thailand, and South Korea data against the United States were used from January 1990 to March 2020. The results showed that MSARCH( 2,1), MS-ARCH(2,1), and MS-GARCH(2,1,1) are for Indonesia, Thailand, and South Korea, respectively. The real exchange rate indicator can detect crises in Indonesia and South Korea in the 1997 and 2008. Whereas in Thailand, it was only able to detect crises occured in the 1997. The prediction results of the smoothed probability showed no signal of the financial crisis in Indonesia, Thailand, and South Korea one year later.

In this paper we compare a set of different standard GARCH models with a group of Markov Regime-Switching GARCH (MRS-GARCH) in terms of their ability to forecast the US stock market volatility at horizons that range from one day to one month. To take into account the excessive persistence usually found in GARCH models that implies too smooth and too high volatility forecasts, in the MRS-GARCH models all parameters switch between a low and a high volatility regime. Both gaussian and fat-tailed conditional distributions for the residuals are assumed, and the degrees of freedom can also be state-dependent to capture possible time-varying kurtosis. The forecasting performances of the competing models are evaluated both with statistical and risk-management loss functions. Under statistical losses, we use both tests of equal predictive ability of the Diebold-Mariano-type and test of superior predictive ability. Under risk-management losses, we use a two-step selection procedure where we first check which models pass the tests of correct unconditional or conditional coverage and then we compare the best models under two subjective VaR-based loss functions. The empirical analysis demonstrates that MRS-GARCH models do really outperform all standard GARCH models in forecasting volatility at horizons shorter than one week under both statistical and VaR-based risk-management loss functions. In particular, all tests reject the presence of a better model than the MRS-GARCH with normal innovations. However, at forecast horizons longer than one week, standard asymmetric GARCH models tend to be superior.

Volatility models applied to geophysics and high frequency financial market data

Due to the illiquidity of inventories pledged, the essential of price risk management of supply chain finance is to long-term price risk measure. Long memory in volatility, which attests a slower than exponential decay in the autocorrelation function of standard proxies of volatility, yields an additional improvement in specification of multi-period volatility models and further impact on the term structure of risk. Thus, long memory is indispensable to model and measure long-term risk. This paper sheds new light on the impact of the existence and persistence of long memory in volatility on inventory portfolio optimization. Firstly, we investigate the existence of long memory in volatility of the inventory returns, and examine the impact of long memory on the modeling and forecasting of multi-period volatility, the dependence structure between inventory returns and portfolio optimization. Secondly, we further explore the impact of the persistence of long memory in volatility on the efficient frontier of inventory portfolio via a data generation process with different long memory parameter in the FIGARCH model. The extensive Monte Carlo evidence reveals that both GARCH and IGARCH models without accounting for long memory will misestimate the actual long-term risk of the inventory portfolio and further bias the efficient frontier; besides, through A sensitive analysis of long memory parameter d, it is proved that the portfolio with higher long memory parameter possesses higher expected return and lower risk level. In conclusion, banks and other participants will benefit from the long memory taken into the long-term price risk measure and portfolio optimization in supply chain finance.

This study performs a comparative analysis of various GARCH and stochastic volatility (SV) models using the BIST 100 index. The models we examine include traditional GARCH (1,1) models and SV models with an AR (1) log-volatility process. Additionally, we consider more flexible models that incorporate jump components, volatility-in-mean, leverage effects, and innovations following a t-distribution or a moving average. The empirical findings reveal the following findings: (1) Stochastic Volatility (SV) models generally demonstrate better performance when compared to their GARCH counterparts. (2) The inclusion of a jump component and innovations following a tdistribution notably enhances the performance of the standard GARCH model while having less impact on the SV model. (3) The presence of a

Based on the data information of Shanghai and Shenzhen CSI 300 stock index futures, the performance of the GARCH model and implied volatility prediction in different time periods were studied. This paper mainly discusses the volatility of index returns and uses Matlab and Minitab to measure the performance of the GARCH model and implied volatility model in volatility prediction, and then comments on the prediction results. The results show that the GARCH model has a good prediction effect in the short term, while the implied volatility has a good prediction power in the long term. Option prices can mirror market information in a more comprehensive way. As a result, implied volatility is more reasonable to predict future volatility.

A partir de uma base de dados de ações da Telemar S.A. para o período de 21/09/1998 a 21/10/2002 e de opções desta mesma empresa para o período de 02/10/2000 a 21/10/2002 foi avaliada a precisão na previsão da volatilidade futura usando-se as volatilidades implícita e estatística. A volatilidade implícita foi obtida por indução retroativa da fórmula de Black-Scholes. As previsões estatísticas da volatilidade foram obtidas pelos modelos de média móvel ponderada igualmente, GARCH, EGARCH e FIGARCH. A estatística de Wald revela que os modelos EGARCH e FIGARCH são previsores eficientes e não viesados da variação absoluta dos retornos da Telemar S.A. entre t e t+1. Na avaliação da volatilidade ao longo do tempo de vida da opção, os resultados rejeitam a hipótese de volatilidade implícita ser um melhor previsor da volatilidade futura, e a estatística Wald mostra que o modelo FIGARCH é um previsor eficiente e não viesado.

Long memory or regime switching in volatility? Evidence from high-frequency returns on the U.S. stock indices

Uncertainty is often associated with travel-time prediction. Traditional point prediction methods only provide point values that are unable to offer enough information on the reliability of prediction results. The recent development of statistical volatility models has given us an effective way to capture uncertainties in data. Generalized autoregressive conditional heteroskedasticity (GARCH) models have been widely used in transportation systems as a way to account for this uncertainty by providing more accurate prediction intervals. However, a GARCH model arguably does not consider the trend and seasonality in data. If there is a trend or seasonality, the performance of the GARCH model may be affected. In the context of travel-time prediction, this paper proposes two component GARCH models that are able to model trend and seasonal components through decomposition. The travel-time data obtained along a freeway corridor in Houston, TX, USA, were used to empirically test the performance of the proposed models. The study results indicate that the proposed models perform well when capturing uncertainties associated with travel-time prediction.

Bivariate FIGARCH and Fractional Cointegration

This paper estimates the volatility of the won-dollar exchange rate during the 2008-9 crisis. We find that the volatility increased in September 2008 and decreased in May 2009. The volatility rose gradually for one month and subdued in a similar manner, which implies that the volatility was not governed by any specific event or government policy. The overall changes in the volatility are similar to the movements of the CDS premium. We also find that the UK foreign exchange market experienced a similar pattern of volatility shifts and suffered smaller but longer volatility than the Korean one. The volatility shifts are estimated using a Markov switching GARCH model and a Bayesian method is suggested.Keywords: Bayesian Inference, Markov Switching GARCH Models, Exchange Rate Volatility, Credit CrisisJEL classification: C11, C22, F31(ProQuest: ... denotes formulae omitted.)1. INTRODUCTIONThe Korean foreign exchange market has experienced two crises during the last two decades, as shown in Figure 1. The exchange rate was managed by the government before the Asian financial crisis in 1997-8. The Korean currency, or the won, depreciated sharply during the crisis and showed a trend of appreciating during the next decade. The foreign exchange market suffered from another foreign capital flight during the global credit crisis in 2008-9. Contrary to the case of the 1997-8 crisis, the 2008-9 credit crisis stemmed from the developed economies. However, the credit crisis led many developing countries, including South Korea, to an economic or financial crisis. Many policies were implemented to stabilize the financial and foreign exchange markets in Korea. The Bank of Korea has swiftly lowered the policy rate from 5.25% to 2% for 4 months since October 2008. The government announced the Financial Market Stabilization Measures, which included government warrants of the foreign currency debt of the commercial banks and provision of dollar liquidity to them, on October 19, 2008. The Bank of Korea has also made a 30-billion US dollar swap arrangement with the Federal Reserve on October 30, 2008 and other deals with the People's Bank of China and the Bank of Japan on December 12, 2008. From October 2008 to February 2009, it provided around 30-billion dollar liquidity to financial institutions which had difficulties in overseas fund raising.This paper estimates the volatility of the won-dollar exchange rate during the 2008-9 crisis and investigates what determined the volatility. We find that the volatility increased in September 2008 and decreased in May 2009. The volatility rose gradually for one month and subdued in a similar manner, which suggests that the volatility was not governed by any specific event or government policy. The overall changes in the volatility are similar to the movements of the CDS premium. We also find that the dollar-pound exchange rate experienced a similar pattern of volatility shifts to that of the won-dollar exchange rate. But, the UK foreign exchange market suffered smaller but longer volatility than the Korean one.Since the Autoregressive Conditional Heteroskedastic (ARCH) model was suggested by Engle (1982), the conditional heteroskedastic models have been updated and developed to analyze the volatility of the financial markets. Researchers, including Bollerslev (1986), generalized the ARCH model to GARCH (generalized ARCH) and its variants, such as IGARCH, GARCH-M, and EGARCH. The models are known to describe well the many features of volatility, such as volatility clustering and the leverage effect.1 However, as Schwert (1990) and Engle and Mustaffa (1992) show, the GARCH models imply too much persistence in the conditional variance. To overcome this shortcoming, Cai (1994) and Hamilton and Susmel (1994) incorporate the Markov switching component into the ARCH model. Gray (1996) and Dueker (1997) generalize their model to Markov switching GARCH (hereafter, MS-GARCH) models. …