The objective of this study is to create optimal two-asset portfolios consisting of stocks from Western Europe, the United States, and the BRICS (Brazil, China, India, Russia, and South Africa), as well as sixteen commodity types during the BREXIT period. We utilized dynamic variances and covariances from the GARCH model to derive weights for the two-asset portfolios, with each portfolio consisting of one equity factor and one commodity factor. Subsequently, hedge ratios were calculated for these various assets. Our findings indicate that portfolios consisting of European stocks do not require the inclusion of commodities, whereas the other equities do.

This study examines the price discovery patterns in the three BRICS countries’ stock index futures markets that were launched after 2000 – China, India, and Russia. We detect two structural breaks in these three futures price series and their underlying spot price series, and use them to form subsamples. Employing a Vector Error Correction Model (VECM) and the Hasbrouck (1995) test, we find the price discovery function of stock index futures markets generally improves over time in China and India, but declines in Russia. A closer examination not only confirms the findings of Yang et al. (2012) and Hou and Li (2013) regarding price discovery in China’s stock index markets, but also reveals the inconsistency of futures’ leading role in the price discovery process. Further, we find some evidence of day-of-the-week effects in earlier part of the sample in China, but not in India or Russia. And our GARCH model results show bidirectional volatility spillover between futures and spot in China and India, but only unidirectional in Russia.

In recent years, with the rapid expansion of commercial banks' non-standardized business, the systematic correlation between shadow banking and commercial banks in China has been gradually enhanced, which enables the partial liquidity crisis of shadow banking to spread rapidly to commercial banks, leading to the increased vulnerability of China's financial system. Based on this, we built shadow banking indexes of trusts, securities, private lending and investment, introduced the dynamic correlation coefficient calculated by the dynamic conditional correlation multivariate GARCH model into the improved CoVaR model, and used the DCC-BEKK-MVGARCH-Time-Varying CoVaR Model to measure the risk overflow contribution of shadow banking in China. We find that shadow banking and commercial banks have an inherent relationship. Due to their own risks, different types of shadow banking contribute to the risk spillover to commercial banks in different degrees. The risk correlation between shadow banking and commercial banks fluctuates.

The topic about the nexus of economic fluctuation and financial development in China is being on cutting-edge research. Using monthly time series data from 2001 to 2012 in China, the present paper examines the nexus of fluctuation of economic growth and financial development. Based on an exponential generalized autoregressive conditional heteroskedasticity (EGARCH) model with exogenous variables, the present paper suggests that financial development has statistically significantly reduced fluctuation of economic growth, which is in line with theoretical expectation that financial development as a shock absorber to mitigate economic volatility.

This paper examines whether there is evidence of spillovers of volatility from the Chinese stock market to its neighbours and trading partners, including Australia, Hong Kong, Singapore, Japan and USA. China's increasing integration into the global market may have important consequences for investors in related markets. In order to capture these potential eects, we explore these issues using an Autoregressive Moving Average (ARMA) return equation. A univariate GARCH model is then adopted to test for the persistence of volatility in stock market returns, as represented by stock market indices. Finally, univariate GARCH, multivariate VARMA-GARCH, and multivariate VARMA-AGARCH models are used to test for constant conditional correlations and volatility spillover eects across these markets. Each model is used to calculate the conditional volatility between both the Shenzhen and Shanghai Chinese markets and several other markets around the Pacic Basin Area, including Australia, Hong Kong, Japan, Taiwan and Singapore, during four distinct periods, beginning 27 August 1991 and ending 17 November 2010. The empirical results show some evidence of volatility spillovers across these markets in the pre-GFC periods, but there is little evidence of spillover eects from China to related markets during the GFC. This is presumably because the GFC was initially a US phenomenon, before spreading to developed markets around the globe, so that it was not a Chinese phenomenon.

This study employs the Gerneralised Autoregressive Conditional Heteroskedasticity (GARCH) model to investigate the sensitivity of Chinese bank stock returns to market, interest rate and foreign exchange rate risks. Daily data are used to model these risks over the period 2007 to 2010. The results suggest that market risk is an important factor of Chinese bank stock returns, along with foreign exchange risk. However, interest rates risk tends to be insignificant factors in Chinese bank equity pricing process over the period considered.

In this paper, we derive the corresponding implied VIX formulas under the locally riskneutral valuation relationship proposed by Duan (1995) when various forms of GARCH model are proposed for S&P 500 index. The empirical study shows that the GARCH implied VIX is consistently and significantly lower than the CBOE VIX for all kinds of GARCH model investigated. Moreover, the magnitude of the difference suggests that the GARCH option pricing model is not capable of capturing the variance premium, which indicates the incompleteness of the GARCH option pricing under the locally risk-neutral valuation relationship. The source of this kind of incompleteness is then theoretically analyzed. It is shown that the framework of GARCH option pricing model fails to incorporate the price of volatility risk or variance premium.

This paper examines the impact of idiosyncratic risk on the cross-section of weekly stock returns from 1963 to 2006. I use an exponential GARCH model to forecast expected idiosyncratic volatility and employ a combination of the size e§ect, value premium, return momentum and short-term reversal to measure relative mispricing. I ?nd that stock returns monotonically increase in idiosyncratic risk for relatively undervalued stocks and monotonically decrease in idiosyncratic risk for relatively overvalued stocks. This phenomenon is robust to various subsamples and industries, and cannot be explained by risk factors or ?rm characteristics. Further, transaction costs, short-sale constraints and information uncertainty cannot account for the role of idiosyncratic risk. Overall, these ?ndings are consistent with the limits of arbitrage arguments and demonstrate the importance of idiosyncratic risk as an arbitrage cost.

Volatility long memory is a stylized fact that has been documented for a long time. Existing literature have two ways to model volatility long memory: component volatility models and fractionally integrated volatility models. This paper develops a new fractionally integrated GARCH model, and investigates its performance by using the Standard and Poor’s 500 index returns and cross-sectional European option data. The fractionally integrated GARCH model signi?cantly outperforms the simple GARCH(1, 1) model by generating 37% less option pricing errors. With stronger volatility persistence, it also dominates a component volatility model, who has enjoyed a reputation for its outstanding option pricing performance, by generating 15% less option pricing errors. We also con?rm the fractionally integrated GARCH model’s robustness with the latest option prices. This paper indicates that capturing volatility persistence represents a very promising direction for future study.

This paper examines the impact of idiosyncratic risk on the cross-section of weekly stock returns from 1963 to 2006. I use an exponential GARCH model to forecast expected idiosyncratic volatility and employ a combination of the size effect, value premium, return momentum and short-term reversal to measure relative mispricing. I ?find that stock returns monotonically increase in idiosyncratic risk for relatively undervalued stocks and monotonically decrease in idiosyncratic risk for relatively overvalued stocks. This phenomenon is robust to various subsamples and industries, and cannot be explained by risk factors or ?rm characteristics. Further, transaction costs, short-sale constraints and information uncertainty cannot account for the role of idiosyncratic risk. Overall, these ?findings are consistent with the limits of arbitrage arguments and demonstrate the importance of idiosyncratic risk as an arbitrage cost.