Traditional portfolio optimization typically relies on a single fitted return distribution, thus ignores non-normality and uncertainty across distributional states. Mean–variance–ambiguity (MVA) models, motivated by the smooth-ambiguity preferences of Klibanoff, Marinacci, and Mukerji (2005) and the KMM-to-MVA Arrow–Pratt reduction of Maccheroni, Marinacci, and Ruffino (2013), extend conventional risk penalties to account for distributional uncertainty, but they missed how state-conditional return distributions affect portfolio optimization stability. We develop Deep Mean–Variance–Ambiguity (Deep MVA) to resolve this gap by learning state-conditional return distributions and embedding the resulting conditional information loss into the ambiguity penalty. The resulting local certainty equivalent combines reduced-law mean–variance risk with a quadratic penalty for second-order disagreement. Conditional-mixture state resolution yields a Deep ambiguity covariance equal to the Traditional ambiguity covariance plus a positive-semidefinite state-feature increment. This increment is the conditional L2 loss from averaging state-specific distributions before optimization. On compact convex feasible sets, we show that the state-resolving program has stronger ambiguity-relevant curvature, lower mean-input sensitivity, and a unique global solution under restricted positive curvature or a common ridge; its projected iterations converge linearly. An LSTM-MDN learns state-conditional distribution densities from 60-minute bars, and Probability and VoV scores enter weekly MVA, with GARCH_Resid as a comparator. Tests on the SSE 50, CSI 300, and CSI 500 universes from 2017–2025 find statistically significant Sharpe out-of-sample improvements over Traditional MVA and MVO across all three universes and ambiguity specifications.

This paper proposes the two-component realized EGARCH model with dynamic jump intensity (hereafter REGARCH-C-DJI model) to model and forecast stock market volatility. The key feature of our REGARCH-C-DJI model is its ability to exploit the high-frequency information as well as to capture the long memory volatility and jump dynamics. An empirical application to Shanghai Stock Exchange Composite (SSEC) index data shows the presence of high persistence of volatility and dynamic jumps in China’s stock market. More importantly, the REGARCH-C-DJI model dominates the GARCH, EGARCH, REGARCH and REGARCH-C models in terms of out-of-sample forecast performance. Our findings highlight the importance of accommodating the realized volatility, volatility components and jump dynamics in forecasting stock market volatility.

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 investigates the pricing and hedging of a new volatility derivative in Mainland China, called volatility-linked notes. Firstly, we describe its underlying volatility-historical volatility of SHSCI and its specific clauses, then calibrate the underlying volatility using GARCH(1,1). It finds that the mean-reverting phenomenon of SHSCI volatility exists. Secondly, we propose two pricing model using replicated method and Monte-Carlo simulation, respectively. It works out similar outcomes. Finally, a Delta-hedging scheme of the volatility-linked notes is shown, however, the estimated result is not satisfactory as the absence of more efficient hedging instruments like index future.

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.

We propose a new joint model of intraday returns and durations to study the dynamics of several Chinese stocks. We include IBM from the U.S. market for comparison purposes. Flexible innovation distributions are used for durations and returns, and the total variance of returns is decomposed into different volatility components associated with different transaction horizons. Our new model strongly dominates existing specifications in the literature. The conditional hazard functions are non-monotonic and there is strong evidence for different volatility components. Although diurnal patterns, volatility components, and market microstructure implications are similar across the markets, there are interesting differences. Durations for lightly traded Chinese stocks tend to carry more information than heavily traded stocks. Chinese investors usually have longer investment horizons, which may be explained by the specific trading rules in China.

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.