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Understanding currency fluctuations carries a high level of risk. A currency can slide or spike as a response of an economic indicators revelation or an unexpected political event, both of which are unforeseeable. As foreign investors become more optimistic about the country’s future, a healthier economy usually requires a strong currency. Therefore, it is necessary to assess the exchange rate volatility risk in the context of direct investment in order to develop preventive policy routes that would encourage foreign investors into the country. To this purpose, the autoregressive distributive least square (ARDL) technique has been employed to investigate the symmetric effect of exchange rate volatility on foreign direct investment (FDI) during global financial crises and political regimes from January 2000 to December 2018. In order to eliminate arbitrariness, the study uses the most accredited estimate of volatility, GARCH (1 1), as part of the re-estimation process. Besides this, the interaction has been studied under various regimes to see how the political environment affects foreign market participants’ expectations for future gains. The findings suggest that exchange rate volatility is adversely related to FDI and is a source of decreased net foreign investment in Pakistan. It also illustrates that during times of crises and apolitical regimes, Pakistan’s average FDI falls dramatically. The findings are extended to the context of Pakistan that has seen significant rupee volatility for the past few years. Our study recommends that policymakers should pursue exchange rate measures that promote exchange rate stability, which might assist to minimize risk of exchange rate volatility and so attract higher FDI. It is also crucial to formulate more sustainable investment methods that allow for efficient capital allocation during times of economic uncertainty.

We estimate an AR(1)/GARCH(1, 1) model that shows the impact of natural-gas prices, hydro conditions, and temperatures on wholesale on-peak electricity prices at the Mid-Columbia (Mid-C) trading hub in the Pacific Northwest of the United States. After controlling for the effects of these three factors, prices are seen to exhibit a weak seasonal pattern, but a strong day-of-week pattern. It is also shown that price spikes can persist for several days. Finally, in support of the GARCH hypothesis, Mid-C prices are seen to have a time-dependent variance that primarily moves with natural-gas prices, and that large price variances tend to persist. Thus, even though buyers might cross hedge using natural-gas futures and temperature-based weather futures, the effectiveness of any hedge is compromised by randomness in hydro conditions. To be sure, a buyer can eliminate the electricity price risk by entering into a forward contract, but only at the expense of what is likely to be a large risk premium embodied in the forward price.

We investigate the stock market comovements in Australia, Brazil, Canada, China, Germany, Hong Kong, Japan, Russia, South Africa, the UK, and the USA, both at the market and sectoral level in 2000-2010. Using multivariate GARCH models, our results suggest that the correlation among equity returns during the financial crisis (2008-2010) somewhat increased, suggesting that the crisis represented a common shock to all countries. The U.S. stock market is found to be the most correlated with the stock markets in Brazil, Canada and UK. The correlation of U.S. and Chinese stock market is essentially zero before the crisis; it becomes slightly positive during the crisis. The sectoral indices are less correlated than the market indices over the whole period, but, again, the correlations increase during the crisis.

To improve the quality of service and network performance for the Flash P2P video-on-demand, the prediction Flash P2P network traffic flow is beneficial for the control of the network video traffic. In this paper, a novel prediction algorithm to forecast the traffic rate of Flash P2P video is proposed. This algorithm is based on the combination of the ensemble local mean decomposition (ELMD) and the generalized autoregressive conditional heteroscedasticity (GARCH). The ELMD is used to decompose the original long-related flow into the summation of the short-related flow. Then, the GRACH is utilized to predict the short-related flow. The developed algorithm is tested in a university’s campus network. The predicted results show that our proposed method can further achieve higher accuracy than those obtained by existing algorithms, such as GARCH and Local Mean Decomposition and Generalized AutoRegressive Conditional Heteroskedasticity (LMD-GARCH) while keeping lower computational complexity.

In this paper, we compare the performance of Islamic stock indices (ISI) and conventional stock indices (CSI) from FTSE, DJ, MSCI, S&Ps and Jakarta series using common risk-return metrics. The sample consists of 64 ISI and CSI, and covers the period from 2002 to 2017. The majority of the stock indices are from the Pacific Rim countries’ stock markets. Additionally, we employ the GARCH-M model to examine the impact of past volatility on spot returns. Findings suggest that the ISI are less sensitive to the average market movements compared to the CSI, but surprisingly offer similar raw returns suggesting primary support for the low risk-high return paradox. On further examination, results reveal that M², Omega, Sharpe and Treynor measures indicate that ISI underperform CSI while Jensen’s alpha and Sortino ratio put ISI ahead of CSI. Moreover, findings show that pre-crisis winners (CSI) were losers during the 2008 crisis but subsequently recovered and ended up with higher returns than ISI. Findings also show that the previous volatility of stock returns can be potentially used for predicting future returns.

It is shown empirically that likelihood function of the GARCH is multi-modal. Hence, the maximum likelihood estimates at local and global maxima will be quantitatively different. Therefore, it is important to start an estimation method with consistent starting value that converge to global maxima. This study compares two estimation methods, BFGS and DE, on the basis of simulation and surface constructed by changing the value of GARCH $(1,1)$ model. DE is superior and consistent throughout the surface, and across distributions. PSX is used as real-world application and it has been found that the estimates obtained from DE are best and unbiased.

We extend generalized autoregressive conditional heteroscedastic (GARCH) errors in the Euclidean plane of the scalar field to the tensor field and to the spinor field ${\mathrm{\text{HP}}}^1$, the so-called spinor garch, S-GARCH. We use the model of S-GARCH to explain the stylized fact in financial time series, the so-called volatility cluster, by using hyperbolic coordinate with induced complex lag of delay time scale in mirror symmetry concept. As the result of this theory, we obtain an equivalent form of Yang–Mills equation for financial time series as the interaction between the behavior of traders, the so-called, fundamentalist, chatlist and noise trader, by using volatility in spinor field with invariant of the gauge group $\mathrm{\text{SO}}(32)$, the so-called modeling of the financial market in icosahedral supersymmetry gauge group.

Analyzing the statistical features of fluctuation is remarkably significant for financial risk identification and measurement. In this study, the asymmetric detrended fluctuation analysis (A-DFA) method was applied to evaluate asymmetric multifractal scaling behaviors in the Shanghai and New York gold markets. Our findings showed that the multifractal features of the Chinese and international gold spot markets were asymmetric. The gold return series persisted longer in an increasing trend than in a decreasing trend. Moreover, the asymmetric degree of multifractals in the Chinese and international gold markets decreased with the increase in fluctuation range. In addition, the empirical analysis using sliding window technology indicated that multifractal asymmetry in the Chinese and international gold markets was characterized by its time-varying feature. However, the Shanghai and international gold markets basically shared a similar asymmetric degree evolution pattern. The American subprime mortgage crisis (2008) and the European debt crisis (2010) enhanced the asymmetric degree of the multifractal features of the Chinese and international gold markets. Furthermore, we also make statistical tests for the results of multifractatity and asymmetry, and discuss the origin of them. Finally, results of the empirical analysis using the threshold autoregressive conditional heteroskedasticity (TARCH) and exponential generalized autoregressive conditional heteroskedasticity (EGARCH) models exhibited that good news had a more significant effect on the cyclical fluctuation of the gold market than bad news. Moreover, good news exerted a more significant effect on the Chinese gold market than on the international gold market.

Monte Carlo estimators of sensitivity indices and the marginal density of the price dynamics are derived for the Hobson-Rogers stochastic volatility model. Our approach is based mainly upon the Kolmogorov backward equation by making full use of the Markovian property of the dynamics given the past information. Some numerical examples are presented with a GARCH-like volatility function and its extension to illustrate the effectiveness of our formulae together with a clear exhibition of the skewness and the heavy tails of the price dynamics.

We investigate the effectiveness of two recent regulatory policy changes on market efficiency in the Chinese A- and B-share markets. Overall, the opening of the B-share market to domestic Chinese investors and the limited opening of the A-share market to foreign investors increase market efficiency. The opening of the B-share market significantly reduces the price differential between A- and B-shares. Furthermore, there is no longer feedback in returns between the two markets in recent years. Our results provide evidence that there is no detrimental effect to market efficiency by integrating Chinese investors to international markets and foreign investors to the Chinese stock markets.

Using returns of 4,916 stocks from 22 developed countries and 15 developing countries, this study examines the relative magnitude of conditional volatility and the international market systematic risk of stock prices in countries at different developmental stages and in various geographical areas. Consistent with the finding of Bekaert et al. (2008), the results of non-parametric Mann-Whitney tests suggest that the stock prices in emerging markets are riskier than the ones in developed countries, measured by both conditional volatility and global beta. Our empirical findings also support the geographical variation in stock risks. Specifically, the equity values in Southeast Asia, South Europe, and Latin America are more volatile than the rest of the world. Similar results can be found in the country-level tests. The time-series analysis suggests that the stock returns in high risk countries tend to be less volatile but the conditional volatility of stock return in less risky countries leans to increase.

The model in this paper is similar to Brailsford and Faff (1997), using a conditional CAPM model with the GARCH-M framework, but with a significant additional dummy term (in the conditional mean of the share return) that will help explain the models better in both economic and statistical sense. The relatively simpler asymmetric model in this paper is compatible to other more complex asymmetric models and hence should be easier to model and explain for practical purposes. The model in this paper is also a more effective model, in both economical and statistical terms, as compared to some other models in the GARCH family as it captures the asymmetric effect in the modeling process in both the conditional first and second moments. The findings in this paper have contributed in re-evaluating the nature and process of time varying behavior of time series of stock returns and will provide researchers and practitioners additional options and incentives to explore for future research. We have also provided statistical and practical reasons to support these findings.

This paper studies the model risk; the risk of selecting a model for estimating the Value-at-Risk (VaR). By considering four GARCH-type volatility processes exponentially weighted moving average (EWMA), generalized autoregressive conditional heteroskedasticity (GARCH), exponential GARCH (EGARCH), and fractionally integrated GARCH (FIGARCH), we evaluate the performance of the estimated VaRs using statistical tests including the Kupiec's likelihood ratio (LR) test, the Christoffersen's LR test, the CHI (Christoffersen, Hahn, and Inoue) specification test, and the CHI nonnested test. The empirical study based on Shanghai Stock Exchange A Share Index indicates that both EGARCH and FIGARCH models perform much better than the other two in VaR computation and that the two CHI tests are more suitable for analyzing model risk.

Information provided by the US Department of Homeland Security regarding potential terrorist attacks significantly affects US Treasury securities markets. When the government announces heightened terror alert levels, investors' perceptions of risk increase and investors purchase 1-month and 1-year Treasury bills and 3-year, 5-year, 7-year, and 10-year US Treasuries in a "flight-to-quality" episode. Partial anticipation of increased threat level announcements is stronger than the anticipation of announcements regarding the federal funds rate during the 10 days prior to an announcement.

Simple, fast methods for modeling the portfolio distribution corresponding to a non-elliptical, leptokurtic, asymmetric, and conditionally heteroskedastic set of asset returns are entertained. Portfolio optimization via simulation is demonstrated, and its benefits are discussed. An augmented mixture of normals model is shown to be superior to both standard (no short selling) Markowitz and the equally weighted portfolio in terms of out of sample returns and Sharpe ratio performance.

This study investigates whether the trading range breakout technical trading rule can be applied in exchange-traded funds. Using the samples of crude oil exchange-traded funds, namely USO, USL, UCO, and DBO, that track West Texas intermediate (WTI), the results indicate that the trading range breakout technical trading rule outperforms the benchmark buy-and-hold strategy. In addition, a volatility-based trading range breakout technical trading rule is proposed to enhance trading performance. The results suggest that the proposed TGARCH-MA can be used as a technical trading rule to assist investors and fund managers interested in using the trading range breakout in exchange-traded funds.