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The current paper aims to fill a gap in the literature by analyzing the nature of volatility on the Karachi Stock Exchange (KSE) 100 index of the KSE, and develop an understanding as to which model is most suitable for measuring volatility among those used. The study contributes significantly to the literature as, compared with the limited previous studies of Pakistan undertaken in the past, it covers three types of data (i.e. daily, weekly and monthly) for the whole period from the introduction of the KSE 100 index on November 2, 1991 to December 31, 2013. In addition, to analyze the impact of global financial crises upon volatility, the data have been divided into pre-crisis (1991-2007) and post-crisis (2008-2013) periods.

This study has used an advanced set of volatility models such as autoregressive conditional heteroskedasticity [ARCH (1)], generalized autoregressive conditional heteroskedasticity [GARCH (1, 1)], GARCH in mean [GARCH-M (1, 1)], exponential GARCH [E-GARCH (1, 1)], threshold GARCH [T-GARCH (1, 1)], power GARCH [P-GARCH (1, 1)] and also a simple exponentially weighted moving average (EWMA) model.

The results reveal that daily, weekly and monthly return series show non-normal distribution, stationarity and volatility clustering. However, the heteroskedasticity is absent only in the monthly returns making only the EWMA model usable to measure the volatility level in the monthly series. The P-GARCH (1, 1) model proved to be a better model for modeling volatility in the case of daily returns, while the GARCH (1, 1) model proved to be the most appropriate for weekly data based on the Schwarz information criterion (SIC) and log likelihood (LL) functionality. The study shows high persistence of volatility, a mean reverting process and an absence of a risk premium in the KSE market with an insignificant leverage effect only in the case of weekly returns. However, a significant leverage effect is reported regarding the daily series of the KSE 100 index. In addition, to analyze the impact of global financial crises upon volatility, the findings show that the subperiods demonstrated a slightly low volatility and the global economic crisis did not cause a rise in volatility levels.

Previously, the literature about volatility modeling in Pakistan’s markets has been limited to a few models of relatively small sample size. The current thesis has attempted to overcome these limitations and used diverse models for three types of data series (daily, weekly and monthly). In addition, the Pakistani economy has been beset by turmoil throughout its history, experiencing a range of shocks from the mild to the extreme. This paper has measured the impact of those shocks upon the volatility levels of the KSE.

The purpose of this paper is to assess the informational efficiency of S&P CNX Nifty index options in Indian securities market. The S&P CNX Nifty index is a leading stock index of India, consists of 50 most frequently traded securities listed on NSE. For the purpose, the study covers a period of six years from 4 June 2001 (the starting date for index options in India) to 30 June 2007.

The informational efficiency of implied volatilities (IVs) has been tested vis‐à‐vis select conditional volatilities models, namely, GARCH(1,1) and EGARCH(1,1). The tests have been carried out for “in‐the‐sample” as well as “out‐of‐the‐sample” forecast efficiency of implied volatilities.

The results of the study reveal that implied volatilities do not impound all the information available in the past returns; therefore, these are indicative of the violation of efficient market hypothesis in the case of S&P CNX Nifty index options market in India.

The finance managers, in Indian context, should rely on conditional volatility models (especially the EGARCH(1,1) model) compared to IV‐based forecasts to predict volatility for the horizon of one week. The stock exchanges and market regulator (SEBI) need to take certain initiatives in terms of extending the short‐selling facility and start trading of volatility index (VIX) to enhance the accuracy of IV‐based forecasts.

The paper addresses an issue which is still unexplored in the context of Indian securities market and in that sense makes an important contribution to literature on microstructure studies.

Investors aim for returns when investing in stocks, making return volatility a crucial concern. This study compares symmetric and asymmetric GARCH models to forecast volatility in emerging nations like the G4 countries. Accurate volatility forecasting is vital for investors to make well-informed investment decisions, forming the core purpose of this study.

From January 1993 to May 2021, the study spans four periods, focusing on the global economic crisis of 2008, the Russian crisis of 2015 and the COVID-19 pandemic. Standard generalized autoregressive conditional heteroscedasticity (GARCH), exponential GARCH (E-GARCH) and Glosten-Jagannathan-Runkle GARCH models were employed to analyse the data. Robustness was assessed using the Akaike information criterion, Schwarz information criterion and maximum log-likelihood criteria.

The study's findings show that the E-GARCH model is the best model for forecasting volatility in emerging nations. This is because the E-GARCH model is able to capture the asymmetric effects of positive and negative shocks on volatility.

This unique study compares symmetric and asymmetric GARCH models for forecasting volatility in emerging nations, a novel approach not explored in prior research. The insights gained can aid investors in constructing more effective risk-adjusted international portfolios, offering a better understanding of stock market volatility to inform strategic investment decisions.

This paper aims to analyse the volatility of the fixed income market from 11 countries (Brazil, Russia, India, China, South Africa, Argentina, Chile, Mexico, USA, Germany and Japan) from January 2000 to December 2011 by examining the interbank interest rates from each market.

To the volatility of interest rates returns, the study used models of auto-regressive conditional heteroscedasticity, autoregressive conditional heteroscedasticity (ARCH), generalized autoregressive conditional heteroscedasticity (GARCH), exponential generalized autoregressive conditional heteroscedasticity (EGARCH), threshold generalized autoregressive conditional heteroscedasticity (TGARCH) and periodic generalized autoregressive conditional heteroscedasticity (PGARCH), and a combination of these with autoregressive integrated moving average (ARIMA) models, checking which of these processes were more efficient in capturing volatility of interest rates of each of the sample countries.

The results suggest that for most markets, studied volatility is best modelled by asymmetric GARCH processes – in this case the EGARCH – demonstrating that bad news leads to a higher increase in the volatility of these markets than good news. In addition, the causes of increased volatility seem to be more associated with events occurring internally in each country, as changes in macroeconomic policies, than the overall external events.

It is expected that this study has contributed to a better understanding of the volatility of interest rates and the main factors affecting this market.

Este estudio analiza la volatilidad del mercado de renta fija de once países (Brasil, Rusia, India, China, Sudáfrica, Argentina, Chile, México, Estados Unidos, Alemania y Japón) de enero de 2000 a diciembre de 2011, mediante el examen de las tasas de interés interbancarias de cada mercado.

Para la volatilidad de los retornos de las tasas de interés, se utilizaron modelos de heteroscedasticidad condicional autorregresiva: ARCH, GARCH, EGARCH, TGARCH y PGARCH, y una combinación de estos con modelos ARIMA, comprobando cuáles de los procesos eran más eficientes para capturar la volatilidad de interés de cada uno de los países de la muestra.

Los resultados sugieren que para la mayoría de los mercados estudiados la volatilidad es mejor modelada por procesos GARCH asimétricos —en este caso el EGARCH— demostrando que las malas noticias conducen a un mayor incremento en la volatilidad de estos mercados que las buenas noticias. Además, las causas de una mayor volatilidad parecen estar más asociadas a eventos que ocurren internamente en cada país, como cambios en las políticas macroeconómicas, que los eventos externos generales.

Se espera que este estudio contribuya a un mejor entendimiento de la volatilidad de las tasas de interés y de los principales factores que afectan a este mercado.

Ingreso fijo, Volatilidad, Países emergentes, Modelos ARCH-GARCH

Artículo de investigación

In their seminal papers on ARCH and GARCH models, Engle (1982) and Bollerslev (1986) specified parametric inequality constraints that were sufficient for non-negativity and weak stationarity of the estimated conditional variance function. This paper uses Bayesian methodology to impose these constraints on the parameters of an ARCH(3) and a GARCH(1,1) model. The two models are used to explain volatility in the London Metals Exchange Index. Model uncertainty is resolved using Bayesian model averaging. Results include estimated posterior pdfs for one-step-ahead conditional variance forecasts.

Several empirical studies have proven that emerging countries are attractive destinations for Foreign Institutional Investors (FIIs) because of high expected returns, weak market efficiency and high growth that make them attractive destination for diversification of funds. But higher expected returns come coupled with high risk arising from political and economic instability. This study aims to compare the linear (symmetric) and non-linear (asymmetric) Generalized Autoregressive Conditional Heteroscedasticity (GARCH) models in forecasting the volatility of top five major emerging countries among E7, that is, China, India, Indonesia, Brazil and Mexico.

The volatility of financial markets of five major emerging countries has been empirically investigated for a period of two decades from January 2000 to December 2019 using univariate volatility models including GARCH 1, 1, Exponential Generalized Autoregressive Conditional Heteroscedasticity (E-GARCH 1, 1) and Threshold Generalized Autoregressive Conditional Heteroscedasticity (T-GARCH-1, 1) models. Further, to examine time-varying volatility, the distinctions of structural break have been captured in view of the global financial crisis of 2008. Thus, the period under the study has been segregated into pre- and post-crisis, that is, January 2001–December 2008 and January 2009–December 2019, respectively.

The findings indicate that GARCH (1, 1) model is superior to non-linear GARCH models for forecasting volatility because the effect of leverage is insignificant. China has been considered as most volatile, whereas India is volatile but positively skewed and Indonesia is the least volatile country. The results can help investors in better international diversification of their portfolio and identifying best suitable hedging opportunities.

This study can help investors to construct a more risk-adjusted returns international portfolio. Further, it adds to the scant literature available on the inconclusive debate on the choice of linear versus non-linear models to forecast market volatility.

Earlier studies related to univariate volatility models are mostly applications of the models. Only few studies have considered the robustness while applying the models. However, none of the studies to the best of the authors’ searches have considered these models for identifying the diversification opportunity among the emerging countries. Hence, this study is able to derive diversification and hedging opportunities by applying wide ranges of the statistical applications and models, that is, descriptive, correlations and univariate volatility models. It makes the study more rigorous and unique compared to the previous literature.

Volatility is a permanent behavior of the stock market around the globe. The presence of the volatility in the stock price makes it possible to earn abnormal profits by risk seeking investors and creates hesitancy among risk averse investors as high volatility means high return with high risk. Investors always consider market volatility before making any investment decisions. Random fluctuations are termed as volatility of stock market. Volatility in financial markets is reflected because of uncertainty in the price and return, unexpected events and non-constant variance that can be measured through the generalized autoregressive conditional heteroscedasticity family models and that will give an insight for investment decision-making.

Daily data of the closing value of Bombay Stock Exchange (BSE) (Sensex) and National Stock Exchange (NSE) (Nifty) from April 1, 2011 to March 31, 2017 is collected through the web-portal of BSE (www.bseindia.com) and NSE (www.nseindia.com) for the analysis purpose.

The outcome of the study suggested that P-GARCH model is most suitable to predict and forecast the stock market volatility for both the markets.

Future research can be extended to other stock market segments and sectoral indices to explore and forecast the volatility to establish a trade-off between risk and return.

The results of previous studies available are not conducive to this research, and very limited scholarly work is available in the Indian context, so required to be re-explored to identify the appropriate model to predict market volatility.

This paper aims to examine whether the crypto-currencies’ market returns are symmetric or asymmetric informative, through analysing the daily logarithmic returns of bitcoin currency over the period of 2011-2017.

In doing so, the symmetric informative analysis is estimated by applying the generalised auto-regressive conditional heteroscedasticity (GARCH) (1,1) model, whereas asymmetric informative or leverage effects analysis is estimated by exponential GARCH (1,1), asymmetric power ARCH (1,1) and threshold GARCH (1,1) models. In addition, the generalized autoregressive conditional heteroskedasticity in mean (GARCH-M (1,1)) was applied to examine whether the risk-return trade-off phenomenon was persistent in crypto-currencies market.

The main findings indicate that bitcoin market return or volatility is symmetric informative and has a long memory to persist in the future. Furthermore, the sympatric volatility is found to be more sensitive to its past values (lagged) than to the new shock of the market values. However, asymmetric informative response of volatility to the negative and the positive shocks do not exist in the bitcoin market or, in other words, there is no leverage effect. This suggests that the bitcoin market is in harmony with the efficient market hypothesis (EMH) with respect to the asymmetric information and violated the EMH with regard to the symmetric information. Hence, the market price or return of bitcoin currency could not be predicted by simply exercising such past market information in the short-run investment. In addition, the estimated coefficient of conditional variance or risk premium (λ) in the mean equation of CHARCH–M (1,1) model is positive however, statistically insignificant. This indicates the absence of risk-return trade-off, in which case the higher market risk will not essentially lead to higher market returns. This paper has proposed that an investment in the crypto-currency market is more appropriate for risk-averse investors than risk takers.

The findings of the study will provide investors with necessary information about the bitcoin market price efficiency, hedging effectiveness and risk management.

The purposes of this article are to evaluate models of stock market risk developed by Robert Engle, and related models (ARCH, GARCH, VAR, etc.); to establish whether prospect theory, cumulative prospect theory, expected utility theory, and market‐risk models (ARCH, GARCH, VAR, etc.) are related and have the same foundations.

The author critiques existing academic work on risk, decision making, prospect theory, cumulative prospect theory, expected utility theory, VAR and other market‐risk models (ARCH, GARCH, etc.) and analyzes the shortcomings of various measures of risk (standard deviation, VAR, etc.).

Prospect theory, cumulative prospect theory, expected utility theory, and market‐risk models are conceptually the same and do not account for many facets of risk and decision making. Risk and decision making are better quantified and modeled using a mix of situation‐specific dynamic, quantitative, and qualitative factors. Belief systems (a new model developed by the author) can better account for the multi‐dimensional characteristics of risk and decision making. The market‐risk models developed by Engle and related models (ARCH, GARCH, VAR, etc.) are inaccurate, do not incorporate many factors inherent in stock markets and asset prices, and thus are not useful and accurate in many asset markets.

Areas for further research include: development of dynamic market‐risk models that incorporate asset‐market psychology, liquidity, market size, frequency of trading, knowledge differences among market participants, and trading rules in each market; and further development of concepts in belief systems.

Decision making and risk assessment are multi‐criteria processes that typically require some processing of information, and thus cannot be defined accurately by rigid quantitative models. Existing market‐risk models are inaccurate – many international banks, central banks, government agencies, and financial institutions use these models for risk management, capital allocation, portfolio management, and investments, and thus the international financial system may be compromised.

The critiques, ideas, and new theories in the article were all developed by the author. The issues discussed in the article are relevant to a multiplicity of situations and people in any case that requires decision making and risk assessment.

Apart from the well-known, high persistence of daily financial volatility data, there is also a short correlation structure that reverts to the mean in less than a month. We find this short correlation time scale in six different daily financial time series and use it to improve the short-term forecasts from generalized auto-regressive conditional heteroskedasticity (GARCH) models. We study different generalizations of GARCH that allow for several time scales. On our holding sample, none of the considered models can fully exploit the information contained in the short scale. Wavelet analysis shows a correlation between fluctuations on long and on short scales. Models accounting for this correlation as well as long-memory models for absolute returns appear to be promising.