Expected shortfall in the presence of asymmetry and long memory

2017 ◽  
Vol 29 (2) ◽  
pp. 132-151 ◽  
Author(s):  
Thomas Walther
Keyword(s):  
Risk Management ◽  
Stock Market ◽  
Long Memory ◽  
Value At Risk ◽  
Expected Shortfall ◽  
Memory Effects ◽  
Garch Models ◽  
Stock Market Volatility ◽  
Conditional Volatility ◽  
Content Type

Purpose This study aims to analyse the conditional volatility of the Vietnam Index (Ho Chi Minh City) and the Hanoi Exchange Index (Hanoi) with a specific focus on their application to risk management tools such as Expected Shortfall (ES). Design/methodology/approach First, the author tests both indices for long memory in their returns and squared returns. Second, the author applies several generalised autoregressive conditional heteroskedasticity (GARCH) models to account for asymmetry and long memory effects in conditional volatility. Finally, the author back tests the GARCH models’ forecasts for Value-at-Risk (VaR) and ES. Findings The author does not find long memory in returns, but does find long memory in the squared returns. The results suggest differences in both indices for the asymmetric impact of negative and positive news on volatility and the persistence of shocks (long memory). Long memory models perform best when estimating risk measures for both series. Practical implications Short-time horizons to estimate the variance should be avoided. A combination of long memory GARCH models with skewed Student’s t-distribution is recommended to forecast VaR and ES. Originality/value Up to now, no analysis has examined asymmetry and long memory effects jointly. Moreover, studies on Vietnamese stock market volatility do not take ES into consideration. This study attempts to overcome this gap. The author contributes by offering more insight into the Vietnamese stock market properties and shows the necessity of considering ES in risk management. The findings of this study are important to domestic and foreign practitioners, particularly for risk management, as well as banks and researchers investigating international markets.

Modeling Conditional Volatility of the Indian Stock Markets

2005 ◽  
Vol 30 (3) ◽  
pp. 21-38 ◽  
Author(s):  
Madhusudan Karmakar
Keyword(s):  
Stock Market ◽  
Realized Volatility ◽  
Market Volatility ◽  
Garch Models ◽  
Time Varying ◽  
Stock Market Volatility ◽  
Conditional Volatility ◽  
Volatility Clustering ◽  
Share Prices ◽  
Out Of Sample

Traditional econometric models assume a constant one period forecast variance. However, many financial time series display volatility clustering, that is, autoregressive conditional heteroskedasticity (ARCH). The aim of this paper is to estimate conditional volatility models in an effort to capture the salient features of stock market volatility in India and evaluate the models in terms of out-ofsample forecast accuracy. The paper also investigates whether there is any leverage effect in Indian companies. The estimation of volatility is made at the macro level on two major market indices, namely, S&P CNX Nifty and BSE Sensex. The fitted model is then evaluated in terms of its forecasting accuracy on these two indices. In addition, 50 individual companies' share prices currently included in S&P CNX Nifty are used to examine the heteroskedastic behaviour of the Indian stock market at the micro level. The vanilla GARCH (1, 1) model has been fitted to both the market indices. We find: a strong evidence of time-varying volatility a tendency of the periods of high and low volatility to cluster a high persistence and predictability of volatility. Conditional volatility of market return series from January 1991 to June 2003 shows a clear evidence of volatility shifting over the period where violent changes in share prices cluster around the boom of 1992. Though the higher price movement started in response to strong economic fundamentals, the real cause for abrupt movement appears to be the imperfection of the market. The forecasting ability of the fitted GARCH (1, 1) model has been evaluated by estimating parameters initially over trading days of the in-sample period and then using the estimated parameters to later data, thus forming out-of-sample forecasts on two market indices. These out-of-sample volatility forecasts have been compared to true realized volatility. Three alternative methods have been followed to measure three pairs of forecast and realized volatility. In each method, the volatility forecasts are evaluated and compared through popular measures. To examine the information content of forecasts, a regression-based efficiency test has also been performed. It is observed that the GARCH (1, 1) model provides reasonably good forecasts of market volatility. While turning to 50 individual underlying shares, it is observed that the GARCH (1, 1) model has been fitted for almost all companies. Only for four companies, GARCH models of higher order may be more successful. In general, volatility seems to be of a persistent nature. Only eight out of 50 shares show significant leverage effects and really need an asymmetric GARCH model such as EGARCH to capture their volatility clustering which is left for future research. The implications of the study are as follows: The various GARCH models provide good forecasts of volatility and are useful for portfolio allocation, performance measurement, option valuation, etc. Given the anticipated high growth of the economy and increasing interest of foreign investors towards the country, it is important to understand the pattern of stock market volatility in India which is time-varying, persistent, and predictable. This may help diversify international portfolios and formulate hedging strategies.

scholarly journals Previsão de value-at-risk e expected shortfall para mercados emergentes usando modelos FIGARCH

2015 ◽  
Vol 13 (3) ◽  
pp. 394
Author(s):  
Alex Sandro Monteiro De Moraes ◽  
Antonio Carlos Figueiredo Pinto ◽  
Marcelo Cabus Klotzle
Keyword(s):  
At Risk ◽  
Long Memory ◽  
Value At Risk ◽  
Expected Shortfall ◽  
Error Distribution ◽  
Memory Models ◽  
Garch Models ◽  
Daily Data ◽  
Short Memory ◽  
Forecasting Volatility

This paper compares the performance of long-memory models (FIGARCH) with short-memory models (GARCH) in forecasting volatility for calculating value-at-risk (VaR) and expected shortfall (ES) for multiple periods ahead for six emerging markets stock indices. We used daily data from 1999 to 2014 and an adaptation of the Monte Carlo simulation to estimate VaR and ES forecasts for multiple steps ahead (1, 10 and 20 days ), using FIGARCH and GARCH models for four errors distributions. The results suggest that, in general, the FIGARCH models improve the accuracy of forecasts for longer horizons; that the error distribution used may influence the decision about the best model; and that only for FIGARCH models the occurrence of underestimation of the true VaR is less frequent with increasing time horizon. However, the results suggest that rolling sampled estimated FIGARCH parameters change less smoothly over time compared to the GARCH models.

scholarly journals Searching for long memory effects in time series of central Europe stock market indices

2008 ◽  
Vol 56 (3) ◽  
pp. 187-200
Author(s):  
Luboš Střelec
Keyword(s):  
Time Series ◽  
Stock Market ◽  
Central Europe ◽  
Long Memory ◽  
Hurst Exponent ◽  
Financial Time Series ◽  
Memory Effects ◽  
Stock Index ◽  
Source Data ◽  
Independent Process

This article deals with one of the important parts of applying chaos theory to financial and capital markets – namely searching for long memory effects in time series of financial instruments. Source data are daily closing prices of Central Europe stock market indices – Bratislava stock index (SAX), Budapest stock index (BUX), Prague stock index (PX) and Vienna stock index (ATX) – in the period from January 1998 to September 2007. For analysed data R/S analysis is used to calculate the Hurst exponent. On the basis of the Hurst exponent is characterized formation and behaviour of analysed financial time series. Computed Hurst exponent is also statistical compared with his expected value signalling independent process. It is also operated with 5-day returns (i.e. weekly returns) for the purposes of comparison and identification nonperiodic cycles.

scholarly journals Risk Model Validation: An Intraday VaR and ES Approach Using the Multiplicative Component GARCH

Risks ◽  
2019 ◽  
Vol 7 (1) ◽  
pp. 10
Author(s):  
Ravi Summinga-Sonagadu ◽  
Jason Narsoo
Keyword(s):  
Loss Function ◽  
Value At Risk ◽  
Garch Model ◽  
Innovation Process ◽  
Expected Shortfall ◽  
Error Distribution ◽  
Garch Models ◽  
Intraday Data ◽  
Distributional Assumptions ◽  
T Distribution

In this paper, we employ 99% intraday value-at-risk (VaR) and intraday expected shortfall (ES) as risk metrics to assess the competency of the Multiplicative Component Generalised Autoregressive Heteroskedasticity (MC-GARCH) models based on the 1-min EUR/USD exchange rate returns. Five distributional assumptions for the innovation process are used to analyse their effects on the modelling and forecasting performance. The high-frequency volatility models were validated in terms of in-sample fit based on various statistical and graphical tests. A more rigorous validation procedure involves testing the predictive power of the models. Therefore, three backtesting procedures were used for the VaR, namely, the Kupiec’s test, a duration-based backtest, and an asymmetric VaR loss function. Similarly, three backtests were employed for the ES: a regression-based backtesting procedure, the Exceedance Residual backtest and the V-Tests. The validation results show that non-normal distributions are best suited for both model fitting and forecasting. The MC-GARCH(1,1) model under the Generalised Error Distribution (GED) innovation assumption gave the best fit to the intraday data and gave the best results for the ES forecasts. However, the asymmetric Skewed Student’s-t distribution for the innovation process provided the best results for the VaR forecasts. This paper presents the results of the first empirical study (to the best of the authors’ knowledge) in: (1) forecasting the intraday Expected Shortfall (ES) under different distributional assumptions for the MC-GARCH model; (2) assessing the MC-GARCH model under the Generalised Error Distribution (GED) innovation; (3) evaluating and ranking the VaR predictability of the MC-GARCH models using an asymmetric loss function.

Stock market stress from the central counterparty’s perspective

2019 ◽  
Vol 36 (1) ◽  
pp. 51-62
Author(s):  
Barbara Dömötör ◽  
Kata Váradi
Keyword(s):  
Risk Management ◽  
Stock Market ◽  
Stress Measurement ◽  
Risk Measure ◽  
Moving Averages ◽  
Stress Indicators ◽  
Content Type ◽  
Stress Signals ◽  
Relative Spread ◽  
Extreme Returns

Purpose The purpose of this paper is to investigate the possibility of monitoring stress on stock markets from the perspective of a central counterparty (CCP). Due to their balanced positions, CCPs are exposed to extreme price movements in both directions; thus, the major risk for them derives from extreme returns and market illiquidity. The authors examined the connection of the stress alarms of return- and liquidity-based measures to find an objective basis for stress measurement. Design/methodology/approach The authors defined two types of stress measures: indicators based on extreme returns and liquidity. It is suggested that the stress indicators should be based on the existing risk management methodology that examines different risk measure oversteps. The stress signals of the past nine years on the German stock market were analyzed. The authors investigated the connection between the chosen stress measures to obtain a robust measure for alarming stress. Findings Although extreme returns and illiquidity are both characteristics of stress, the correlation of returns- and liquidity-based stress indicators is low when taking daily values. On the other hand, the moving averages of the indicators correlate significantly in the case of measures of downward and upward extreme returns and liquidity measured by the relative spread. The results are robust enough to be used for monitoring stress periods. Originality/value This paper contributes to understanding the characteristics of stress periods and points to the fact that stress signals measured by different aspects can also differ within the same asset class. The moving averages of returns- and relative spread-based indicators, however, could provide a cost-effective quantitative support for the risk management of a CCP and make the margin calculation predictable for clearing members as well.

Stock prices' long memory in China and the United States

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Zhengxun Tan ◽  
Yao Fu ◽  
Hong Cheng ◽  
Juan Liu
Keyword(s):  
Stock Market ◽  
Stock Prices ◽  
Long Memory ◽  
Stock Markets ◽  
Information Disclosure ◽  
Structural Breaks ◽  
Efficient Market Hypothesis ◽  
The United States ◽  
Chinese Stock Market ◽  
Content Type

PurposeThis study aims to examine the long memory as well as the effect of structural breaks in the US and the Chinese stock markets. More importantly, it further explores possible causes of the differences in long memory between these two stock markets.Design/methodology/approachThe authors employ various methods to estimate the memory parameters, including the modified R/S, averaged periodogram, Lagrange multiplier, local Whittle and exact local Whittle estimations.FindingsChina's two stock markets exhibit long memory, whereas the two US markets do not. Furthermore, long memory is robust in Chinese markets even when we test break-adjusted data. The Chinese stock market does not meet the efficient market hypothesis (EMHs), including the efficiency of information disclosure, regulations and supervision, investors' behavior, and trading mechanisms. Therefore, its stock prices' sluggish response to information leads to momentum effects and long memory.Originality/valueThe authors elaborately illustrate how long memory develops by analyzing not only stock market indices but also typical individual stocks in both the emerging China and the developed US, which diversifies the EMH with wider international stylized facts and findings when compared with previous literature. A couple of tests conducted to analyze structural break effects and spurious long memory demonstrate the reliability of the results. The authors’ findings have significant implications for investors and policymakers worldwide.

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