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Forecasting Realized Intra-Day Volatility and Value at Risk

Forecasting Realized Intra-Day Volatility and Value at Risk
Author: Stavros Antonios Degiannakis
Publisher:
Total Pages: 24
Release: 2018
Genre:
ISBN:

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Predicting the one-step-ahead volatility is of great importance in measuring and managing investment risk more accurately. Taking into consideration the main characteristics of the conditional volatility of asset returns, I estimate an asymmetric Autoregressive Conditional Heteroscedasticity (ARCH) model. The model is extended to also capture i) the skewness and excess kurtosis that the asset returns exhibit and ii) the fractional integration of the conditional variance. The model, which takes into consideration both the fractional integration of the conditional variance as well as the skewed and leptokurtic conditional distribution of innovations, produces the most accurate one-day-ahead volatility forecasts. The study recommends to portfolio managers and traders that extended ARCH models generate more accurate volatility forecasts of stock returns.


VAR and Intraday Volatility Forecasting

VAR and Intraday Volatility Forecasting
Author: Timotheos Angelidis
Publisher:
Total Pages: 12
Release: 2018
Genre:
ISBN:

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We evaluate the performance of symmetric and asymmetric ARCH models in forecasting one-day-ahead Value-at-Risk (VaR) and realized intra day volatility of two equity indices in the Athens Stock Exchange (ASE). Under the framework of three distributional assumptions, we find out that the most appropriate method for the Bank index in forecasting the one-day-ahead VaR is the symmetric model with normally distributed innovations, while the asymmetric model with asymmetric conditional distribution applies for the General index. On the other hand, the asymmetric model tracks closer the one-step-ahead intra day realized volatility with conditional normally distributed innovations for the Bank index but with asymmetric and leptokurtic distributed innovations for the General index. Therefore, as concerns the Greek stock market, there are adequate methods for predicting market risk but it does not seem to be a specific model that is the most accurate for all the forecasting tasks.


Forecasting Daily Stock Volatility

Forecasting Daily Stock Volatility
Author: Ana-Maria Fuertes
Publisher:
Total Pages: 72
Release: 2013
Genre:
ISBN:

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Several recent studies advocate the use of nonparametric estimators of daily price variability that exploit intraday information. This paper compares four such estimators, realised volatility, realised range, realised power variation and realised bipower variation, by examining their in-sample distributional properties and out-of-sample forecast ranking when the object of interest is the conventional conditional variance. The analysis is based on a 7-year sample of transaction prices for 14 NYSE stocks. The forecast race is conducted in a GARCH framework and relies on several loss functions. The realized range fares relatively well in the in-sample fit analysis, for instance, regarding the extent to which it brings normality in returns. However, overall the realised power variation provides the most accurate 1-day-ahead forecasts. Forecast combination of all four intraday measures produces the smallest forecast errors in about half of the sampled stocks. A market conditions analysis reveals that the additional use of intraday data on day t-1 to forecast volatility on day t is most advantageous when day t is a low volume or an up-market day. The results have implications for value-at-risk analysis.


VaR and Intra-Day Volatility Forecasting

VaR and Intra-Day Volatility Forecasting
Author: Timotheos Angelidis
Publisher:
Total Pages: 12
Release: 2005
Genre:
ISBN:

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We evaluate the performance of symmetric and asymmetric ARCH models in forecasting one-day-ahead Value-at-Risk (VaR) and realized intra-day volatility of two equity indices in the Athens Stock Exchange (ASE). Under the framework of three distributional assumptions, we find out that the most appropriate method for the Bank index in forecasting the one-day-ahead VaR is the symmetric model with normally distributed innovations, while the asymmetric model with asymmetric conditional distribution applies for the General index. On the other hand, the asymmetric model tracks closer the one-step-ahead intra-day realized volatility with conditional normally distributed innovations for the Bank index but with asymmetric and leptokurtic distributed innovations for the General index. Therefore, as concerns the Greek stock market, there are adequate methods for predicting market risk but it does not seem to be a specific model that is the most accurate for all the forecasting tasks.


Modelling Daily Value-at-Risk Using Realized Volatility and Arch Type Models

Modelling Daily Value-at-Risk Using Realized Volatility and Arch Type Models
Author: Pierre Giot
Publisher:
Total Pages: 25
Release: 2003
Genre:
ISBN:

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In this paper we show how to compute a daily VaR measure for two stock indexes (CAC40 and SP500) using the one-day-ahead forecast of the daily realized volatility. The daily realized volatility is equal to the sum of the squared intraday returns over a given day and thus uses intraday information to define an aggregated daily volatility measure. While the VaR specification based on an ARFIMAX(0,d,1)-skewed Student model for the daily realized volatility provides adequate one-day-ahead VaR forecasts, it does not really improve on the performance of a VaR model based on the skewed Student APARCH model and estimated using daily data. Thus, for the two financial assets considered in an univariate framework, both methods seem to be equivalent. This paper also shows that daily returns standardized by the square root of the one-day-ahead forecast of the daily realized volatility are not normally distributed.


Forecasting One-Day-Ahead VAR and Intra-Day Realized Volatility in the Athens Stock Exchange Market

Forecasting One-Day-Ahead VAR and Intra-Day Realized Volatility in the Athens Stock Exchange Market
Author: Timotheos Angelidis
Publisher:
Total Pages: 18
Release: 2007
Genre:
ISBN:

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We evaluate the performance of symmetric and asymmetric ARCH models in forecasting one-day-ahead Value-at-Risk (VaR) and realized intra day volatility of two equity indices in the Athens Stock Exchange (ASE). Under the framework of three distributional assumptions, we find out that the most appropriate method for the Bank index in forecasting the one-day-ahead VaR is the symmetric model with normally distributed innovations, while the asymmetric model with asymmetric conditional distribution applies for the General index. On the other hand, the asymmetric model tracks closer the one-step-ahead intra day realized volatility with conditional normally distributed innovations for the Bank index but with asymmetric and leptokurtic distributed innovations for the General index. Therefore, as concerns the Greek stock market, there are adequate methods for predicting market risk but it does not seem to be a specific model that is the most accurate for all the forecasting tasks.


Daily VAR Forecasts with Realized Volatility and GARCH Models

Daily VAR Forecasts with Realized Volatility and GARCH Models
Author: Barbara Bedowska-Sojka
Publisher:
Total Pages:
Release: 2017
Genre:
ISBN:

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In this paper we evaluate alternative volatility forecasting methods under Value at Risk (VaR) modelling. We calculate one-step-ahead forecasts of daily VaR for the WIG20 index quoted on the Warsaw Stock Exchange within the period from 2007 to 2011. Our analysis extends the existing research by broadening the class of the models, including both the GARCH class models based on daily data and models for realized volatility based on intraday returns (HAR-RV, HAR-RV-J and ARFIMA). We find that the VaR estimates obtained from the models for daily returns and realized volatility give comparable results. Both long memory features and asymmetry are found to improve the VaR forecasts. However, when loss functions are considered, the models based on daily data allow minimizing regulatory loss function, whereas the models based on realized volatility allow minimizing the opportunity cost of capital.


Modelling and Forecasting Intraday Market Risk with Application to Stock Indices

Modelling and Forecasting Intraday Market Risk with Application to Stock Indices
Author: Abhay Kumar Singh
Publisher:
Total Pages: 25
Release: 2014
Genre:
ISBN:

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On the afternoon of May 6, 2010 the Dow Jones Industrial Average (DJIA) plunged about 1000 points (about 9%) in a matter of minutes before rebounding almost as quickly. This was the biggest one day point decline on an intraday basis in the DJIA's history. An almost similar dramatic change in intraday volatility was observed on April 4, 2000 when the DJIA dropped by 4.8%. These historical events present a very compelling argument for the need for robust econometrics models which can forecast intraday asset volatility. There are numerous models available in the finance literature to model financial asset volatility. Various Autoregressive Conditional Heteroskedastic (ARCH) time series models are widely used for modelling daily (end of day) volatility of the financial assets. The family of basic GARCH models works well for modelling daily volatility but they are proven to be not as efficient for intraday volatility. The last two decades have seen some research augmenting the GARCH family of models to forecast intraday volatility, the Multiplicative Component GARCH (MCGARCH) model of Engle & Sokalska (2012) being the most recent of them. MCGARCH models the conditional variance as the multiplicative product of daily, diurnal, and stochastic intraday volatility of the financial asset. In this paper we use the MCGARCH model to forecast the intraday volatility of Australia's S&P/ASX-50 stock market index and the USA Dow Jones Industrial Average (DJIA) stock market index. We also use the model to forecast their intraday Value at Risk (VaR) and Expected Shortfall (ES). As the model requires a daily volatility component, we test a GARCH based estimate of the daily volatility component against the daily realized volatility (RV) estimates obtained from the Heterogeneous Autoregressive model for Realized Volatility (HARRV). The results in the paper show that 1 minute VaR forecasts obtained from the MCGARCH model using the HARRV based daily volatility component outperform the ones obtained using the GARCH based daily volatility component.


Essays on the Economic Value of Intraday Covariation Estimators for Risk Prediction

Essays on the Economic Value of Intraday Covariation Estimators for Risk Prediction
Author: Wei Liu
Publisher:
Total Pages:
Release: 2012
Genre:
ISBN:

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This thesis investigates the economic value of incorporating intraday volatility estimators into the volatility forecasting process. The increased reliance on volatility forecasting in the financial industry has intensified the need for more rigorous analysis from an economic perspective instead of merely statistical point of view. A better understanding of the available methods has implications for portfolio optimization, volatility trading and risk management. More recently, volatility of asset returns was once again under spotlight during the 2008-2009 financial crisis. The study contributes to the extant volatility forecasting literature in three areas. First, it addresses the question of how to practically and effectively exploit intraday price information for variance and covariance modelling and forecasting. Second, it addresses the development of an 'optimal' intraday volatility model that accommodates market practitioners preferences. Third, it evaluates the economic value of combining realized (intraday) volatility estimators for utilizing unique information embedded in each estimator. The thesis is organised as follows. One of the most visible indicators of the crisis that captured the attention of the financial industry was the extremely high level of asset return volatility. This uncertainty prompted much interest for a more accurate, yet practically applicable approach for volatility forecasting. Chapter 2 introduces the various realized volatility estimators, volatility forecasting procedures and their corresponding realized extensions used in our subsequent empirical investigations. Chapter 3 evaluates the economic value of various intraday covariance estimation approaches for mean-variance portfolio optimization. Economic loss functions overwhelmingly favour intraday covariance matrix models instead of their daily counterparts. The constant conditional correlation (CCC) augmented with realized volatility produces the highest economic value when applied with a time-varying volatility timing strategy. Chapter 4 compares the practical value of intraday based single index (univariate) and portfolio (multivariate) models through the lens of Value-at-Risk (VaR) forecasting. VaR predictions are generated from standard daily univariate or multivariate GARCH models, as well as GARCH models extended with ARFIMA forecasted realized measures. Conditional coverage test results indicate that intraday models, both univariate and multivariate ones, outperform their daily counterparts by providing more accurate VaR forecasts. Chapter 5 investigates the economic value of combining intraday volatility estimators for volatility trading. The simulated option trading results indicate that a naive combination of an intraday estimator and implied volatility cannot be outperformed by the best individual estimator. In addition, trading performance can be further boosted by applying more complex combination models such as a regression based combination of 42 single volatility estimators.


Volatility and Correlation

Volatility and Correlation
Author: Riccardo Rebonato
Publisher: John Wiley & Sons
Total Pages: 864
Release: 2005-07-08
Genre: Business & Economics
ISBN: 0470091401

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In Volatility and Correlation 2nd edition: The Perfect Hedger and the Fox, Rebonato looks at derivatives pricing from the angle of volatility and correlation. With both practical and theoretical applications, this is a thorough update of the highly successful Volatility & Correlation – with over 80% new or fully reworked material and is a must have both for practitioners and for students. The new and updated material includes a critical examination of the ‘perfect-replication’ approach to derivatives pricing, with special attention given to exotic options; a thorough analysis of the role of quadratic variation in derivatives pricing and hedging; a discussion of the informational efficiency of markets in commonly-used calibration and hedging practices. Treatment of new models including Variance Gamma, displaced diffusion, stochastic volatility for interest-rate smiles and equity/FX options. The book is split into four parts. Part I deals with a Black world without smiles, sets out the author’s ‘philosophical’ approach and covers deterministic volatility. Part II looks at smiles in equity and FX worlds. It begins with a review of relevant empirical information about smiles, and provides coverage of local-stochastic-volatility, general-stochastic-volatility, jump-diffusion and Variance-Gamma processes. Part II concludes with an important chapter that discusses if and to what extent one can dispense with an explicit specification of a model, and can directly prescribe the dynamics of the smile surface. Part III focusses on interest rates when the volatility is deterministic. Part IV extends this setting in order to account for smiles in a financially motivated and computationally tractable manner. In this final part the author deals with CEV processes, with diffusive stochastic volatility and with Markov-chain processes. Praise for the First Edition: “In this book, Dr Rebonato brings his penetrating eye to bear on option pricing and hedging.... The book is a must-read for those who already know the basics of options and are looking for an edge in applying the more sophisticated approaches that have recently been developed.” —Professor Ian Cooper, London Business School “Volatility and correlation are at the very core of all option pricing and hedging. In this book, Riccardo Rebonato presents the subject in his characteristically elegant and simple fashion...A rare combination of intellectual insight and practical common sense.” —Anthony Neuberger, London Business School