Physical Sciences and Mathematics Commons^™

Reactions Of Stock Market To Monetary Policy Shocks During The Global Financial Crisis: The Nigerian Case, Aliyu Shehu U.R.

CBN Journal of Applied Statistics (JAS)

This paper seeks to assess the reactions of Nigeria’s stock market to monetary policy innovations during the period of global financial crisis on the basis of monthly data over the period January, 2007 to August, 2011. In particular, stock market return was regressed against major monetary policy instruments; money stock (M1, and M2) and monetary policy rate (MPR). The theoretical basis for the paper stems from the works of new classical macroeconomics and rational expectation hypothesis (REH). Lucas (1972) postulated that only the unanticipated monetary shock influences real economic activity. Using the GARCH by developed Engle and Bollerslev (1986) and …

Modeling Time Series With Conditional Heteroscedastic Structure, Ratnayake Mudiyanselage Isuru Panduka Ratnayake

Doctoral Dissertations

"Models with a conditional heteroscedastic variance structure play a vital role in many applications, including modeling financial volatility. In this dissertation several existing formulations, motivated by the Generalized Autoregressive Conditional Heteroscedastic model, are further generalized to provide more effective modeling of price range data well as count data. First, the Conditional Autoregressive Range (CARR) model is generalized by introducing a composite range-based multiplicative component formulation named the Composite CARR model. This formulation enables a more effective modeling of the long and short-term volatility components present in price range data. It treats the long-term volatility as a stochastic component that in …

Garch Modeling Of Value At Risk And Expected Shortfall Using Bayesian Model Averaging, Ismail Kheir

Theses and Dissertations

This thesis conducts Value at Risk (VaR) and Expected Shortfall (ES) estimation using GARCH modeling and Bayesian Model Averaging (BMA). BMA considers multiple models weighted by some information criterion. Through BMA, this thesis finds that VaR and ES estimates can be improved through enhanced modeling of the data generation process.

Predictive Distributions Via Filtered Historical Simulation For Financial Risk Management, Tyson Clark

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

Filtered historical simulation with an underlying GARCH process can be used as a valuable tool in VaR analysis, as it derives risk estimates that are sensitive to the distributional properties of the historical data of the produced predictive density. I examine the applications to risk analysis that filtered historical simulation can provide, as well as an interpretation of the predictive density as a poor man’s Bayesian posterior distribution. The predictive density allows us to make associated probabilistic statements regarding the results for VaR analysis, giving greater measurement of risk and the ability to maintain the optimal level of risk per …

Pricing Asian Options: Volatility Forecasting As A Source Of Downside Risk, Adam T. Diehl

Undergraduate Economic Review

Asian options are a class of derivative securities whose payoffs average movements in the underlying asset as a means of hedging exposure to unexpected market behavior. We find that despite their volatility smoothing properties, the price of an Asian option is sensitive to the choice of volatility model employed to price them from market data. We estimate the errors induced by two common schemes of forecasting volatility and their potential impact upon trading.

Modelling The Common Risk Among Equities Using A New Time Series Model, Jingjia Chu

Electronic Thesis and Dissertation Repository

A new additive structure of multivariate GARCH model is proposed where the dynamic changes of the conditional correlation between the stocks are aggregated by the common risk term. The observable sequence is divided into two parts, a common risk term and an individual risk term, both following a GARCH type structure. The conditional volatility of each stock will be the sum of these two conditional variance terms. All the conditional volatility of the stock can shoot up together because a sudden peak of the common volatility is a sign of the system shock.

We provide sufficient conditions for strict stationarity …

Misspecification Of Variants Of Autoregressive Garch Models And Effect On In-Sample Forecasting, Olusanya E. Olubusoye, Olaoluwa S. Yaya, Oluwadare O. Ojo

Journal of Modern Applied Statistical Methods

Generally, in empirical financial studies, the determination of the true conditional variance in GARCH modelling is largely subjective. In this paper, we investigate the consequences of choosing a wrong conditional variance specification. The methodology involves specifying a true conditional variance and then simulating data to conform to the true specification. The estimation is then carried out using the true specification and other plausible specification that are appealing to the researcher, using model and forecast evaluation criteria for assessing performance. The results show that GARCH model could serve as better alternative to other asymmetric volatility models.

Garch(1,1) With Sifted Gamma-Distributed Errors, Alan C. Budd

Electronic Theses and Dissertations

Typical General Autoregressive Conditional Heteroskedastic (GARCH) processes involve normally-distributed errors, and they model strictly-positive error processes poorly. This thesis will present a method for estimating the parameters of a GARCH(1,1) process with shifted Gamma-distributed errors, conduct a simulation study to test the method, and apply the method to real time series data.

Day Of The Week Effect In Returns And Volatility Of The S&P 500 Sector Indices, Juan Liu

Masters Theses

"Previous studies have shown that returns associated with the stock market or foreign exchange's futures show variations across the day of the week. On such study, that employs a modified GARCH model for estimation, shows that returns associated with the S&P 500 stock index is highest on Wednesday and lowest returns on Monday. The same study shows that volatility is highest on Fridays and lowest on Wednesdays. In this study we investigate if this day-of-the-week effect on returns and volatility is present in the different sectors that constitute the S&P 500 index. The data set used provides daily returns from …

Estimates And Forecasts Of Garch Model Under Misspecified Probability Distributions: A Monte Carlo Simulation Approach, Olaoluwa S. Yaya, Olusanya E. Olubusoye, Oluwadare O. Ojo

Journal of Modern Applied Statistical Methods

The effect of misspecification of correct sampling probability distribution of Generalized Autoregressive Conditionally Heteroscedastic (GARCH) processes is considered. The three assumed distributions are the normal, Student t, and generalized error distributions. The GARCH process is sampled using one of the distributions and the model is estimated based on the three distributions in each sample. Parameter estimates and forecast performance are used to judge the estimated model for performance. The AR-GARCH-GED performed better on the three assumed distributions; even, when Student t distribution is assumed, AR-GARCH-Student t does not perform as the best model.

Asymptotic Theory For Garch-In-Mean Models, Weiwei Liu

Electronic Thesis and Dissertation Repository

The GARCH-in-mean process is an important extension of the standard GARCH (generalized autoregressive conditional heteroscedastic) process and it has wide applications in economics and finance. The parameter estimation of GARCH type models usually involves the quasi-maximum likelihood (QML) technique as it produces consistent and asymptotically Gaussian distributed estimators under certain regularity conditions. For a pure GARCH model, such conditions were already found with asymptotic properties of its QML estimator well understood. However, when it comes to GARCH-in-mean models those properties are still largely unknown. The focus of this work is to establish a set of conditions under which the QML …

Exchange–Rates Volatility In Nigeria: Application Of Garch Models With Exogenous Break, Bala A. Dahiru, Joseph O. Asemota

CBN Journal of Applied Statistics (JAS)

This paper examines exchange–rate volatility with GARCH models using monthly exchange–rate return series from 1985:1 to 2011:7 for Naira/US dollar return and from 2004:1 to 2011:7 for Naira/British Pounds and Naira/Euro returns. The study compare estimates of variants of GARCH models with break in respect of the US dollar rates with exogenously determined break points. Our results reveal presence of volatility in the three currencies and equally indicate that most of the asymmetric models rejected the existence of a leverage effect except for models with volatility break. Evaluating the models through standard information criteria, volatility persistence and the log likelihood …

Asymptotics For The Arc Length Of A Multivariate Time Series And Its Applications As A Measure Of Risk, Tharanga Wickramarachchi

All Dissertations

The necessity of more trustworthy methods for measuring the risk (volatility) of financial assets has come to the surface with the global market downturn This dissertation aims to propose sample arc length of a time series, which provides a measure of the overall magnitude of the one-step-ahead changes over the observation time period, as a new approach for quantifying the risk. The Gaussian functional central limit theorem is proven under finite second moment conditions. Without loss of generality we consider equally spaced time series when first differences of the series follow a variety of popular stationary models including autoregressive moving …

Arma-Garch Model Applied To Exchange-Traded Funds, Rebecca Davis

Open Access Theses & Dissertations

In this paper, time-varying volatility of some of the leading exchange-traded funds are studied. The ARMA mean equation with GARCH errors is used to model the series correlations and the conditional heteroscadesticity in the asset

returns. The conditional distributions of the standardized residuals are assumed to be skew-generalized error distribution. The high kurtosis and fat tail of the returns, were captured in all the data by fitting an ARMA-GARCH model with the conditional distribution of, skew-generalized error distribution.

Furthermore, the sample cross-correlations of these significant exchange-traded funds and the corresponding financial indices they mimic were computed. The empirical conclusion was …

Study Of Volatility Structures In Geophysics And Finance Using Garch Models, Francis Biney

Open Access Theses & Dissertations

This work investigates the underlying volatility processes in earthquake series, explosive series, high frequency (tick) data and financial indices. Furthermore it examines the applicability of a range of GARCH specifications for modeling volatility of these series in order to identify similarities and differences in the volatility structures. The GARCH

variants considered include the basic GARCH, IGARCH, ARFIMA (0,d,0)-GARCH and FIGARCH specifications. In all the applications the methodology provides insight into features of these series volatility.

The Effect Of Garch (1,1) On The Granger Causality Test In Stable Var Models, Panagiotis Mantalos, Ghazi Shukur, Pär Sjölander

Journal of Modern Applied Statistical Methods

Using Monte Carlo methods, the properties of Granger causality test in stable VAR models are studied under the presence of different magnitudes of GARCH effects in the error terms. Analysis reveals that substantial GARCH effects influence the size properties of the Granger causality test, especially in small samples. The power functions of the test are usually slightly lower when GARCH effects are imposed among the residuals compared with the case of white noise residuals.

A Class Of Nonlinear Stochastic Volatility Models, Jun Yu, Zhenlin Yang

Research Collection School Of Economics

This paper proposes a class of nonlinear stochastic volatility models based on the Box-Cox transformation which offers an alternative to the one introduced in Andersen (1994). The proposed class encompasses many parametric stochastic volatility models that have appeared in the literature, including the well known lognormal stochastic volatility model, and has an advantage in the ease with which different specifications on stochastic volatility can be tested. In addition, the functional form of transformation which induces marginal normality of volatility is obtained as a byproduct of this general way of modeling stochastic volatility. The efficient method of moments approach is used …

Forecasting Volatility In European Stock Markets With Non-Linear Garch Models, Giancarlo Forte, Matteo Manera

Matteo Manera

This paper investigates the forecasting performance of three popular variants of the nonlinear GARCH models, namely VS-GARCH, GJR-GARCH and Q-GARCH, with the symmetric GARCH(1,1) model as a benchmark. The application involves ten European stock price indexes. Forecasts produced by each non-linear GARCH model and each index are evaluated using a common set of classical criteria, as well as forecast combination techniques with constant and non-constant weights. With respect to the standard GARCH specification, the non-linear models generally lead to better forecasts in terms of both smaller forecast errors and lower biases. In-sample forecast combination regressions are better than those from …