GARCH models with leverage effect : differences and similarities

In this paper, we compare the statistical properties of some of the most popular GARCH models with leverage e?ect when their parameters satisfy the positivity, stationarity and nite fourth order moment restrictions. We show that the EGARCH speci cation is the most exible while the GJR model may have important limitations when restricted to have nite kurtosis. On the other hand, we show empirically that the conditional standard deviations estimated by the TGARCH and EGARCH models are almost identical and very similar to those estimated by the APARCH model. However, the estimates of the QGARCH and GJR models di?er among them and with respect to the other three speci cations

The smooth transition autoregressive target zone model with the Gaussian stochastic volatility and TGARCH error terms with applications

This paper proposes to model the error term in smooth transition autoregressive target zone model as Gaussian with stochastic volatility (STARTZ-SV) or as Student-t with GARCH volatility (STARTZ-TGARCH). Using the dynamics of Norwegian krone exchange rate index, we show that both models produce standardized residuals that are closer to assumed distributions and do not produce a hump in the estimated marginal distribution of exchange rate which is more consistent with theoretical predictions. We apply developed models to test whether the dynamics of oil price can be well approximated by the Krugman’s target zone model. Our estimates of conditional volatility and marginal distribution reject the target zone hypothesis.target zone, oil price, exchange rate, stochastic volatility, griddy Gibbs, smooth transition

Parameterizing Unconditional Skewness in Models for Financial Time Series

In this paper we consider the third-moment structure of a class of nonlinear time series models. Empirically it is often found that the marginal distribution of financial time series is skewed. Therefore it is of importance to know what properties a model should possess if it is to accommodate for unconditional skewness. We consider modelling the unconditional mean and variance using models which respond nonlinearly or asymmetrically to shocks. We investigate the implications these models have on the third moment structure of the marginal distribution and different conditions under which the unconditional distribution exhibits skewness as well as nonzero third-order autocovariance structure. With this respect, the asymmetric or nonlinear specification of the conditional mean is found to be of greater importance than the properties of the conditional variance. Several examples are discussed and, whenever possible, explicit analytical expressions are provided for all third order moments and cross-moments. Finally, we introduce a new tool, shock impact curve, that can be used to investigate the impact of shocks on the conditional mean squared error of the return.asymmetry; GARCH; nonlinearity; stock impact curve; time series; unconditional skewness

Identifying common dynamic features in stock returns

This paper proposes volatility and spectral based methods for cluster analysis of stock returns. Using the information about both the estimated parameters in the threshold GARCH (or TGARCH) equation and the periodogram of the squared returns, we compute a distance matrix for the stock returns. Clusters are formed by looking to the hierarchical structure tree (or dendrogram) and the computed principal coordinates. We employ these techniques to investigate the similarities and dissimilarities between the "blue-chip" stocks used to compute the Dow Jones Industrial Average (DJIA) index.Asymmetric effects, Cluster analysis, DJIA stock returns, Periodogram, Threshold GARCH model, Volatility

Foreign Exchange Interventions in Croatia and Turkey: Should We Give a Damn?

This paper studies the impact of daily official foreign exchange interventions on the exchange rates of two EU candidate countries, namely Croatia and Turkey for the periods from 1996 to 2004 and from 2001 to 2004, respectively. Using the event study methodology and a variety of GARCH models reveals that both the Croatian and the Turkish central banks were in a position to influence, to some extent, the level of the exchange rate during the period studied. This lends support to the view that foreign exchange intervention may be effective to a limited extent in emerging market economies.http://deepblue.lib.umich.edu/bitstream/2027.42/40141/3/wp755.pd

Jump starting GARCH: pricing and hedging options with jumps in returns and volatilities

This paper considers the pricing of options when there are jumps in the pricing kernel and correlated jumps in asset returns and volatilities. Our model nests Duan’s GARCH option models, where conditional returns are constrained to being normal, as well as mixed jump processes as used in Merton. The diffusion limits of our model have been shown to include jump diffusion models, stochastic volatility models and models with both jumps and diffusive elements in both returns and volatilities. Empirical analysis on the S&P 500 index reveals that the incorporation of jumps in returns and volatilities adds significantly to the description of the time series process and improves option pricing performance. In addition, we provide the first-ever hedging effectiveness tests of GARCH option models.Options (Finance) ; Hedging (Finance)

Market Efficiency and the Euro: The case of the Athens Stock Exchange

The behaviour of an emerging market, the Athens Stock Exchange (ASE), after the introduction of the euro is investigated. The underlying assumption is that stock prices would be more transparent; their performance easier to compare; the exchange rate risk eliminated and as a result we expect the new currency to strengthen the argument, in favour of the EMH. The General ASE Composite Index and the FTSE/ASE 20, which consists of “high capitalisation” companies, are used. Five statistical tests are employed to test the residuals of the random walk model: the BDS, McLeod-Li, Engle LM, Tsay and Bicovariance test. Bootstrap and asymptotic values of these tests are estimated. Alternative models from the GARCH family (GARCH, EGARCH and TGARCH) are also presented in order to investigate the behaviour of the series. Lastly, linear, asymmetric and non-linear error correction models are estimated and compared.Non-Linearity, Market Efficiency, Random Walk, GARCH, non- linear error correction

Market efficiency and the Euro: the case of the Athens Stock Exchange

The efficient market hypothesis (EMH) is tested in the case of the Athens Stock Exchange (ASE) after the introduction of the euro. The underlying assumption is that stock prices would be more transparent; their performance easier to compare; the exchange rate risk eliminated and as a result we expect the new currency to strengthen argument in favour of the EMH. The General ASE Composite Index and the FTSE/ASE 20, which consists of “high capitalisation” companies, are used. Five statistical tests are employed to test the residuals of the random walk model: the BDS, McLeod-Li, Engle LM, Tsay and Bicovariance test. Bootstrap as well as asymptotic values of these tests are estimated. Alternative models from the GARCH family (GARCH, EGARCH and TGARCH) are also presented in order to investigate the behaviour of the series. Lastly, linear, asymmetric and non-linear error correction models are estimated and compared

Modelling and Forecasting Volatility of Returns on the Ghana Stock Exchange Using GARCH Models

This paper models and forecasts volatility (conditional variance) on the Ghana Stock Exchange using a random walk (RW), GARCH(1,1), EGARCH(1,1), and TGARCH(1,1) models. The unique ‘three days a week’ Databank Stock Index (DSI) is used to study the dynamics of the Ghana stock market volatility over a 10-year period. The competing volatility models were estimated and their specification and forecast performance compared with each other, using AIC and LL information criteria and BDS nonlinearity diagnostic checks. The DSI exhibits the stylized characteristics such as volatility clustering, leptokurtosis and asymmetry effects associated with stock market returns on more advanced stock markets. The random walk hypothesis is rejected for the DSI. Overall, the GARCH (1,1) model outperformed the other models under the assumption that the innovations follow a normal distribution.Ghana Stock Exchange; developing financial markets; volatility; GARCH model