Este trabalho consiste em um estudo comparativo de diversos modelos para cálculo do Valor em Risco de um portifólio. São comparados modelos que consideram a série univariada de log-retornos do portifólio versus mo- delos multivariados, que consideram as séries de log-retornos de cada ativo que compõe o portifólio e suas correlações condicionais. Além disso, são testados modelo propostos recentemente, que possuem pouca literatura a respeito, como o PS-GARCH e o VARMA-GARCH. Também propomos um novo modelo, que utiliza o resultado acumulado do portifólio nos últimos dias como variável exógena. Os diferentes modelos são avaliados em termos de sua adequação às exigëncias do Acordo de Basileia e seu impacto financeiro, em um período que inclui épocas de alta volatilidade. De forma geral, não foram notadas grandes diferenças de performance entre modelos univariados e multivariados. Os modelos mais complexos mostraram-se mais eficientes, produzindo resultados satisfatórios inclusive em tempos de crise. / The present work consists of a comparative study of several portfolio Value-at-Risk models. Univariate models, which consider only the portfolio log-returns series, are compared to multivariate models, which consider the log-returns series of each asset individually and their conditional correlations. Additionally, recently proposed models such as PS-GARCH and VARMA-GARCH are tested. We also propose a new model that uses past cumulative returns as exogenous variables. All models are evaluated in terms of their compliance to Basel Accord and financial impact, in period that includes high volatility times. In general, univariate and multivariate models performed similarly. More complex models yielded more accurate results, with satisfactory performance including in crisis periods.

This thesis,firstly, studies the impact of financial liberalization and political instability on economic growth and quantitatively examines the relative importance of the identified underling reasons of Argentine riddle by using an innovative econometric methodology and unique data set: it presents power ARCH estimates for Argentina from 1896 to 2000. The main results show that the long-run effect of financial liberalization on economic growth is positive while the short-run effect is negative, albeit substantially smaller. The political instability effects are substantially larger in the short-run than in the long-run. We also investigate potential mechanisms for the effects of financial liberalization and political instability on economic growth: direct impact or happening through the variation of growth volatility. Our results also suggest that financial development, trade openness and political instability are the main factors to explain the Argentine decline. Furthermore, real business cycle variability - growth relationship and the link between inflation and its uncertainty are investigated by using monthly data of four Asian countries/regions (Japan, South Korea, Singapore and Taiwan) and parametric power ARCH methodology to proxy uncertainty. We fnd that more uncertainty about output leads to a higher rate of growth in three of the four countries/regions and the form of the uncertainty matters. Output growth reduces its uncertainty in all countries/regions via inflation uncertainty except Singapore. For all countries/regions, inflation significantly raises inflation uncertainty as predicted by Friedman. On the other hand, increased uncertainty affects inflation positively in Japan and Singapore, which support the Cukierman-Meltzer hypothesis. We find a negative sign for Taiwan which is in accordance with the Holland hypothesis when error term was normally distributed, however, this result is not statistically significant when the student-t distribution is applied. Interestingly, South Korea’s data reveals a positive sign initially, however, it turns around when a structural dummy is incorporated. This dramatic outcome in favour of the Holland hypothesis, and chimes in with Dueker and Kim (1999), who claim that the inflation was strictly controlled by the South Korean monetary authority. In addition, this thesis investigates two-way causal relationships between spread, volatility and volume in the FTSE100 stock index over the period from 1992 to 2004 by using bivariate AR-FI-GARCH model and multiple measurements of risk and spread. The measurements of the spread include relative bid-ask spread, effective bid-ask spread, the inventory cost component of the bid-ask spread and the information cost component of the bid-ask spread. Risk is proxied by two measurements of price volatility: the close-to-close volatility and the range-based volatility. We also take the impact of electronic trading into account. Our results suggest that the spread and volume are positively impacted by volatility simultaneously. In addition, both volatility and volume are negatively affected by the spread. Furthermore, we find that the inventory cost component of the spread has a negative effect on volatility, in contrast, the information component of the spread positively impacts volatility. These results support the argument that speculation generates volatility in the market and higher transaction costs bene t stability of the market.

No description available.

Ingeniero Civil Industrial / Dentro del trabajo de memoria, se analizaron los modelos de volatilidad de Desviación Estándar, Alisamiento Exponencial de la Varianza, GARCH con distribución Normal y Normal Inversa Gaussiana y el GJR GARCH, los cuales se aplicaron al precio del cobre, al tipo de cambio dólar-peso observado, al precio de la acción de Copec, al IPSA y a la TIR de un BCP a 10 años, buscando establecer las ventajas y desventajas de cada uno con la finalidad de generar una métrica que permita, al tomador de decisión, escoger el mejor modelo de volatilidad a usar bajo sus requerimientos y recursos. Además, se estudiarán efectos causales de la volatilidad en los activos escogidos para entender de mejor forma las causas que la originan. Se observó que los modelos GARCH están por sobre los otros dos modelos en todos los criterios escogidos, exceptuando el costo computacional. Además, los resultados de estos modelos son consistentes con la literatura en cuanto a determinar las características de la volatilidad (sensibilidad al corto plazo, persistencia y velocidad de reversión) y que cuando los retornos distribuyen cercanos a una Normal, los modelos GARCH entregan valores similares, los cuales difieren al cambiar la distribución por otra con asimetría o colas más gruesas, donde los modelos NIG y GJR son capaces de capturar información que el otro no puede. Además se observa que existe una relación fuerte entre el riesgo del cobre con el tipo de cambio dólar-peso, donde el metal genera cambios en el valor de la moneda norteamericana. Adicional a ésta se encontraron otras relaciones débiles. Se concluye que la volatilidad es causada por tres principales factores, la persistencia, el retorno del activo y el contagio de riesgo con otros activos de la economía. Finalmente, se concluye que una adecuada medición de la volatilidad es de suma importancia, ya que tal como se observó para el caso del tipo de cambio dólar-peso, sin necesariamente cambiar la forma de estimar la provisión, sino utilizando una diferente forma de medir la volatilidad, se puede ahorrar una significativa cantidad de dinero.

This study attempts to analyze the efficiency of intervention policy in Turkey during the period between 4.1.2005 and 31.12.2012 with a sub period which is between 4.1.2007 and 31.12.2010. For our study purpose, therefore we investigated how interventions with pre-announced auctions as a whole influence the exchange rates. Further, we analyze whether there is an asymmetric effect among the buying and selling transactions with respect to their impact on the exchange rates. In the study, the E-GARCH model is employed to find the asymmetric effect. The final object of this study is whether buying auctions which are conducted to serve for only purpose of increasing international reserves influence the exchange rates. We evaluate the efficiency of transactions in the same direction of central bank statements. In conclusion, the findings did not amount to any significant impact of total transaction on exchange rates. The study findings also suggest that there is asymmetric effect among the selling and buying transactions. The amounts of selling transaction have a negative impact on both level and volatility while buying auctions did not have any significant effect on them. As a new research result, we found that buying auctions served well with respect to their contributions to reserves while they do not...

The present work deals with selected methods suitable to work with financial time series. Firstly, univariate linear models ARMA are introduced, followed by the description of volatility models ARCH and their generalization to GARCH models. There are many modifications of standard GARCH models designed with respect to the nature of financial data, some of which are presented. Another part of the work dealing with multiple time series focuses on VAR models and bivariate GARCH models. The most important part of the work are practical examples of building the theoretically described models in various types of software with built-in procedures for time series analysis. We apply five different types of commercial and non-commercial software, namely EViews, Mathematica, R, S-PLUS and XploRe. The used software products are presented and compared in terms of their capabilities and the results obtained for particular methods.

Tang, Sheung Yin. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2010. / Includes bibliographical references (leaves 76-82). / Abstracts in English and Chinese. / Abstract --- p.i / Acknowledgement --- p.iii / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Literature Review --- p.9 / Chapter 3 --- Models --- p.20 / Chapter 3.1 --- Single Regime GARCH Models --- p.20 / Chapter 3.1.1 --- "GARCH (1,1) Model" --- p.22 / Chapter 3.1.2 --- "EGARCH (1, 1) Model" --- p.24 / Chapter 3.1.3 --- GARCH-M (1，1) Model --- p.25 / Chapter 3.2 --- Markov Regime Switching GARCH Model --- p.26 / Chapter 4 --- Data and Descriptive Analysis --- p.37 / Chapter 4.1 --- Data --- p.37 / Chapter 4.1.1 --- Unit Root and Stationary Tests --- p.39 / Chapter 4.1.2 --- Tests for Conditional Heteroskedasticity --- p.40 / Chapter 5 --- Empirical Results and Discussion --- p.43 / Chapter 5.1 --- In-Sample Statistics --- p.44 / Chapter 5.2 --- Forecasting Performance --- p.54 / Chapter 5.2.1 --- Results of Statistical Loss Functions --- p.55 / Chapter 5.3 --- Tests of Equal Predictive Ability --- p.62 / Chapter 5.3.1 --- Diebold-Mariano Test --- p.62 / Chapter 5.3.2 --- Results of DM Test --- p.64 / Chapter 6 --- Conclusion --- p.68 / A Forecasts from the Models --- p.72 / Bibliography --- p.76

Beginning in the early 1990s several countries, including Australia, have pursued programs of deregulation and restructuring of their electricity supply industries. Dissatisfaction with state-run monopoly suppliers and a desire for increased competition and choice for consumers have been the major motivations for reform. In Australia, the historical, vertically-integrated, government-owned electricity authorities were separated into separate generation, transmission, distribution and retail sectors in each State and a competitive, wholesale market for electricity, the National Electricity Market (NEM) began operation in December 1998. The goal of deregulation was (and remains) increased competition in electricity supply, so that consumers may enjoy wider choice and lower prices. The first benefit has largely been delivered but it is arguable whether the second benefit of lower prices has been realised. Increased competition has come at the price of increased wholesale price volatility, which brings with it increased cost as market participants seek to trade profitably and manage the increase in price risk. In the NEM, generators compete to sell into a pool market and distributors purchase electricity from the pool at prices determined by demand and supply, on a half-hourly basis. These market-clearing prices can be extremely volatile. Electricity prices are generally characterised by significant seasonal patterns, on an intra-day, weekly and monthly basis, as demand and supply conditions vary. Prices are also characterised by strong mean-reversion and extremely high spikes in price. While long-run mean prices typically range between $30 and $45 per megawatt hour, prices can spike to levels above $9,000 or $10,000 per megawatt hour from time to time. These spikes tend to be sporadic and very short-lived, rarely lasting for more than an hour or two. Although infrequent, spikes are the major contributor to price volatility and their evolution and causes need to be investigated and understood. The purpose of this thesis is to investigate and model Australian electricity prices. The research work presented is mostly empirical, with the early analytical chapters focusing on investigating the presence and significance of seasonal factors and spikes in electricity price and demand. In subsequent chapters this work is extended into analysis of the underlying volatility processes and the interaction between extreme values in demand and price is specifically investigated. The findings of the thesis are that while the characteristics of strong seasonal patterns and spikes that are generally observed in similar electricity markets are present in the NEM in both price and demand, there is significant variation in their presence and effect between the regional pools. The study also finds that while time-varying volatility is evident in the price series there is again some variation in the way this is characterised between states. A further finding challenges the accepted wisdom that demand peaks drive price spikes at the extremes and shows empirically that price spikes are more likely to be caused by supply disruptions than extremes of demand. The findings provide useful insight into this highly idiosyncratic but economically important national market.

This thesis is concerned with the modelling of the term structure of interest rates, with a particular focus on empirical aspects of the modelling. In this thesis, we explore the ??-parameterised (?? being the length of time to maturity) term structure of interest rates, corresponding to the traditional T-parameterised (T being the time of maturity) term structure of interest rates. The constructions of Australian yield curves are illustrated using generic yield curves produced by the Reserve Bank of Australia based on bonds on issue and by constructed yield curves of the Commonwealth Bank of Australia derived from swap rates. The data used to build the models is Australian Treasury yields from January 1996 to December 2001 for maturities of 1, 2, 3, 5 and 10 years, and the second data used to validate the model is Australian Treasury yields from July 2000 to April 2004 for maturities of all years from 1-10. Both data were supplied by the Reserve Bank of Australia. Initially, univariate Generalised Autoregressive Conditional Heteroskedasticity (GARCH), with models of individual yield increment time series are developed for a set of fixed maturities. Then, a multivariate Matrix-Diagonal GARCH model with multivariate asymmetric t-distribution of the term structure of yield increments is developed. This model captures many important properties of financial data such as volatility mean reversion, volatility persistency, stationarity and heavy tails. There are two innovations of GARCH modelling in this thesis: (i) the development of the Matrix-Diagonal GARCH model with multivariate asymmetric t-distribution using meta-elliptical distribution in which the degrees of freedom of each series varies with maturity, and the estimation is given; (ii) the development of a GARCH model of term structure of interest rates (TS-GARCH). The TS-GARCH model describes the parameters specifying the GARCH model and the degrees of freedom using simple smooth functions of time to maturity of component series. TS-GARCH allows an empirical description of complete interest rate yield curve increments therefore allowing the model to be used for interpolation to additional maturity beyond those used to construct the model. Diagnostics of TS-GARCH model are provided using Australian Treasury bond yields.

<p>Condfidence in the future is a signicant factor for business development. However frequently, accurate and specific purposes are spread over the market environment influence.Thus,it is necessary to make an appropriate consideration of instability, which is peculiar to the dynamic development. Volatility, variance and standard deviation are used to</p><p>characterize the deviation of the investigated quantity from mean value.</p><p>Volatility is one of the main instruments to measure the risk of the asset.</p><p>The increasing availability of financial market data has enlarged volatility research potential but has also encouraged research into longer horizon volatility forecasts.</p><p>In this paper we investigate stock index volatility with respect to capitalization with help of GARCH-modelling.</p><p>There are chosen three indexes of OMX Nordic Exchange for our research. The Nordic list segment indexes comprising Nordic Large Cap,</p><p>Mid Cap and Small Cap are based on the three market capitalization groups.</p><p>We implement GARCH-modeling for considering indexes and compare our results in order to conclude which ones of the indexes is more volatile.</p><p>The OMX Nordic list indexis quiet new(2002)and reorganized as late as October 2006. The current value is now about 300 and no options do exist. In current work we are also interested in estimation of the Heston</p><p>model(SVmodel), which is popular in financial world and can be used in option pricing in the future.</p><p>The results of our investigations show that Large Cap Index is more volatile then Middle and Small Cap Indexes.</p>