"The VIX was introduced in 1993 by the CBOE and has been commonly referred to as the fear gauge due to decreases in market sentiment leading market participants to purchase protection from declining asset prices. As market sentiment improves, declines in the VIX are generally observed. In reality the VIX measures the markets expectations about future volatility with asset prices either rising or falling in value. With the VIX gaining popularity in the marketplace a proliferation of derivative products has emerged allowing investors to trade volatility. In observance of the behavior of the VIX we attempt to model the derivative VXX as a mean reverting process via the Ornstein-Uhlenbeck stochastic differential equation. We extend this analysis by calibrating VIX options with observed market prices in order to extract the market density function. Using these parameters as the diffusion process in our Ornstein-Uhlenbeck model we derive futures prices on the VIX which serves to value our target derivative VXX."

<p>In this paper we aim to investigate volatility and correlation of sector</p><p>indexes of Nordic Market. More precisely we work with OMX Stockholm</p><p>Exchange Indexes, considering the Paper, the Energy and the Bank</p><p>sectors.</p><p>We use daily returns over the period from 5 January 2001 to 13 April</p><p>2007 and compute and forecast return volatility using the GARCH(1; 1)</p><p>model. We also calculate the correlation matrix of the indexes.</p><p>The GARCH(1; 1) model ¯t the empirical data well for all three sectors</p><p>and can therefore be used for volatility forecasts. Here, we have pre-</p><p>dicted the one-day-ahead forecasts and based on these data calculated</p><p>the correlation matrix. The results from these calculations show that</p><p>all three sectors are highly correlated. We obtained however the small-</p><p>est correlation between Paper and Energy which was surprising as the</p><p>Paper industry is very energy consuming. This result indicates other</p><p>relations between Paper and Energy.</p>

This study investigates the impact of IT investments and several contextual variables on the volatility of future earnings. We find evidence that IT investments strongly increases the volatility of future earnings and that four contextual factors - industry concentration, sales growth, diversification, and leverage - strongly moderate IT's effect on earnings volatility. It is notable that while the main effect of IT spending on earnings volatility is strongly positive, not all of the moderators are. This suggests that there are conditions under which the positive risk-return relation can be either offset or even reversed. Taken together, these results suggest an explanation for what has recently been termed the "new productivity paradox", i.e. the apparent under-investment in information technology despite evidence of highly positive returns for doing so.

In this paper we aim to investigate volatility and correlation of sector indexes of Nordic Market. More precisely we work with OMX Stockholm Exchange Indexes, considering the Paper, the Energy and the Bank sectors. We use daily returns over the period from 5 January 2001 to 13 April 2007 and compute and forecast return volatility using the GARCH(1; 1) model. We also calculate the correlation matrix of the indexes. The GARCH(1; 1) model ¯t the empirical data well for all three sectors and can therefore be used for volatility forecasts. Here, we have pre- dicted the one-day-ahead forecasts and based on these data calculated the correlation matrix. The results from these calculations show that all three sectors are highly correlated. We obtained however the small- est correlation between Paper and Energy which was surprising as the Paper industry is very energy consuming. This result indicates other relations between Paper and Energy.

In this thesis we consider estimation of the tail index for heavy tailed stochastic volatility models with long memory. We prove a central limit theorem for a Hill estimator. In particular, it is shown that neither the rate of convergence nor the asymptotic variance is affected by long memory. The theoretical findings are verified by simulation studies.

In this thesis we consider estimation of the tail index for heavy tailed stochastic volatility models with long memory. We prove a central limit theorem for a Hill estimator. In particular, it is shown that neither the rate of convergence nor the asymptotic variance is affected by long memory. The theoretical findings are verified by simulation studies.

This paper discusses the performance of modeling and forecasting volatility ofdaily stock returns of A-shares in Shanghai Stock Exchange. The volatility is modeledby GARCH family models which are GARCH, EGARCH and GJR-GARCHmodels with three distributions, namely Gaussian distribution, student-t distributionand generalized error distribution (GED). In order to determine the performanceof forecasting volatility, we compare the models by using the Root MeanSquared Error (RMSE). The results show that the EGARCH models work so wellin most of daily stock returns and the symmetric GARCH models are better thanasymmetric GARCH models in this paper.

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We consider the stochastic volatility model with smooth transition and persistent la- tent factors. We argue that this model has advantages over the conventional stochastic model for the persistent volatility factor. Though the linear filtering is widely used in the state space model, the simulation result, as well as theory, shows that it does not work in our model. So we apply the density-based filtering method; in particular, we develop two methods to get solutions. One is the conventional approach using the Maximum Likelihood estimation and the other is the Bayesian approach using Gibbs sampling. We do a simulation study to explore their characteristics, and we apply both methods to actual macroeconomic data to extract the volatility generating process and to compare macro fundamentals with them. Next we extend our model into multivariate model extracting common and id- iosyncratic volatility for multivariate processes. We think it is interesting to apply this multivariate model into measuring time-varying uncertainty of macroeconomic variables and studying the links to market returns via a consumption-based asset pric- ing model. Motivated by Bansal and Yaron (2004), we extract a common volatility factor using consumption and dividend growth, and we find that this factor predicts post-war business cycle recessions quite well. Then, we estimate a long-run risk model of asset prices incorporating this macroeconomic uncertainty. We find that both risk aversion and the intertemporal elasticity of substitution are estimated to be around two, and our simulation results show that the model can match the first and second moments of market return and risk-free rate, hence the equity premium.