Modeling Asymmetries in Financial Data with Multiplicative Error Models

This thesis addresses modeling of financial time series, especially stock market returns and daily price ranges. Modeling data of this kind can be approached with so-called multiplicative error models (MEM). These models nest several well known time series models such as GARCH, ACD and CARR models. They are able to capture many well established features of financial time series including volatility clustering and leptokurtosis. In contrast to these phenomena, different kinds of asymmetries have received relatively little attention in the existing literature. In this thesis asymmetries arise from various sources. They are observed in both conditional and unconditional distributions, for variables with non-negative values and for variables that have values on the real line. In the multivariate context asymmetries can be observed in the marginal distributions as well as in the relationships of the variables modeled. New methods for all these cases are proposed. Chapter 2 considers GARCH models and modeling of returns of two stock market indices. The chapter introduces the so-called generalized hyperbolic (GH) GARCH model to account for asymmetries in both conditional and unconditional distribution. In particular, two special cases of the GARCH-GH model which describe the data most accurately are proposed. They are found to improve the fit of the model when compared to symmetric GARCH models. The advantages of accounting for asymmetries are also observed through Value-at-Risk applications. Both theoretical and empirical contributions are provided in Chapter 3 of the thesis. In this chapter the so-called mixture conditional autoregressive range (MCARR) model is introduced, examined and applied to daily price ranges of the Hang Seng Index. The conditions for the strict and weak stationarity of the model as well as an expression for the autocorrelation function are obtained by writing the MCARR model as a first order autoregressive process with random coefficients. The chapter also introduces inverse gamma (IG) distribution to CARR models. The advantages of CARR-IG and MCARR-IG specifications over conventional CARR models are found in the empirical application both in- and out-of-sample. Chapter 4 discusses the simultaneous modeling of absolute returns and daily price ranges. In this part of the thesis a vector multiplicative error model (VMEM) with asymmetric Gumbel copula is found to provide substantial benefits over the existing VMEM models based on elliptical copulas. The proposed specification is able to capture the highly asymmetric dependence of the modeled variables thereby improving the performance of the model considerably. The economic significance of the results obtained is established when the information content of the volatility forecasts derived is examined.

Diagnostic Tests Based on Quantile Residuals for Nonlinear Time Series Models

This thesis studies quantile residuals and uses different methodologies to develop test statistics that are applicable in evaluating linear and nonlinear time series models based on continuous distributions. Models based on mixtures of distributions are of special interest because it turns out that for those models traditional residuals, often referred to as Pearson's residuals, are not appropriate. As such models have become more and more popular in practice, especially with financial time series data there is a need for reliable diagnostic tools that can be used to evaluate them. The aim of the thesis is to show how such diagnostic tools can be obtained and used in model evaluation. The quantile residuals considered here are defined in such a way that, when the model is correctly specified and its parameters are consistently estimated, they are approximately independent with standard normal distribution. All the tests derived in the thesis are pure significance type tests and are theoretically sound in that they properly take the uncertainty caused by parameter estimation into account. -- In Chapter 2 a general framework based on the likelihood function and smooth functions of univariate quantile residuals is derived that can be used to obtain misspecification tests for various purposes. Three easy-to-use tests aimed at detecting non-normality, autocorrelation, and conditional heteroscedasticity in quantile residuals are formulated. It also turns out that these tests can be interpreted as Lagrange Multiplier or score tests so that they are asymptotically optimal against local alternatives. Chapter 3 extends the concept of quantile residuals to multivariate models. The framework of Chapter 2 is generalized and tests aimed at detecting non-normality, serial correlation, and conditional heteroscedasticity in multivariate quantile residuals are derived based on it. Score test interpretations are obtained for the serial correlation and conditional heteroscedasticity tests and in a rather restricted special case for the normality test. In Chapter 4 the tests are constructed using the empirical distribution function of quantile residuals. So-called Khmaladze s martingale transformation is applied in order to eliminate the uncertainty caused by parameter estimation. Various test statistics are considered so that critical bounds for histogram type plots as well as Quantile-Quantile and Probability-Probability type plots of quantile residuals are obtained. Chapters 2, 3, and 4 contain simulations and empirical examples which illustrate the finite sample size and power properties of the derived tests and also how the tests and related graphical tools based on residuals are applied in practice.

Transverse momentum and pseudorapidity distributions of charged hadrons in pp collisions at sqrt(s) = 0.9 and 2.36 TeV

Measurements of inclusive charged-hadron transverse-momentum and pseudorapidity distributions are presented for proton-proton collisions at sqrt(s) = 0.9 and 2.36 TeV. The data were collected with the CMS detector during the LHC commissioning in December 2009. For non-single-diffractive interactions, the average charged-hadron transverse momentum is measured to be 0.46 +/- 0.01 (stat.) +/- 0.01 (syst.) GeV/c at 0.9 TeV and 0.50 +/- 0.01 (stat.) +/- 0.01 (syst.) GeV/c at 2.36 TeV, for pseudorapidities between -2.4 and +2.4. At these energies, the measured pseudorapidity densities in the central region, dN(charged)/d(eta) for |eta|

Essays on Stock Options, Incentives, and Managerial Action

Executive compensation and managerial behavior have received an increasing amount of attention in the financial economics literature since the mid 1970s. The purpose of this thesis is to extend our understanding of managerial compensation, especially how stock option compensation is linked to the actions undertaken by the management. Furthermore, managerial compensation is continuously and heatedly debated in the media and an emerging consensus from this discussion seems to be that there still exists gaps in our knowledge of optimal contracting. In Finland, the first executive stock options were introduced in the 1980s and throughout the last 15 years it has become increasingly popular for Finnish listed firms to use this type of managerial compensation. The empirical work in the thesis is conducted using data from Finland, in contrast to most previous studies that predominantly use U.S. data. Using Finnish data provides insight of how market conditions affect compensation and managerial action and provides an opportunity to explore what parts of the U.S. evidence can be generalized to other markets. The thesis consists of four essays. The first essay investigates the exercise policy of the executive stock option holders in Finland. In summary, Essay 1 contributes to our understanding of the exercise policies by examining both the determinants of the exercise decision and the markets reaction to the actual exercises. The second essay analyzes the factors driving stock option grants using data for Finnish publicly listed firms. Several agency theory based variables are found to have have explanatory power on the likelihood of a stock option grant. Essay 2 also contributes to our understanding of behavioral factors, such as prior stock return, as determinants of stock option compensation. The third essay investigates the tax and stock option motives for share repurchases and dividend distributions. We document strong support for the tax motive for share repurchases. Furthermore, we also analyze the dividend distribution decision in companies with stock options and find a significant difference between companies with and without dividend protected options. We thus document that the cutting of dividends found in previous U.S. studies can be avoided by dividend protection. In the fourth essay we approach the puzzle of negative skewness in stock returns from an altogether different angle than in previous studies. We suggest that negative skewness in stock returns is generated by management disclosure practices and find proof for this. More specifically, we find that negative skewness in daily returns is induced by returns for days when non-scheduled firm specific news is disclosed.

Evaluating the Predictability of the Volatility Smile Using Return Distributions

In this paper, we examine the predictability of observed volatility smiles in three major European index options markets, utilising the historical return distributions of the respective underlying assets. The analysis involves an application of the Black (1976) pricing model adjusted in accordance with the Jarrow-Rudd methodology as proposed in 1982. Thereby we adjust the expected future returns for the third and fourth central moments as these represent deviations from normality in the distributions of observed returns. Thus, they are considered one possible explanation to the existence of the smile. The obtained results indicate that the inclusion of the higher moments in the pricing model to some extent reduces the volatility smile, compared with the unadjusted Black-76 model. However, as the smile is partly a function of supply, demand, and liquidity, and as such intricate to model, this modification does not appear sufficient to fully capture the characteristics of the smile.

Toxicant distributions and impact models in environmental risk analysis of waste sites

Myrkyllisten aineiden jakaumat ja vaikutusmallit jätealueiden ympäristöriskien analyysissä.

Properties of Toeplitz operators on analytic function spaces : from function symbols to distributions

Toeplitz operators are among the most important classes of concrete operators with applications to several branches of pure and applied mathematics. This doctoral thesis deals with Toeplitz operators on analytic Bergman, Bloch and Fock spaces. Usually, a Toeplitz operator is a composition of multiplication by a function and a suitable projection. The present work deals with generalizing the notion to the case where the function is replaced by a distributional symbol. Fredholm theory for Toeplitz operators with matrix-valued symbols is also considered. The subject of this thesis belongs to the areas of complex analysis, functional analysis and operator theory. This work contains five research articles. The articles one, three and four deal with finding suitable distributional classes in Bergman, Fock and Bloch spaces, respectively. In each case the symbol class to be considered turns out to be a certain weighted Sobolev-type space of distributions. The Bergman space setting is the most straightforward. When dealing with Fock spaces, some difficulties arise due to unboundedness of the complex plane and the properties of the Gaussian measure in the definition. In the Bloch-type spaces an additional logarithmic weight must be introduced. Sufficient conditions for boundedness and compactness are derived. The article two contains a portion showing that under additional assumptions, the condition for Bergman spaces is also necessary. The fifth article deals with Fredholm theory for Toeplitz operators having matrix-valued symbols. The essential spectra and index theorems are obtained with the help of Hardy space factorization and the Berezin transform, for instance. The article two also has a part dealing with matrix-valued symbols in a non-reflexive Bergman space, in which case a condition on the oscillation of the symbol (a logarithmic VMO-condition) must be added.

Structure of Relativistic States

QCD factorization in the Bjorken limit allows to separate the long-distance physics from the hard subprocess. At leading twist, only one parton in each hadron is coherent with the hard subprocess. Higher twist effects increase as one of the active partons carries most of the longitudinal momentum of the hadron, x -> 1. In the Drell-Yan process \pi N -> \mu^- mu^+ + X, the polarization of the virtual photon is observed to change to longitudinal when the photon carries x_F > 0.6 of the pion. I define and study the Berger-Brodsky limit of Q^2 -> \infty with Q^2(1-x) fixed. A new kind of factorization holds in the Drell-Yan process in this limit, in which both pion valence quarks are coherent with the hard subprocess, the virtual photon is longitudinal rather than transverse, and the cross section is proportional to a multiparton distribution. Generalized parton distributions contain information on the longitudinal momentum and transverse position densities of partons in a hadron. Transverse charge densities are Fourier transforms of the electromagnetic form factors. I discuss the application of these methods to the QED electron, studying the form factors, charge densities and spin distributions of the leading order |e\gamma> Fock state in impact parameter and longitudinal momentum space. I show how the transverse shape of any virtual photon induced process, \gamma^*(q)+i -> f, may be measured. Qualitative arguments concerning the size of such transitions have been previously made in the literature, but without a precise analysis. Properly defined, the amplitudes and the cross section in impact parameter space provide information on the transverse shape of the transition process.