Elements of Volatility at High Frequency

Volatility is central in options pricing and risk management. It reflects the uncertainty of investors and the inherent instability of the economy. Time series methods are among the most widely applied scientific methods to analyze and predict volatility. Very frequently sampled data contain much valuable information about the different elements of volatility and may ultimately reveal the reasons for time varying volatility. The use of such ultra-high-frequency data is common to all three essays of the dissertation. The dissertation belongs to the field of financial econometrics. The first essay uses wavelet methods to study the time-varying behavior of scaling laws and long-memory in the five-minute volatility series of Nokia on the Helsinki Stock Exchange around the burst of the IT-bubble. The essay is motivated by earlier findings which suggest that different scaling laws may apply to intraday time-scales and to larger time-scales, implying that the so-called annualized volatility depends on the data sampling frequency. The empirical results confirm the appearance of time varying long-memory and different scaling laws that, for a significant part, can be attributed to investor irrationality and to an intraday volatility periodicity called the New York effect. The findings have potentially important consequences for options pricing and risk management that commonly assume constant memory and scaling. The second essay investigates modelling the duration between trades in stock markets. Durations convoy information about investor intentions and provide an alternative view at volatility. Generalizations of standard autoregressive conditional duration (ACD) models are developed to meet needs observed in previous applications of the standard models. According to the empirical results based on data of actively traded stocks on the New York Stock Exchange and the Helsinki Stock Exchange the proposed generalization clearly outperforms the standard models and also performs well in comparison to another recently proposed alternative to the standard models. The distribution used to derive the generalization may also prove valuable in other areas of risk management. The third essay studies empirically the effect of decimalization on volatility and market microstructure noise. Decimalization refers to the change from fractional pricing to decimal pricing and it was carried out on the New York Stock Exchange in January, 2001. The methods used here are more accurate than in the earlier studies and put more weight on market microstructure. The main result is that decimalization decreased observed volatility by reducing noise variance especially for the highly active stocks. The results help risk management and market mechanism designing.

Geochemistry and petrology of the ferropicrite dikes and associated rocks of Vestfjella, western Dronning Maud Land, Antarctica

This study provides insights into the composition and origin of ferropicrite dikes (FeOtot = 13 17 wt. %; MgO = 13 19 wt. %) and associated meimechite, picrite, picrobasalt, and basalt dikes found at Vestfjella, western Dronning Maud Land, Antarctica. The dikes crosscut Jurassic Karoo continental flood basalts (CFB) that were emplaced during the early stages of the breakup of the Gondwana supercontinent ~180 Ma ago. Selected samples (31 overall from at least eleven dikes) were analyzed for their mineral chemical, major element, trace element, and Sr, Nd, Pb, and Os isotopic compositions. The studied samples can be divided into two geochemically distinct types: (1) The depleted type (24 samples from at least nine dikes) is relatively depleted in the most incompatible elements and exhibits isotopic characteristics (e.g., initial εNd of +4.8 to +8.3 and initial 187Os/188Os of 0.1256 0.1277 at 180 Ma) similar to those of mid-ocean ridge basalts (MORB); (2) The enriched type (7 samples from at least two dikes) exhibits relatively enriched incompatible element and isotopic characteristics (e.g., initial εNd of +1.8 to +3.6 and initial 187Os/188Os of 0.1401 0.1425 at 180 Ma) similar to those of oceanic island basalts. Both magma types have escaped significant contamination by the continental crust. The depleted type is related to the main phase of Karoo magmatism and originated as highly magnesian (MgO up to 25 wt. %) partial melts at high temperatures (mantle potential temperature >1600 °C) and pressures (~5 6 GPa) from a sublithospheric, water-bearing, depleted peridotite mantle source. The enriched type sampled pyroxene-bearing heterogeneities that can be traced down to either recycled oceanic crust or melt-metasomatized portions of the sublithospheric or lithospheric mantle. The source of the depleted type represents a sublithospheric end-member source for many Karoo lavas and has subsequently been sampled by the MORBs of the Indian Ocean. These observations, together with the purported high temperatures, indicate that the Karoo CFBs were formed in an extensive melting episode caused mainly by internal heating of the upper mantle beneath the Gondwana supercontinent. My research supports the view that ferropicritic melts can be generated in several ways: the relative Fe-enrichment of mantle partial melts is most readily achieved by (1) relatively low degree of partial melting, (2) high pressure of partial melting, and (3) melting of enriched source components (e.g., pyroxenite and metasomatized peridotite). Ferropicritic whole-rock compositions could also result from accumulation, secondary alteration, and fractional crystallization, however, and caution is required when addressing the parental magma composition.

Integral Transformations of Volterra Gaussian Processes

We study integral representations of Gaussian processes with a pre-specified law in terms of other Gaussian processes. The dissertation consists of an introduction and of four research articles. In the introduction, we provide an overview about Volterra Gaussian processes in general, and fractional Brownian motion in particular. In the first article, we derive a finite interval integral transformation, which changes fractional Brownian motion with a given Hurst index into fractional Brownian motion with an other Hurst index. Based on this transformation, we construct a prelimit which formally converges to an analogous, infinite interval integral transformation. In the second article, we prove this convergence rigorously and show that the infinite interval transformation is a direct consequence of the finite interval transformation. In the third article, we consider general Volterra Gaussian processes. We derive measure-preserving transformations of these processes and their inherently related bridges. Also, as a related result, we obtain a Fourier-Laguerre series expansion for the first Wiener chaos of a Gaussian martingale. In the fourth article, we derive a class of ergodic transformations of self-similar Volterra Gaussian processes.

Thyroid Hormone Control of Cardiac Substrate Metabolism

Thyroid hormone (TH) plays an important role in maintaining a homeostasis in all the cells of our body. It also has significant cardiovascular effects, and abnormalities of its concentration can cause cardiovascular disease and even morbidity. Especially development of heart failure has been connected to low levels of thyroid hormone. A decrease in TH levels or TH-receptor binding adversely effects cardiac function. Although, this occurs in part through alterations in excitation-contraction and transport proteins, recent data from our laboratory indicate that TH also mediates changes in myocardial energy metabolism. Thyroid dysfunction may limit the heart s ability to shift substrate pathways and provide adequate energy supply during stress responses. Our goals of these studies were to determine substrate oxidation pattern in systemic and cardiac specific hypothyroidism at rest and at higher rates of oxygen demand. Additionally we investigated the TH mediated mechanisms in myocardial substrate selection and established the metabolic phenotype caused by a thyroid receptor dysfunction. We measured cardiac metabolism in an isolated heart model using 13Carbon isotopomer analyses with MR spectroscopy to determine function, oxygen consumption, fluxes and fractional contribution of acetyl-CoA to the citric acid cycle (CAC). Molecular pathways for changes in cardiac function and substrate shifts occurring during stress through thyroid receptor abnormalities were determined by protein analyses. Our results show that TH modifies substrate selection through nuclear-mediated and rapid posttranscriptional mechanisms. It modifies substrate selection differentially at rest and at higher rates of oxygen demand. Chronic TH deficiency depresses total CAC flux and selectively fatty acid flux, whereas acute TH supplementation decreases lactate oxidation. Insertion of a dominant negative thyroid receptor (Δ337T) alters metabolic phenotype and contractive efficiency in heart. The capability of the Δ337T heart to increase carbohydrate oxidation in response to stress seems to be limited. These studies provided a clearer understanding of the TH role in heart disease and shed light to identification of the molecular mechanisms that will facilitate in finding targets for heart failure prevention and treatment.

Sydämen hypertrofian ja kroonisen vajaatoiminnan farmakologinen hoito

Sydämen krooninen vajaatoiminta on merkittävä maailmanlaajuinen ongelma. Se on erilaisten sydän- ja verisuonisairauksien aiheuttama monimuotoinen oireyhtymä. Sydämen vasemman kammion hypertrofia eli sydämen seinämien paksuuntuminen on yksi keskeinen tekijä, joka voi olla sydämen vajaatoiminnan taustalla. Kohonnut verenpaine on yleisin syy, joka johtaa sydänlihaksen paksuuntumiseen. Tämä johtaa sydämen pumppaustoiminnan häiriintymiseen, erilaisten neurohormonaalisten mekanismien aktivaatioon ja edelleen sydämen vajaatoimintaan. Sydämen vajaatoiminnan neurohormonaalisista mekanismeista tärkeimmät ovat reniini-angiotensiini-aldosteroni-järjestelmän ja sympaattisen hermoston aktivaatio, sydämen rakenteiden uudelleenmuovautuminen, sydänlihassolujen apoptoosi ja systeeminen tulehdustila. Sydämen hypertrofiaa ja sen syntymistä pyritään estämään kohonneen verenpaineen lääkehoidolla. Reniini-angiotensiini-aldosteronijärjestelmällä on keskeinen merkitys sydämen vajaatoiminnassa. Sydämen vajaatoiminnan ennusteeseen vaikuttavista lääkeaineista angiotensiinikonvertasin estäjät (ACEestäjät) ovat säilyttäneet johtoasemansa jo vuosikymmenten ajan. Angiotensiinireseptoreiden salpaajien (AT1-salpaajien) odotettiin syrjäyttävän ACE-estäjät sydämen vajaatoiminnan hoidossa, mutta toistaiseksi niitä pidetään vain vaihtoehtoisina lääkkeinä. Sympaattisen hermoston aktivaatiota vähentävät β-salpaajat ovat vakiinnuttaneet asemansa toiseksi tärkeimpänä lääkeryhmänä. Diureetit ovat paljon käytetty lääkeaineryhmä sydämen vajaatoiminnan hoidossa, mutta niistä ainoastaan aldosteroniantagonisteilla on tutkitusti ennustetta parantavaa vaikutusta. Kroonisen vajaatoiminnan hoidossa käytetään edelleen myös digoksiinia. Tulevaisuudessa sydämen vajaatoiminnan ennusteeseen vaikuttavia lääkeaineita voivat olla reniinin estäjät, neutraaliendopeptidaasin estäjät, vasopressiinin antagonistit tai inflammatroisiin sytokiineihin vaikuttavat molekyylit. Erikoistyön kokeellisessa osiossa tarkoituksena oli tutkia sydämen hypertrofian kehittymistä vatsa-aortta kuristetuilla rotilla ja kalsiumherkistäjä levosimendaanin sekä AT1-salpaaja valsartaanin vaikutuksia hypertrofian kehittymiseen. Kokeellisessa osiossa arvioitiin myös sydämen hypertrofian ja vajaatoiminnan jyrsijämallina käytetyn vatsa-aortan kuristuksen (koarktaation) toimivuutta ja vaikutuksia ultraäänen avulla määritettyihin kardiovaskulaarisiin parametreihin. Vatsa-aortta kuristettiin munuaisvaltimoiden yläpuolelta. Kuristus saa aikaan verenpaineen kohoamisen ja sydämen työtaakan lisääntymisen. Pitkittyessään tila johtaa sydänlihaksen hypertrofiaan ja vajaatoimintaan. 64 eläintä jaettiin ryhmiin, siten että jokaiseen ryhmään tuli kahdeksan eläintä. Ryhmistä kolmelle annettiin lääkeaineena levosimendaania kolmella eri päiväannoksella (0,01 mg/kg; 0,10 mg/kg; 1,00 mg/kg) ja kolmelle valsartaania kolmella eri päiväannoksella (0,10 mg/kg; 1,00 mg/kg; 10,00 mg/kg) juomaveden mukana. Lääkitys aloitettiin leikkauksen jälkeen ja jatkettiin kahdeksan viikon ajan. Kardiovaskulaariset parametrit, kuten isovolumetrinen relaksaatioaika (IVRT), vasemman kammion läpimitta systolessa ja diastolessa sekä seinämäpaksuudet, ejektiofraktio (EF), supistuvuusosuus (FS), minuuttitilavuus (CO) ja iskutilavuus (SV) määritettiin kahdeksan viikon kuluttua leikkauksesta ultraäänitutkimuksen avulla. Lisäksi määritettiin eläinten sydämen paino suhteessa ruumiin painoon. Tuloksia verrattiin ilman lääkehoitoa olleeseen koarktaatioryhmään. Eläinmallin toimivuutta arvioitiin vertaamalla koarktaatioryhmän tuloksia sham-operoidun ryhmän tuloksiin. Levosimendaanilla havaittiin työssä sydämen systolista toimintaa parantava vaikutus. Tämä näkyi tendenssinä parantaa ejektiofraktioita ja vasemman kammion supistuvuusosuuksia. Sydämen diastoliseen toimintaan ei kummallakaan lääkeaineella ollut merkittävää vaikutusta. Diastolista toimintaa arvioitiin isovolumetrisen relaksaatioajan muutoksilla. Sydämen hypertrofian kehittymiseen ei kummallakaan lääkeaineella ollut merkittävää vaikutusta. Eläinmallin todettiin mallintavan hyvin sydämen hypetrofiaa ihmisellä, mutta ei niinkään sydämen vajaatoimintaa.

Society by Numbers : Studies on Model-Based Explanations in the Social Sciences

The aim of this dissertation is to provide conceptual tools for the social scientist for clarifying, evaluating and comparing explanations of social phenomena based on formal mathematical models. The focus is on relatively simple theoretical models and simulations, not statistical models. These studies apply a theory of explanation according to which explanation is about tracing objective relations of dependence, knowledge of which enables answers to contrastive why and how-questions. This theory is developed further by delineating criteria for evaluating competing explanations and by applying the theory to social scientific modelling practices and to the key concepts of equilibrium and mechanism. The dissertation is comprised of an introductory essay and six published original research articles. The main theses about model-based explanations in the social sciences argued for in the articles are the following. 1) The concept of explanatory power, often used to argue for the superiority of one explanation over another, compasses five dimensions which are partially independent and involve some systematic trade-offs. 2) All equilibrium explanations do not causally explain the obtaining of the end equilibrium state with the multiple possible initial states. Instead, they often constitutively explain the macro property of the system with the micro properties of the parts (together with their organization). 3) There is an important ambivalence in the concept mechanism used in many model-based explanations and this difference corresponds to a difference between two alternative research heuristics. 4) Whether unrealistic assumptions in a model (such as a rational choice model) are detrimental to an explanation provided by the model depends on whether the representation of the explanatory dependency in the model is itself dependent on the particular unrealistic assumptions. Thus evaluating whether a literally false assumption in a model is problematic requires specifying exactly what is supposed to be explained and by what. 5) The question of whether an explanatory relationship depends on particular false assumptions can be explored with the process of derivational robustness analysis and the importance of robustness analysis accounts for some of the puzzling features of the tradition of model-building in economics. 6) The fact that economists have been relatively reluctant to use true agent-based simulations to formulate explanations can partially be explained by the specific ideal of scientific understanding implicit in the practise of orthodox economics.

Jumping numbers of a simple complete ideal in a two-dimensional regular local ring

The multiplier ideals of an ideal in a regular local ring form a family of ideals parametrized by non-negative rational numbers. As the rational number increases the corresponding multiplier ideal remains unchanged until at some point it gets strictly smaller. A rational number where this kind of diminishing occurs is called a jumping number of the ideal. In this manuscript we shall give an explicit formula for the jumping numbers of a simple complete ideal in a two dimensional regular local ring. In particular, we obtain a formula for the jumping numbers of an analytically irreducible plane curve. We then show that the jumping numbers determine the equisingularity class of the curve.

Magnetorotational instability driven dynamos at low magnetic Prandtl numbers

Numerical simulations of the magnetorotational instability (MRI) with zero initial net flux in a non-stratified isothermal cubic domain are used to demonstrate the importance of magnetic boundary conditions. In fully periodic systems the level of turbulence generated by the MRI strongly decreases as the magnetic Prandtl number (Pm), which is the ratio of kinematic viscosity and magnetic diffusion, is decreased. No MRI or dynamo action below Pm=1 is found, agreeing with earlier investigations. Using vertical field conditions, which allow magnetic helicity fluxes out of the system, the MRI is found to be excited in the range 0.1