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.

Oxidative stability of phytosterols in food models and foods

An important safety aspect to be considered when foods are enriched with phytosterols and phytostanols is the oxidative stability of these lipid compounds, i.e. their resistance to oxidation and thus to the formation of oxidation products. This study concentrated on producing scientific data to support this safety evaluation process. In the absence of an official method for analyzing of phytosterol/stanol oxidation products, we first developed a new gas chromatographic - mass spectrometric (GC-MS) method. We then investigated factors affecting these compounds' oxidative stability in lipid-based food models in order to identify critical conditions under which significant oxidation reactions may occur. Finally, the oxidative stability of phytosterols and stanols in enriched foods during processing and storage was evaluated. Enriched foods covered a range of commercially available phytosterol/stanol ingredients, different heat treatments during food processing, and different multiphase food structures. The GC-MS method was a powerful tool for measuring the oxidative stability. Data obtained in food model studies revealed that the critical factors for the formation and distribution of the main secondary oxidation products were sterol structure, reaction temperature, reaction time, and lipid matrix composition. Under all conditions studied, phytostanols as saturated compounds were more stable than unsaturated phytosterols. In addition, esterification made phytosterols more reactive than free sterols at low temperatures, while at high temperatures the situation was the reverse. Generally, oxidation reactions were more significant at temperatures above 100°C. At lower temperatures, the significance of these reactions increased with increasing reaction time. The effect of lipid matrix composition was dependent on temperature; at temperatures above 140°C, phytosterols were more stable in an unsaturated lipid matrix, whereas below 140°C they were more stable in a saturated lipid matrix. At 140°C, phytosterols oxidized at the same rate in both matrices. Regardless of temperature, phytostanols oxidized more in an unsaturated lipid matrix. Generally, the distribution of oxidation products seemed to be associated with the phase of overall oxidation. 7-ketophytosterols accumulated when oxidation had not yet reached the dynamic state. Once this state was attained, the major products were 5,6-epoxyphytosterols and 7-hydroxyphytosterols. The changes observed in phytostanol oxidation products were not as informative since all stanol oxides quantified represented hydroxyl compounds. The formation of these secondary oxidation products did not account for all of the phytosterol/stanol losses observed during the heating experiments, indicating the presence of dimeric, oligomeric or other oxidation products, especially when free phytosterols and stanols were heated at high temperatures. Commercially available phytosterol/stanol ingredients were stable during such food processes as spray-drying and ultra high temperature (UHT)-type heating and subsequent long-term storage. Pan-frying, however, induced phytosterol oxidation and was classified as a rather deteriorative process. Overall, the findings indicated that although phytosterols and stanols are stable in normal food processing conditions, attention should be paid to their use in frying. Complex interactions between other food constituents also suggested that when new phytosterol-enriched foods are developed their oxidative stability must first be established. The results presented here will assist in choosing safe conditions for phytosterol/stanol enrichment.

Tailoring polyolefin properties by metallocene catalysis

This doctoral thesis deals with the syntheses of olefin homo- and copolymers using different kind of metallocene catalyst. Ethene, propene, 1-hexene, 1-hexadecene, vinylcyclohexane and phenylnorbornene were homo- or copolymerized with the catalysts. The unbridged benzyl substituted zirconium dichloride catalysts (1-4), ansa- bridged acenaphtyl substituted zirconium dichloride catalysts, ( 5, 6), rac- and meso-ethylene-bis(1-indenyl)zirconium dichlorides, (rac- and meso-8), rac-ethylene-bis(1-indenyl)hafnium dichloride, ( 12), bis(9-fluorenyl)hafnium dichloride (14 ) enantiomerically pure (R)- phenylethyl[(9-fluorenyl-1-indenyl)]ZrCl2, (11), 14 and asymmetric dimethylsilyl[(3-benzylindenyl-(2-methylbenzen[e]indenyl)] zirconium dichloride, (13), were prepared in our laboratory. Dimethylsilyl-bis(1-indenyl)zirconium dichloride, (9), isopropylidene(9-fluorenyl-cyclopentadienyl)zirconium dichloride, (10), and were obtained commercially. The solid-state structures of the catalysts rac- and meso-1 were determined by X-ray crystallography. Computational methods were used for the structure optimization of the catalyst rac- and meso-1 in order to compare the theoretical calculations with the experimental results. Polymerization experiments were conducted in a highly purified autoclave system using low pressures (< 5 bar) of gaseous monomers. The experiments were designed to attain the optimal catalytic activity and a uniform copolymer composition. The prepared homo- and copolymers were characterized by the gel permeation chromatography, GPC, differential scanning calorimetry, DSC, nuclear magnetic resonance, NMR, and Fourier transform infrared spectrometry, FTIR . Molar mass (Mw, Mn), molar mass distribution (Mw/Mn), tacticity, comonomer content, melting temperature, glass transition temperature, and end group structures and content were determined. A special attention was paid on the correlation of the polymer properties with the catalyst structures and polymerization conditions. An intramolecular phenyl coordination was found in phenyl substituted benzyl zirconocenes 1-3 explaining the decreased activity of the catalysts. Novel copolymers poly(propene-co-phenylnorbornene) and poly(propene co-vinylcyclohexane), were synthesized and high molar mass poly(ethene-co-1-hexene) and poly(ethene-co-1-hexadecene) copolymers with elastic properties were prepared. Activation of a hafnocene catalyst was studied with UV-Vis spectrometry and activation process for the synthesis of ultra high molar mass poly(1-hexene) was found out.