Intraday and Weekend Volatility Patterns- Implications for Option Pricing

This study examines the intraday and weekend volatility on the German DAX. The intraday volatility is partitioned into smaller intervals and compared to a whole day’s volatility. The estimated intraday variance is U-shaped and the weekend variance is estimated to 19 % of a normal trading day. The patterns in the intraday and weekend volatility are used to develop an extension to the Black and Scholes formula to form a new time basis. Calendar or trading days are commonly used for measuring time in option pricing. The Continuous Time using Discrete Approximations model (CTDA) developed in this study uses a measure of time with smaller intervals, approaching continuous time. The model presented accounts for the lapse of time during trading only. Arbitrage pricing suggests that the option price equals the expected cost of hedging volatility during the option’s remaining life. In this model, time is allowed to lapse as volatility occurs on an intraday basis. The measure of time is modified in CTDA to correct for the non-constant volatility and to account for the patterns in volatility.

Pricing Index Options with Stochastic Volatility

The objective of this paper is to investigate the pricing accuracy under stochastic volatility where the volatility follows a square root process. The theoretical prices are compared with market price data (the German DAX index options market) by using two different techniques of parameter estimation, the method of moments and implicit estimation by inversion. Standard Black & Scholes pricing is used as a benchmark. The results indicate that the stochastic volatility model with parameters estimated by inversion using the available prices on the preceding day, is the most accurate pricing method of the three in this study and can be considered satisfactory. However, as the same model with parameters estimated using a rolling window (the method of moments) proved to be inferior to the benchmark, the importance of stable and correct estimation of the parameters is evident.

The prehistory of Suomussalmi, eastern Finland; the first billion years as revealed by isotopes and the composition of granitoid suites

The four papers summarized in this thesis deal with the Archean and earliest Paleoproterozoic granitoid suites observed in the Suomussalmi district, eastern Finland. Geologically, the area belongs to the Kianta Complex of the Western Karelian Terrane in the Karelian Province of the Fennoscandian shield. The inherited zircons up to 3440 Ma old together with Sm Nd and Pb Pb data confirm the existence of previously anticipated Paleoarchean protocrust in Suomussalmi. The general timeline of granitoid magmatism is similar to that of the surrounding areas. TTG magmatism occurred in three distinct phases: ca 2.95 Ga, 2.83 2.78 Ga and 2.76 2.74 Ga. In Suomussalmi the TTGs sensu stricto (K2O/Na2O less than 0.5) belong to the low-HREE type and are interpreted as partial melts of garnet amphibolites, which did not significantly interact with mantle peridotites. Transitional TTGs (K2O/Na2O more than 0.5), present in Suomussalmi and absent from surrounding areas, display higher LILE concentrations, but otherwise closely resemble the TTGs sensu stricto and indicate that recycling of felsic crust commenced in Suomussalmi 200 Ma earlier than in surrounding areas. The youngest TTG phase was coeval with the intrusion of the Likamännikkö quartz alkali feldspar syenite (2741 ± 2 Ma) complex. The complex contains angular fragments of ultrabasic rock, which display considerable compositional heterogeneity and are interpreted as cumulates containing clinopyroxene (generally altered to actinolite), apatite, allanite, epidote, and albite. The quartz alkali feldspar syenite cannot be regarded as alkaline sensu stricto, despite clear alkaline affinities. Within Likamännikkö there are also calcite carbonatite patches, which display mantle-like O- and C-isotope values, as well as trace element characteristics consistent with a magmatic origin, and could thus be among the oldest known carbonatites in the world. Sanukitoid (2.73 2.71 Ga) and quartz diorite suites (2.70 Ga) overlap within error margins and display compositional similarities, but can be differentiated from each other on the basis of higher Ba, K2O and LREE contents of the sanukitoids. The Likamännikkö complex, sanukitoids and quartz diorites are interpreted as originating from the metasomatized mantle and mark the diversification of the granitoid clan after 200 Ma of evolution dominated by the TTG suite. Widespread migmatization and the intrusion of anatectic leucogranitoids as dykes and intrusions of varying size took place at 2.70 2.69 Ga, following collisional thickening of the crust. The leucogranitoids and leucosomes of migmatized TTGs are compositionally alike and characterized by high silica contents and a leucocratic appearance. Due to compositional overlap, definitive discrimination between leucogranitoids and transitional TTGs requires isotope datings and/or knowledge of field relationships. Leucogranitoids represent partial melts of the local TTGs, both the sensu stricto and transitional types, mostly derived under water fluxed conditions, with possible fluid sources being late sanukitoids and quartz diorites as well as dehydrating lower crust. The Paleoproterozoic 2.44 2.39 Ga A-type granitoids of the Kianta Complex emplaced in an extensional environment are linked to the coeval and more widespread mafic intrusions and dykes observed over most of the Archean nucleus of the Fennoscandian shield. The A-type intrusions in the Suomussalmi area are interpreted as partial melts of the Archean lower crust and display differences in composition and magnetite content, which indicate differences in the composition and oxidation state of the source.

Paradigms in Statistical Inference for Finite Populations; Up to the 1950s

Modern sample surveys started to spread after statistician at the U.S. Bureau of the Census in the 1940s had developed a sampling design for the Current Population Survey (CPS). A significant factor was also that digital computers became available for statisticians. In the beginning of 1950s, the theory was documented in textbooks on survey sampling. This thesis is about the development of the statistical inference for sample surveys. For the first time the idea of statistical inference was enunciated by a French scientist, P. S. Laplace. In 1781, he published a plan for a partial investigation in which he determined the sample size needed to reach the desired accuracy in estimation. The plan was based on Laplace s Principle of Inverse Probability and on his derivation of the Central Limit Theorem. They were published in a memoir in 1774 which is one of the origins of statistical inference. Laplace s inference model was based on Bernoulli trials and binominal probabilities. He assumed that populations were changing constantly. It was depicted by assuming a priori distributions for parameters. Laplace s inference model dominated statistical thinking for a century. Sample selection in Laplace s investigations was purposive. In 1894 in the International Statistical Institute meeting, Norwegian Anders Kiaer presented the idea of the Representative Method to draw samples. Its idea was that the sample would be a miniature of the population. It is still prevailing. The virtues of random sampling were known but practical problems of sample selection and data collection hindered its use. Arhtur Bowley realized the potentials of Kiaer s method and in the beginning of the 20th century carried out several surveys in the UK. He also developed the theory of statistical inference for finite populations. It was based on Laplace s inference model. R. A. Fisher contributions in the 1920 s constitute a watershed in the statistical science He revolutionized the theory of statistics. In addition, he introduced a new statistical inference model which is still the prevailing paradigm. The essential idea is to draw repeatedly samples from the same population and the assumption that population parameters are constants. Fisher s theory did not include a priori probabilities. Jerzy Neyman adopted Fisher s inference model and applied it to finite populations with the difference that Neyman s inference model does not include any assumptions of the distributions of the study variables. Applying Fisher s fiducial argument he developed the theory for confidence intervals. Neyman s last contribution to survey sampling presented a theory for double sampling. This gave the central idea for statisticians at the U.S. Census Bureau to develop the complex survey design for the CPS. Important criterion was to have a method in which the costs of data collection were acceptable, and which provided approximately equal interviewer workloads, besides sufficient accuracy in estimation.

Mid-urethral slings for treatment of stress urinary incontinence : long- and mid-term follow-up

Urinary incontinence is a common problem, affecting one third of the women at least at some time during their lives. The prevalence of urinary incontinence increases with advancing age, and the everyday impact of incontinence on women and on health services is enormous. Urinary incontinence is usually divided into three different subtypes, of which stress urinary incontinence (SUI) is the most common. Surgical treatment is often needed to cure SUI, and modern mid-urethral sling procedures give the possibility to cure this condition with a low risk of adverse events, a problem often associated with the so-called traditional incontinence operations. Life expectancy among women in Western countries has grown beyond 80 years of age. Long-term efficacy of treatment options for urinary incontinence therefore becomes an important issue in a world with limited eco-nomic resources. The purpose of the present study was to prospectively evaluate the long-term efficacy and safety of the first minimally invasive mid-urethral tape procedure, the Tension-free Vaginal Tape (TVT) procedure. The long-term (5-year) follow-up results of the TVT procedure as a repeat operation af-ter an unsuccessful mid-urethral tape operation were studied and the reasons for failure of the first operation were analyzed. Another purpose was to compare the original TVT procedure with a newer modification, the Tension-free Vaginal Tape Obturator (TVT-O) procedure within a multi-centre, randomized context in order to find out possible differences between these procedures re-garding efficacy and complications and the effects on symptoms of urgency. The first study of the present thesis is a prospective, Nordic, three-centre follow-up study of 90 women suffering from SUI, who were treated by means of the TVT procedure. The mean follow-up time was more than eleven years, and the study is the first to be published in connection with more than ten years of follow-up. The second study is a retrospective analysis of 26 women who were treated with a repeat TVT procedure after an unsuccessful primary mid-urethral tape procedure. The third and fourth studies concern 273 women in seven centres in Finland who were ran-domly assigned to the TVT and TVT-O procedures, the 3-year follow-up results of which are pre-sented in this thesis. After eleven years of follow-up, 90% of the women had a negative cough stress test result and a negative 24-h pad test result. The subjective cure rate measured as the women s global impression of cure was 77%, the rate of improvement 20%, and only 3% thought that the treatment had failed. No late-onset adverse effects were found. The repeat TVT procedure was successful in 75% of the cases when women who were cured and women who were significantly improved were included. The reasons for failure of the first operation could be separated into four different groups: tape material-related, operation technique-related, concomitant illness-related and a group with no identifiable reason. There were no intra-operative complications during the repeat operation. In the randomized trial comparing the TVT with the TVT-O procedure a cough stress test results were negative in 94.6% and 89.5% of the women in the two groups, respectively, after a 3-year follow-up period. There were no statistical differences in the cure rate or the rate of complications be-tween the two procedures. Symptoms of urgency were analyzed more closely and the main finding was that the prevalence of urgency symptoms decreased significantly after both mid-urethral sling procedures. The TVT operation was found to be an effective and safe procedure even after eleven years of follow-up. Long-term follow-up after a repeat TVT procedure revealed that the TVT procedure can well be considered after an unsuccessful mid-urethra tape procedure, because 75% of the patients showed significantly improvement of their incontinence. The TVT and TVT-O procedures showed no statistically significant differences in efficacy and rate of complications after three years of follow-up. In most cases these procedures alleviate preoperative symptoms of urgency and the risk of developing de novo urgency is low.