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.

Phylogeography and demographic history of Lacerta lepida in the Iberian Peninsula

The Iberian Peninsula is recognized as an important refugial area for species survival and diversification during the climatic cycles of the Quaternary. Recent phylogeographic studies have revealed Iberia as a complex of multiple refugia. However, most of these studies have focused either on species with narrow distributions within the region or species groups that, although widely distributed, generally have a genetic structure that relates to pre-Quaternary cladogenetic events. In this study we undertake a detailed phylogeographic analysis of the lizard species, Lacerta lepida, whose distribution encompasses the entire Iberian Peninsula. We attempt to identify refugial areas, recolonization routes, zones of secondary contact and date demographic events within this species. Results support the existence of 6 evolutionary lineages (phylogroups) with a strong association between genetic variation and geography, suggesting a history of allopatric divergence in different refugia. Diversification within phylogroups is concordant with the onset of the Pleistocene climatic oscillations. The southern regions of several phylogroups show a high incidence of ancestral alleles in contrast with high incidence of recently derived alleles in northern regions. All phylogroups show signs of recent demographic and spatial expansions. We have further identified several zones of secondary contact, with divergent mitochondrial haplotypes occurring in narrow zones of sympatry. The concordant patterns of spatial and demographic expansions detected within phylogroups, together with the high incidence of ancestral haplotypes in southern regions of several phylogroups, suggests a pattern of contraction of populations into southern refugia during adverse climatic conditions from which subsequent northern expansions occurred. This study supports the emergent pattern of multiple refugia within Iberia but adds to it by identifying a pattern of refugia coincident with the southern distribution limits of individual evolutionary lineages. These areas are important in terms of long-term species persistence and therefore important areas for conservation.