Asymptotics for Exponential Levy Processes and their Volatility Smile: Survey and New Results

Exponential L\'evy processes can be used to model the evolution of various financial variables such as FX rates, stock prices, etc. Considerable efforts have been devoted to pricing derivatives written on underliers governed by such processes, and the corresponding implied volatility surfaces have been analyzed in some detail. In the non-asymptotic regimes, option prices are described by the Lewis-Lipton formula which allows one to represent them as Fourier integrals; the prices can be trivially expressed in terms of their implied volatility. Recently, attempts at calculating the asymptotic limits of the implied volatility have yielded several expressions for the short-time, long-time, and wing asymptotics. In order to study the volatility surface in required detail, in this paper we use the FX conventions and describe the implied volatility as a function of the Black-Scholes delta. Surprisingly, this convention is closely related to the resolution of singularities frequently used in algebraic geometry. In this framework, we survey the literature, reformulate some known facts regarding the asymptotic behavior of the implied volatility, and present several new results. We emphasize the role of fractional differentiation in studying the tempered stable exponential Levy processes and derive novel numerical methods based on judicial finite-difference approximations for fractional derivatives. We also briefly demonstrate how to extend our results in order to study important cases of local and stochastic volatility models, whose close relation to the L\'evy process based models is particularly clear when the Lewis-Lipton formula is used. Our main conclusion is that studying asymptotic properties of the implied volatility, while theoretically exciting, is not always practically useful because the domain of validity of many asymptotic expressions is small.Comment: 92 pages, 15 figure

Guds rige mellem forkyndelse og handling

Der tegner sig for tiden en spænding mellem en traditionel forkyndelse af loven og evangeliet og en nyere betoning af gudsriget. Hvordan forholder de to tilgange sig til hinanden? Dette omhandler denne artikel

Inflammation, Immunity, and Vaccines for Helicobacter

Helicobacter pylori represents the major etiologic agent of gastritis, gastric, and duodenal ulcer disease and can cause gastric cancer and mucosa-associated lymphoid tissue B-cell lymphoma. It is clear that the consequences of infection reflect diverse outcomes of the interaction of bacteria and host immune system. The hope is that by deciphering the deterministic rules – if any – of this interplay, we will eventually be able to predict, treat, and ultimately prevent disease. Over the past year, research on the immunology of this infection started to probe the role of small noncoding RNAs, a novel class of immune response regulators. Furthermore, we learned new details on how infection is detected by innate pattern recognition receptors. Induction of effective cell-mediated immunity will be key for the development of a vaccine, and new work published analyzed the relevance and contribution of CD4 T helper cell subsets to the immune reaction. Th17 cells, which are also induced during natural infection, were shown to be particularly important for vaccination. Cost-efficiency of vaccination was re-assessed and confirmed. Thus, induction and shaping of the effector roles of such protective Th populations will be a target of the newly described vaccine antigens, formulations, and modes of application that we also review here

Merging high energy with soft and collinear logarithms using HEJ and PYTHIA

We present a method to combine the all-order treatment of the High Energy Jets exclusive partonic Monte Carlo (HEJ) with the parton shower of Pythia8, while retaining the logarithmic accuracy of both. This procedure enables the generation of fully realistic and hadronised events with HEJ. Furthermore, the combination of the two allorder treatments leads to improvements in the quality of the description of observables, in particular for regions with disparate transverse scales

Making sense: dopamine activates conscious self-monitoring through medial prefrontal cortex

When experiences become meaningful to the self, they are linked to synchronous activity in a paralimbic network of self-awareness and dopaminergic activity. This network includes medial prefrontal and medial parietal/posterior cingulate cortices, where transcranial magnetic stimulation may transiently impair self-awareness. Conversely, we hypothesize that dopaminergic stimulation may improve self-awareness and metacognition (i.e., the ability of the brain to consciously monitor its own cognitive processes). Here, we demonstrate improved noetic (conscious) metacognition by oral administration of 100 mg dopamine in minimal self-awareness. In a separate experiment with extended self-awareness dopamine improved the retrieval accuracy of memories of self-judgment (autonoetic, i.e., explicitly self-conscious) metacognition. Concomitantly, magnetoencephalography (MEG) showed increased amplitudes of oscillations (power) preferentially in the medial prefrontal cortex. Given that electromagnetic activity in this region is instrumental in self-awareness, this explains the specific effect of dopamine on explicit self-awareness and autonoetic metacognition

Taxation of Agriculture in selected countries. Study of The United States, Canada, Australia, Germany, United Kingdom, Ireland, France, Switzerland and Italy with relevance to the WTO

This report looks at the special measures for agriculture within the field of taxation and social security. Chapter 1 and 2 deal with general overview of taxes and taxation principles. Chapter 3 give more detailed information of the tax system in the selected countries, US, Canada, Australia, Germany, UK, France, Ireland, Italy and Switzerland. Chapter four deals with notifications to the Committee on Agriculture in the World Trade Organisation (WTO) concerning tax measures. In chapter 5 we have tried to systematize the different tax schemes in the selected countries.Taxation of Agriculture in selected countries. Study of The United States, Canada, Australia, Germany, United Kingdom, Ireland, France, Switzerland and Italy with relevance to the WTOpublishedVersio