Implied volatility of basket options at extreme strikes

In the paper, we characterize the asymptotic behavior of the implied volatility of a basket call option at large and small strikes in a variety of settings with increasing generality. First, we obtain an asymptotic formula with an error bound for the left wing of the implied volatility, under the assumption that the dynamics of asset prices are described by the multidimensional Black-Scholes model. Next, we find the leading term of asymptotics of the implied volatility in the case where the asset prices follow the multidimensional Black-Scholes model with time change by an independent increasing stochastic process. Finally, we deal with a general situation in which the dependence between the assets is described by a given copula function. In this setting, we obtain a model-free tail-wing formula that links the implied volatility to a special characteristic of the copula called the weak lower tail dependence function

The Opportunity Process for Optimal Consumption and Investment with Power Utility

We study the utility maximization problem for power utility random fields in a semimartingale financial market, with and without intermediate consumption. The notion of an opportunity process is introduced as a reduced form of the value process of the resulting stochastic control problem. We show how the opportunity process describes the key objects: optimal strategy, value function, and dual problem. The results are applied to obtain monotonicity properties of the optimal consumption.Comment: 24 pages, forthcoming in 'Mathematics and Financial Economics

MRI turbulence and thermal instability in accretion discs

A long-standing puzzle in the study of black hole accretion concerns the presence or not of thermal instability. Classical theory predicts that the encircling accretion disc is unstable, as do some self-consistent magnetohydrodynamic simulations of the flow. Yet observations of strongly accreting sources generally fail to exhibit cyclic or unstable dynamics on the expected time-scales. This paper checks whether turbulent fluctuations impede thermal instability. It also asks if it makes sense to conduct linear stability analyses on a turbulent background. These issues are explored with a set of MRI simulations in thermally unstable local boxes in combination with stochastic equations that approximate the disc energetics. These models show that the disc’s thermal behaviour deviates significantly from laminar theory, though ultimately a thermal runaway does occur. We find that the disc temperature evolves as a biased random walk, rather than increasing exponentially, and thus generates a broad spread of outcomes, with instability often delayed for several thermal times. We construct a statistical theory that describes some of this behaviour, emphasizing the importance of the ‘escape time’ and its associated probability distribution. In conclusion, turbulent fluctuations on their own cannot stabilize a disc, but they can weaken and delay thermal instability.This work was partially funded by STFC grants ST/L000636/1 and ST/K501906/1. Some of the simulations were run on the DiRAC Complexity system, operated by the University of Leicester IT Services, which forms part of the STFC DiRAC HPC Facility (www.dirac.ac.uk). This equipment is funded by BIS National E- Infrastructure capital grant ST/K000373/1 and STFC DiRAC Operations grant ST/K0003259/1. DiRAC is part of the UK National E-Infrastructure

Accuracy of working length determination with root ZX apex locator and radiography: An in vivo and ex vivo study

The purpose of this study was to clinically compare working length (WL) determination with root ZX apex locator and radiography, and then compare them with direct visualization method ex vivo. A total of 75 maxillary central and lateral incisors were selected. Working length determination was carried out using radiographic and electronic apex locator methods. Subsequently, the tooth under study was extracted and actual working length was determined directly under a stereomicroscope. Data were analyzed by Wilcoxon signed-rank, Spearman’s correlation coefficient and intra-class correlation tests. All the statistical analyses were set with a significance level of α = 0.05. The absolute measurement errors of the two methods were compared using Wilcoxon signed test, exhibiting no statistically significant difference in measurement errors between the two methods. Descriptive evaluation revealed that in 72% (n = 54) of the specimens, both methods had errors in the same direction and in 28% (n = 21) of the specimens, the two methods had errors in opposite directions. Intra-class correlation coefficient test demonstrated a high degree of agreement between the two methods. In conclusion, this study did not show any difference between radiography, root ZX and direct visualization in WL determination.Key words: Working length, electronic apex locator, root ZX, radiography

Tailoring negative pressure by crystal defects: Crack induced hydride formation in Al alloys

Climate change motivates the search for non-carbon-emitting energy generation and storage solutions. Metal hydrides show promising characteristics for this purpose. They can be further stabilized by tailoring the negative pressure of microstructural and structural defects. Using systematic ab initio and atomistic simulations, we demonstrate that an enhancement in the formation of hydrides at the negatively pressurized crack tip region is feasible by increasing the mechanical tensile load on the specimen. The theoretical predictions have been used to reassess and interpret atom probe tomography experiments for a high-strength 7XXX-aluminium alloy that show a substantial enhancement of hydrogen concentration at structural defects near a stress-corrosion crack tip. These results contain important implications for enhancing the capability of metals as H-storage materials.Comment: 22 pages, 9 figure

Selected heterozygosity at cis-regulatory sequences increases the expression homogeneity of a cell population in humans

Background: Examples of heterozygote advantage in humans are scarce and limited to protein-coding sequences. Here, we attempt a genome-wide functional inference of advantageous heterozygosity at cis-regulatory regions. Results: The single-nucleotide polymorphisms bearing the signatures of balancing selection are enriched in active cis-regulatory regions of immune cells and epithelial cells, the latter of which provide barrier function and innate immunity. Examples associated with ancient trans-specific balancing selection are also discovered. Allelic imbalance in chromatin accessibility and divergence in transcription factor motif sequences indicate that these balanced polymorphisms cause distinct regulatory variation. However, a majority of these variants show no association with the expression level of the target gene. Instead, single-cell experimental data for gene expression and chromatin accessibility demonstrate that heterozygous sequences can lower cell-to-cell variability in proportion to selection strengths. This negative correlation is more pronounced for highly expressed genes and consistently observed when using different data and methods. Based on mathematical modeling, we hypothesize that extrinsic noise from fluctuations in transcription factor activity may be amplified in homozygotes, whereas it is buffered in heterozygotes. While high expression levels are coupled with intrinsic noise reduction, regulatory heterozygosity can contribute to the suppression of extrinsic noise. Conclusions: This mechanism may confer a selective advantage by increasing cell population homogeneity and thereby enhancing the collective action of the cells, especially of those involved in the defense systems in humansope

Magnetic anisotropies and its optical manipulation in epitaxial bismuth ferrite/ferromagnet heterostructure

© 2018 Elsevier B.V. Exchange-coupled BiFeO3/ferromagnet thin film heterostructures are promising for a fast and power efficient control of magnetization of the ferromagnetic layer. In the paper, the results of the study of magnetic properties of the epitaxial Fe2B/BiFeO3heterostructure on (0 0 1)-SrTiO3substrate with ferromagnetic resonance (FMR) spectroscopy are presented. The hierarchy of magnetic anisotropies that determine the angular variation of the resonance field in-plane and in-/out-of the plane of the system include the tetragonal four-fold and uniaxial terms for the Fe2B layer, uniaxial term for antiferromagnetic BiFeO3layer and the exchange coupling at the interface. We find out that the exchange bias direction can be switched by a strong enough applied magnetic field. Both the exchange bias and an in-plane FMR resonance field of the heterostructure are strongly affected by the illumination with λ = 405 nm light. An optical tunability of the exchange bias and ferromagnetic resonance fields of the heterostructure has been demonstrated