Options on realized variance and convex orders

Realized variance option and options on quadratic variation normalized to unit expectation are analysed for the property of monotonicity in maturity for call options at a fixed strike. When this condition holds the risk-neutral densities are said to be increasing in the convex order. For Leacutevy processes, such prices decrease with maturity. A time series analysis of squared log returns on the S&P 500 index also reveals such a decrease. If options are priced to a slightly increasing level of acceptability, then the resulting risk-neutral densities can be increasing in the convex order. Calibrated stochastic volatility models yield possibilities in both directions. Finally, we consider modeling strategies guaranteeing an increase in convex order for the normalized quadratic variation. These strategies model instantaneous variance as a normalized exponential of a Leacutevy process. Simulation studies suggest that other transformations may also deliver an increase in the convex order

The fine structure of asset returns: an empirical investigation

We investigate the importance of diffusion and jumps in a new model for asset returns. In contrast to standard models, we allow for jump components displaying finite or infinite activity and variation. Empirical investigations of time series indicate that index dynamics are devoid of a diffusion component, which may be present in the dynamics of individual stocks. This leads to the conjecture, confirmed on options data, that the risk-neutral process should be free of a diffusion component. We conclude that the statistical and risk-neutral processes for equity prices are pure jump processes of infinite activity and finite variation

Phase diagram of two interacting helical states

We consider two coupled time-reversal-invariant helical edge modes of the same helicity, such as would occur on two stacked quantum spin Hall insulators. In the presence of interaction, the low-energy physics is described by two collective modes, one corresponding to the total current flowing around the edge and the other one describing relative fluctuations between the two edges.We find that quite generically, the relative mode becomes gapped at low temperatures, but only when tunneling between the two helical modes is nonzero. There are two distinct possibilities for the gapped state depending on the relative size of different interactions. If the intraedge interaction is stronger than the interedge interaction, the state is characterized as a spin-nematic phase. However, in the opposite limit, when the interaction between the helical edge modes is strong compared to the interaction within each mode, a spin-density wave forms, with emergent topological properties. First, the gap protects the conducting phase against localization by weak nonmagnetic impurities; second, the protected phase hosts localized zero modes on the ends of the edge that may be created by sufficiently strong nonmagnetic impurities

Viability of primordial black holes as short period gamma-ray bursts

It has been proposed that the short period gamma-ray bursts, which occur at a rate of $\sim 10 {\rm yr^{-1}}$, may be evaporating primordial black holes (PBHs). Calculations of the present PBH evaporation rate have traditionally assumed that the PBH mass function varies as $M_{{\rm BH}}^{-5/2}$. This mass function only arises if the density perturbations from which the PBHs form have a scale invariant power spectrum. It is now known that for a scale invariant power spectrum, normalised to COBE on large scales, the PBH density is completely negligible, so that this mass function is cosmologically irrelevant. For non-scale-invariant power spectra, if all PBHs which form at given epoch have a fixed mass then the PBH mass function is sharply peaked around that mass, whilst if the PBH mass depends on the size of the density perturbation from which it forms, as is expected when critical phenomena are taken into account, then the PBH mass function will be far broader than $M_{{\rm BH}}^{-5/2}$. In this paper we calculate the present day PBH evaporation rate, using constraints from the diffuse gamma-ray background, for both of these mass functions. If the PBH mass function has significant finite width, as recent numerical simulations suggest, then it is not possible to produce a present day PBH evaporation rate comparable with the observed short period gamma-ray burst rate. This could also have implications for other attempts to detect evaporating PBHs.Comment: 5 pages, 2 figures, version to appear in Phys. Rev. D with additional reference

Observational constraints on the nature of very short gamma-ray bursts

We discuss a very peculiar subgroup of gamma-ray bursts among the BATSE sources. These bursts are very short ($T_{90} \le$0.1 s), hard, and came predominantly from a restricted direction of the sky (close to the Galactic anti-center). We analyze their arrival times and possible correlations, as well as the profiles of individual bursts. We find no peculiarities in the arrival times of Very Short Bursts (VSBs) despite their highly non-uniform spatial distribution. There is no dependence in the burst shapes on location. Bursts coming both from the burst-enhancement Galactic Anticenter region and from all other directions show considerable dispersion in their rise and fall times. Significant fraction of VSBs have multiple peaks despite their extremely short duration. Burst time properties are most likely to be consistent with two origin mechanisms: either with binary NS-NS mergers with low total masses passing through a phase of hypermassive neutron star, or with evaporation of the primordial black holes in the scenario of no photosphere formation.Comment: 25 pages, 14 figures; accepted to New Astronom

Spatial variations in lead isotopes, Tasman Element, eastern Australia

Lead isotope data from ore deposits and mineral occurrences in the Tasman Element of eastern Australia have been used to construct isotopic maps of this region. These maps exhibit systematic patterns in parameters derived from isotope ratios. The parameters include μ (238U/204Pb), as calculated using the Cumming and Richards (1975) lead evolution model, and the difference between true age of mineralisation and the Cumming and Richards lead isotope model age of mineralisation (Δt). Variations in μ coincide with boundaries at the orogen, subprovince and zone scales. The boundary between the Lachlan and New England orogens is accompanied by a decrease in μ, and within the Lachlan Orogen, the Central Subprovince is characterised by μ that is significantly higher than in the adjacent Eastern and Western subprovinces. Within the Eastern Subprovince, the Cu-Au-rich Macquarie Arc is characterised by significantly lower μ relative to adjacent rocks. The Macquarie Arc is also characterised by very high Δt (generally above 200 Myr). Other regions characterised by very high Δt include western Tasmania, the southeastern New England Orogen, and the Hodgkinson Province in northern Queensland. These anomalies are within a broad pattern of decreasing Δt from east to west, with Paleozoic deposits within or adjacent to Proterozoic crust characterised by Δt values of 50 Myr or below. The patterns in Δt are interpreted to reflect the presence of the two major tectonic components involved in the Paleozoic Tasman margin in Australia (cf., Münker, 2000): subducting proto-Pacific crust (Δt >150 Myr), and Proterozoic Australia crust (Δt < 50 Myr) on the over-riding plate. Proterozoic Australia crustal sources are interpreted to dominate the western parts of the Tasman Element and Proterozoic crust further to the west, whereas Pacific crustal sources are inferred to characterise western Tasmania and much of the eastern part of the Tasman Element. Contrasts in Δt between the Cambrian Mount Read Volcanics in western Tasmania and similar aged rocks in western Victoria and New South Wales make direct tectonic correlation between these rocks problematic

(An)Isotropic models in scalar and scalar-tensor cosmologies

We study how the constants $G$ and $\Lambda$ may vary in different theoretical models (general relativity with a perfect fluid, scalar cosmological models (\textquotedblleft quintessence\textquotedblright) with and without interacting scalar and matter fields and a scalar-tensor model with a dynamical $\Lambda$) in order to explain some observational results. We apply the program outlined in section II to study three different geometries which generalize the FRW ones, which are Bianchi \textrm{V}, \textrm{VII}$_{0}$ and \textrm{IX}, under the self-similarity hypothesis. We put special emphasis on calculating exact power-law solutions which allow us to compare the different models. In all the studied cases we arrive to the conclusion that the solutions are isotropic and noninflationary while the cosmological constant behaves as a positive decreasing time function (in agreement with the current observations) and the gravitational constant behaves as a growing time function