Robust option replication for a Black-Scholes model extended with nondeterministic trends

Statistical analysis on various stocks reveals long range dependence behavior of the stock prices that is not consistent with the classical Black and Scholes model. This memory or nondeterministic trend behavior is often seen as a reflection of market sentiments and causes that the historical volatility estimator becomes unreliable in practice. We propose an extension of the Black and Scholes model by adding a term to the original Wiener term involving a smoother process which accounts for these effects. The problem of arbitrage will be discussed. Using a generalized stochastic integration theory [8], we show that it is possible to construct a self financing replicating portfolio for a European option without any further knowledge of the extension and that, as a consequence, the classical concept of volatility needs to be re-interpreted. AMS subject classifications: 60H05, 60H10, 90A09

Self-Consistent Response of a Galactic Disk to an Elliptical Perturbation Halo Potential

We calculate the self-consistent response of an axisymmetric galactic disk perturbed by an elliptical halo potential of harmonic number m = 2, and obtain the net disk ellipticity. Such a potential is commonly expected to arise due to a galactic tidal encounter and also during the galaxy formation process. The self-gravitational potential corresponding to the self-consistent, non-axisymmetric density response of the disk is obtained by inversion of Poisson equation for a thin disk. This response potential is shown to oppose the perturbation potential, because physically the disk self-gravity resists the imposed potential. This results in a reduction in the net ellipticity of the perturbation halo potential in the disk plane. The reduction factor denoting this decrease is independent of the strength of the perturbation potential, and has a typical minimum value of 0.75 - 0.9 for a wide range of galaxy parameters. The reduction is negligible at all radii for higher harmonics (m > or = 3) of the halo potential. (abridged).Comment: 26 pages (LaTex- aastex style), 3 .eps figures. To appear in the Astrophysical Journal, Vol. 542, Oct. 20, 200

A Complete Sample of Megaparsec Size Double Radio Sources from SUMSS

We present a complete sample of megaparsec-size double radio sources compiled from the Sydney University Molonglo Sky Survey (SUMSS). Almost complete redshift information has been obtained for the sample. The sample has the following defining criteria: Galactic latitude |b| > 12.5 deg, declination < -50 deg and angular size > 5 arcmin. All the sources have projected linear size larger than 0.7 Mpc (assuming H_o = 71 km/s/Mpc). The sample is chosen from a region of the sky covering 2100 square degrees. In this paper, we present 843-MHz radio images of the extended radio morphologies made using the Molonglo Observatory Synthesis Telescope (MOST), higher resolution radio observations of any compact radio structures using the Australia Telescope Compact Array (ATCA), and low resolution optical spectra of the host galaxies from the 2.3-m Australian National University (ANU) telescope at Siding Spring Observatory. The sample presented here is the first in the southern hemisphere and significantly enhances the database of known giant radio sources. The giant radio sources with linear size exceeding 0.7 Mpc have an abundance of (215 Mpc)^(-3) at the sensitivity of the survey. In the low redshift universe, the survey may be suggesting the possibility that giant radio sources with relict lobes are more numerous than giant sources in which beams from the centre currently energize the lobes.Comment: 67 pages, 29 figures, for full resolution figures see http://www.astrop.physics.usyd.edu.au/SUMSS/PAPERS/Submit-May11-ms.pd

Molecular spectrum of TSHβ subunit gene defects in central hypothyroidism in the UK and Ireland.

OBJECTIVE: Homozygous mutations in the TSH beta subunit gene (TSHB) result in severe, isolated, central congenital hypothyroidism (CCH). This entity evades diagnosis in TSH-based congenital hypothyroidism (CH) screening programmes in the UK and Ireland. Accordingly, genetic diagnosis, enabling ascertainment of affected relatives in families, is critical for prompt diagnosis and treatment of the disorder. DESIGN, PATIENTS AND MEASUREMENTS: Four cases of isolated TSH deficiency from three unrelated families in the UK and Ireland were investigated for mutations or deletions in TSHB. Haplotype analysis, to investigate a founder effect, was undertaken in cases with identical mutations (c.373delT). RESULTS: Two siblings in kindred 1 were homozygous for a previously described TSHB mutation (c.373delT). In kindreds 2 and 3, the affected individuals were compound heterozygous for TSHB c.373delT and either a 5·4-kB TSHB deletion (kindred 2, c.1-4389_417*195delinsCTCA) or a novel TSHB missense mutation (kindred 3, c.2T>C, p.Met1?). Neurodevelopmental retardation, following delayed diagnosis and treatment, was present in 3 cases. In contrast, the younger sibling in kindred 1 developed normally following genetic diagnosis and treatment from birth. CONCLUSIONS: This study, including the identification of a second, novel, TSHB deletion, expands the molecular spectrum of TSHB defects and suggests that allele loss may be a commoner basis for TSH deficiency than previously suspected. Delayed diagnosis and treatment of profound central hypothyroidism in such cases result in neurodevelopmental retardation. Inclusion of thyroxine (T4) plus thyroxine-binding globulin (TBG), or free thyroxine (FT4) in CH screening, together with genetic case ascertainment enabling earlier therapeutic intervention, could prevent such adverse sequelae.Wellcome Trust (Grant IDs: 100585/Z/12/Z, 095564/Z/11/Z), National Institute for Health Research Biomedical Research Centre CambridgeThis is the final version of the article. It first appeared from Wiley via http://dx.doi.org/10.1111/cen.1314

Self-consistent massive disks in triaxial dark matter halos

Galactic disks in triaxial dark matter halos become deformed by the elliptical potential in the plane of the disk in such a way as to counteract the halo ellipticity. We develop a technique to calculate the equilibrium configuration of such a disk in the combined disk-halo potential, which is based on the method of Jog (2000) but accounts for the radial variation in both the halo potential and the disk ellipticity. This crucial ingredient results in qualitatively different behavior of the disk: the disk circularizes the potential at small radii, even for a reasonably low disk mass. This effect has important implications for proposals to reconcile cuspy halo density profiles with low surface brightness galaxy rotation curves using halo triaxiality. The disk ellipticities in our models are consistent with observational estimates based on two-dimensional velocity fields and isophotal axis ratios.Comment: ApJ, in pres

A Photometric Method for Quantifying Asymmetries in Disk Galaxies

A photometric method for quantifying deviations from axisymmetry in optical images of disk galaxies is applied to a sample of 32 face-on and nearly face-on spirals. The method involves comparing the relative fluxes contained within trapezoidal sectors arranged symmetrically about the galaxy center of light, excluding the bulge and/or barred regions. Such a method has several advantages over others, especially when quantifying asymmetry in flocculent galaxies. Specifically, the averaging of large regions improves the signal-to-noise in the measurements; the method is not strongly affected by the presence of spiral arms; and it identifies the kinds of asymmetry that are likely to be dynamically important. Application of this "method of sectors" to R-band images of 32 disk galaxies indicates that about 30% of spirals show deviations from axisymmetry at the 5-sigma level.Comment: 17 pages, 2 tables and 6 figures, uses psfig and AAS LaTex; to appear in A

The Evolution of the ISM in the Mildly Disturbed Spiral Galaxy NGC 4647

We present matched-resolution maps of HI and CO emission in the Virgo Cluster spiral NGC 4647. The galaxy shows a mild kinematic disturbance in which one side of the rotation curve flattens but the other side continues to rise. This kinematic asymmetry is coupled with a dramatic asymmetry in the molecular gas distribution but not in the atomic gas. An analysis of the gas column densities and the interstellar pressure suggests that the H2/HI surface density ratio on the east side of the galaxy is three times higher than expected from the hydrostatic pressure contributed by the mass of the stellar disk. We discuss the probable effects of ram pressure, gravitational interactions, and asymmetric potentials on the interstellar medium and suggest it is likely that a m=1 perturbation in the gravitational potential could be responsible for all of the galaxy's features. Kinematic disturbances of the type seen here are common, but the curious thing about NGC 4647 is that the molecular distribution appears more disturbed than the HI distribution. Thus it is the combination of the two gas phases that provides such interesting insight into the galaxy's history and into models of the interstellar medium.Comment: ApJ, accepte

The Ellipticity of the Disks of Spiral Galaxies

The disks of spiral galaxies are generally elliptical rather than circular. The distribution of ellipticities can be fit with a log-normal distribution. For a sample of 12,764 galaxies from the Sloan Digital Sky Survey Data Release 1 (SDSS DR1), the distribution of apparent axis ratios in the i band is best fit by a log-normal distribution of intrinsic ellipticities with ln epsilon = -1.85 +/- 0.89. For a sample of nearly face-on spiral galaxies, analyzed by Andersen and Bershady using both photometric and spectroscopic data, the best fitting distribution of ellipticities has ln epsilon = -2.29 +/- 1.04. Given the small size of the Andersen-Bershady sample, the two distribution are not necessarily inconsistent. If the ellipticity of the potential were equal to that of the light distribution of the SDSS DR1 galaxies, it would produce 1.0 magnitudes of scatter in the Tully-Fisher relation, greater than is observed. The Andersen-Bershady results, however, are consistent with a scatter as small as 0.25 magnitudes in the Tully-Fisher relation.Comment: 19 pages, 5 figures; ApJ, accepte

Optically Faint Radio Sources: Reborn AGN?

We have discovered a number of relatively strong radio sources in the field-of-view of SDSS galaxy clusters which present no optical counterparts down to the magnitude limits of the SDSS. The optically faint radio sources appear as double-lobed or core-jet objects on the FIRST radio images and have projected angular sizes ranging from 0.5 to 1.0 arcmin. We have followed-up these sources with near-infrared imaging using the wide-field imager HAWK-I on the VLT. K_s-band emitting regions, about 1.5 arcsec in size and coincident with the centers of the radio structures, were detected in all the sources, with magnitudes in the range 17-20 mag. We have used spectral modelling to characterize the sample sources. In general, the radio properties are similar to those observed in 3CRR sources but the optical-radio slopes are consistent with moderate to high redshift (z<4) gigahertz-peaked spectrum sources. Our results suggest that these unusual objects are galaxies whose black hole has been recently re-ignited but retain large-scale radio structures, signatures of previous AGN activity.Comment: Accepted for publication in A&

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