Time-Changed Fast Mean-Reverting Stochastic Volatility Models

We introduce a class of randomly time-changed fast mean-reverting stochastic volatility models and, using spectral theory and singular perturbation techniques, we derive an approximation for the prices of European options in this setting. Three examples of random time-changes are provided and the implied volatility surfaces induced by these time-changes are examined as a function of the model parameters. Three key features of our framework are that we are able to incorporate jumps into the price process of the underlying asset, allow for the leverage effect, and accommodate multiple factors of volatility, which operate on different time-scales

The Nearest Group of Galaxies

The small Antlia-Sextans clustering of galaxies is located at a distance of only 1.36 Mpc from the Sun, and 1.72 Mpc from the adopted barycenter of the Local Group. The latter value is significantly greater than the radius of the zero- velocity surface of the Local Group which, for an assumed age of 14 Gyr, has Ro = 1.18 " 0.15 Mpc. This, together with the observation that the members of the Ant-Sex group have a mean redshift of +114 " 12 km s-1 relative to the centroid of the Local Group, suggests that the Antlia-Sextans group is not bound to our Local Group, and that it is expanding with the Hubble flow. If this conclusion is correct, then Antlia-Sextans may be the nearest external clustering of galaxies. The total galaxian population of the Ant-Sex group is ~ 1/5 that of the Local Group. However, the integrated luminosity of Ant-Sex is two orders of magnitude lower than that of the Local Group. Subject headings: Galaxies - clusters: individual (Antlia-Sextans)Comment: Has been accepted for publication in the Astrophysical Journal Letter

An Atlas of H-alpha and R Images and Radial Profiles of 29 Bright Isolated Spiral Galaxies

Narrow-band H-alpha+[NII] and broadband R images and surface photometry are presented for a sample of 29 bright (M_B < -18) isolated S0-Scd galaxies within a distance of 48 Mpc. These galaxies are among the most isolated nearby spiral galaxies of their Hubble classifications as determined from the Nearby Galaxies Catalog (Tully 1987a).Comment: To appear in Astrophysical Journal Supplement Series. 17 pages, including 8 atlas pages in JPEG format. Version with high resolution figures available at http://www1.union.edu/~koopmanr/preprints.htm

Long-range memory model of trading activity and volatility

Earlier we proposed the stochastic point process model, which reproduces a variety of self-affine time series exhibiting power spectral density S(f) scaling as power of the frequency f and derived a stochastic differential equation with the same long range memory properties. Here we present a stochastic differential equation as a dynamical model of the observed memory in the financial time series. The continuous stochastic process reproduces the statistical properties of the trading activity and serves as a background model for the modeling waiting time, return and volatility. Empirically observed statistical properties: exponents of the power-law probability distributions and power spectral density of the long-range memory financial variables are reproduced with the same values of few model parameters.Comment: 12 pages, 5 figure

Gas Rich Dwarf Spheroidals

We present evidence that nearly half of the dwarf spheroidal galaxies (dSph and dSph/dIrr) in the Local Group are associated with large reservoirs of atomic gas, in some cases larger than the stellar mass. The gas is sometimes found at large distance (~10 kpc) from the center of a galaxy and is not necessarily centered on it. Similarly large quantities of ionized gas could be hidden in these systems as well. The properties of some of the gas reservoirs are similar to the median properties of the High-Velocity Clouds (HVCs); two of the HI reservoirs are catalogued HVCs. The association of the HI with the dwarf spheroidals might thus provide a link between the HVCs and stars. We show that the HI content of the Local Group dSphs and dIrrs exhibits a sharp decline if the galaxy is within 250 kpc of either the Milky Way or M31. This can be explained if both galaxies have a sufficiently massive x-ray emitting halo that produces ram-pressure stripping if a dwarf ventures too close to either giant spiral. We also investigate tidal stripping of the dwarf galaxies and find that although it may play a role, it cannot explain the apparent total absence of neutral gas in most dSph galaxies at distances less than 250 kpc. For the derived mean density of the hot gas, n_0 = 2.5e-5 cm^-2, ram-pressure stripping is found to be more than an order of magnitude more effective in removing the gas from the dSph galaxies. The hot halo, with an inferred mass of 1e10 solar masses, may represent a reservoir of ~1000 destroyed dwarf systems, either HVCs or true dwarf galaxies similar to those we observe now.Comment: AASTex preprint style, 27 pages including 12 figures. Submitted to ApJ. See also http://astro.berkeley.edu/~robisha

Cepheid Period-Radius and Period-Luminosity Relations and the Distance to the LMC

We have used the infrared Barnes-Evans surface brightness technique to derive the radii and distances of 34 Galactic Cepheid variables. Radius and distance results obtained from both versions of the technique are in excellent agreement. The radii of 28 variables are used to determine the period-radius relation. This relation is found to have a smaller dispersion than in previous studies, and is identical to the period-radius relation found by Laney & Stobie from a completely independent method, a fact which provides persuasive evidence that the Cepheid period-radius relation is now determined at a very high confidence level. We use the accurate infrared distances to determine period-luminosity relations in the V, I, J, H and K passbands from the Galactic sample of Cepheids. We derive improved slopes of these relations from updated LMC Cepheid samples and adopt these slopes to obtain accurate absolute calibrations of the PL relation. By comparing these relations to the ones defined by the LMC Cepheids, we derive strikingly consistent and precise values for the LMC distance modulus in each of the passbands which yield a mean value of DM (LMC) = 18.46 +- 0.02. Our results show that the infrared Barnes-Evans technique is very insensitive to both Cepheid metallicity and adopted reddening, and therefore a very powerful tool to derive accurate distances to nearby galaxies by a direct application of the technique to their Cepheid variables, rather than by comparing PL relations of different galaxies, which introduces much more sensitivity to metallicity and absorption corrections which are usually difficult to determine.Comment: LaTeX, AASTeX style, 9 Figures, 10 Tables, The Astrophysical Journal in press (accepted Oct. 14, 1997). Fig. 3 replace

Cepheid variables in the LMC cluster NGC 1866. I. New BVRI CCD photometry

We report BV(RI)c CCD photometric data for a group of seven Cepheid variables in the young, rich cluster NGC 1866 in the Large Magellanic Cloud. The photometry was obtained as part of a program to determine accurate distances to these Cepheids by means of the infrared surface brightness technique, and to improve the LMC Cepheid database for constructing Cepheid PL and PLC relations. Using the new data together with data from the literature, we have determined improved periods for all variables. For five fundamental mode pulsators, the light curves are now of excellent quality and will lead to accurate distance and radius determinations once complete infrared light curves and radial velocity curves for these variables become available.Comment: To appear in ApJ Supp., AASTeX, 24 pages, 8 tables, 8 figure

The Star Blended with the MOA-2008-BLG-310 Source Is Not the Exoplanet Host Star

High resolution Hubble Space Telescope (HST) image analysis of the MOA-2008-BLG-310 microlens system indicates that the excess flux at the location of the source found in the discovery paper cannot primarily be due to the lens star because it does not match the lens-source relative proper motion, $\mu_{\rm rel}$, predicted by the microlens models. This excess flux is most likely to be due to an unrelated star that happens to be located in close proximity to the source star. Two epochs of HST observations indicate proper motion for this blend star that is typical of a random bulge star, but is not consistent with a companion to the source or lens stars if the flux is dominated by only one star, aside from the lens. We consider models in which the excess flux is due to a combination of an unrelated star and the lens star, and this yields 95\% confidence level upper limit on the lens star brightness of $I_L > 22.44$ and $V_L >23.62$. A Bayesian analysis using a standard Galactic model and these magnitude limits yields a host star mass $M_h = 0.21 ^{+0.21}_{-0.09}~ M_\odot$, a planet mass of $m_p = 23.4 ^{+23.9}_{-9.9}~M_\oplus$ at a projected separation of $a_\perp = 1.12^{+0.16}_{-0.17},$AU. This result illustrates excess flux in a high resolution image of a microlens-source system need not be due to the lens. It is important to check that the lens-source relative proper motion is consistent with the microlensing prediction. The high resolution image analysis techniques developed in this paper can be used to verify the WFIRST exoplanet microlensing survey mass measurements.Comment: Submitted to AJ on March 18, 201

Theoretical Models for Classical Cepheids: IV. Mean Magnitudes and Colors and the Evaluation of Distance, Reddening and Metallicity

We discuss the metallicity effect on the theoretical visual and near-infrared PL and PLC relations of classical Cepheids, as based on nonlinear, nonlocal and time--dependent convective pulsating models at varying chemical composition. In view of the two usual methods of averaging (magnitude-weighted and intensity-weighted) observed magnitudes and colors over the full pulsation cycle, we briefly discuss the differences between static and mean quantities. We show that the behavior of the synthetic mean magnitudes and colors fully reproduces the observed trend of Galactic Cepheids, supporting the validity of the model predictions. In the second part of the paper we show how the estimate of the mean reddening and true distance modulus of a galaxy from Cepheid VK photometry depend on the adopted metal content, in the sense that larger metallicities drive the host galaxy to lower extinctions and distances. Conversely, self-consistent estimates of the Cepheid mean reddening, distance and metallicity may be derived if three-filter data are taken into account. By applying the theoretical PL and PLC relations to available BVK data of Cepheids in the Magellanic Clouds we eventually obtain Z \sim 0.008, E(B-V) \sim 0.02 mag, DM \sim 18.63 mag for LMC and Z \sim 0.004, E(B-V) \sim 0.01 mag., DM \sim 19.16 mag. for SMC. The discrepancy between such reddenings and the current values based on BVI data is briefly discussed.Comment: 16 pages, 11 postscript figures, accepted for publication on Ap