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

A Direct Distance to the LMC Cepheid HV 12198 from the Infrared Surface Brightness Technique

We report on a first application of the infrared surface brightness technique on a Cepheid in the Large Magellanic Cloud, the variable HV 12198 in the young globular cluster NGC 1866. From this one star, we determine a distance modulus of 18.42 +- 0.10 (random and systematic uncertainty) to the cluster. When the results on further member Cepheids in NGC 1866 become available, we expect to derive the distance to the LMC with a +- 3-4 percent accuracy, including systematic errors, from this technique.Comment: 4 pages, 4 figures, accepted in ApJ Letter

Distributed Random Process for a Large-Scale Peer-to-Peer Lottery

Most online lotteries today fail to ensure the verifiability of the random process and rely on a trusted third party. This issue has received little attention since the emergence of distributed protocols like Bitcoin that demonstrated the potential of protocols with no trusted third party. We argue that the security requirements of online lotteries are similar to those of online voting, and propose a novel distributed online lottery protocol that applies techniques developed for voting applications to an existing lottery protocol. As a result, the protocol is scalable, provides efficient verification of the random process and does not rely on a trusted third party nor on assumptions of bounded computational resources. An early prototype confirms the feasibility of our approach

Direct Distances to Cepheids in the Large Magellanic Cloud: Evidence for a Universal Slope of the Period-Luminosity Relation up to Solar Abundance

We have applied the infrared surface brightness (ISB) technique to derive distances to 13 Cepheids in the LMC which span a period range from 3 to 42 days. From the absolute magnitudes of the variables calculated from these distances, we find that the LMC Cepheids define tight period-luminosity relations in the V, I, W, J and K bands which agree exceedingly well with the corresponding Galactic PL relations derived from the same technique, and are significantly steeper than the LMC PL relations in these bands observed by the OGLE-II Project in V, I and W, and by Persson et al. in J and K. We find that the tilt-corrected true distance moduli of the LMC Cepheids show a significant dependence on period, which hints at a systematic error in the ISB technique related to the period of the stars. We identify as the most likely culprit the p-factor which converts the radial into pulsational velocities; our data imply a much steeper period dependence of the p-factor than previously thought, and we derive p=1.58 (+/-0.02) -0.15 (+/-0.05) logP as the best fit from our data, with a zero point tied to the Milky Way open cluster Cepheids. Using this revised p-factor law, the period dependence of the LMC Cepheid distance moduli disappears, and at the same time the Milky Way and LMC PL relations agree among themselves, and with the directly observed LMC PL relations, within the 1 sigma uncertainties. Our main conclusion is that the previous, steeper Galactic PL relations were caused by an erroneous calibration of the p-factor law, and that there is now evidence that the slope of the Cepheid PL relation is independent of metallicity up to solar metallicity, in both optical, and near-infrared bands.Comment: ApJ accepte

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

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

Improving the mass determination of Galactic Cepheids

We have selected a sample of Galactic Cepheids for which accurate estimates of radii, distances, and photometric parameters are available. The comparison between their pulsation masses, based on new Period-Mass-Radius (PMR) relations, and their evolutionary masses, based on both optical and NIR Color-Magnitude (CM) diagrams, suggests that pulsation masses are on average of the order of 10% smaller than the evolutionary masses. Current pulsation masses show, at fixed radius, a strongly reduced dispersion when compared with values published in literature.The increased precision in the pulsation masses is due to the fact that our predicted PMR relations based on nonlinear, convective Cepheid models present smaller standard deviations than PMR relations based on linear models. At the same time, the empirical radii of our Cepheid sample are typically accurate at the 5% level. Our evolutionary mass determinations are based on stellar models constructed by neglecting the effect of mass-loss during the He burning phase. Therefore, the difference between pulsation and evolutionary masses could be intrinsic and does not necessarily imply a problem with either evolutionary and/or nonlinear pulsation models. The marginal evidence of a trend in the difference between evolutionary and pulsation masses when moving from short to long-period Cepheids is also briefly discussed. The main finding of our investigation is that the long-standing Cepheid mass discrepancy seems now resolved at the 10% level either if account for canonical or mild convective core overshooting evolutionary models.Comment: 14 pages, 4 postscript figures, accepted for publication on ApJ Letter