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

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

A Digital Archive of HI 21 cm Line Spectra of Optically-targeted Galaxies

We present a homogeneous compilation of HI spectral parameters extracted from global 21 cm line spectra for some 9000 galaxies in the local universe (heliocentric velocity -200 < V_Sun < 28,000 km/s) obtained with a variety of large single dish radio telescopes but reanalyzed using a single set of parameter extraction algorithms. Corrections to the observed HI line flux for source extent and pointing offsets and to the HI line widths for instrumental broadening and smoothing are applied according to model estimates to produce a homogenous catalog of derived properties with quantitative error estimates. Where the redshift is available from optical studies, we also provide flux measurements for an additional 156 galaxies classified as marginal HI detections and rms noise limits for 494 galaxies classified as nondetections. Given the diverse nature of the observing programs contributing to it, the characteristics of the combined dataset are heterogeneous, and as such, the compilation is neither integrated HI line flux nor peak flux limited. However, because of the large statistical base and homogenous reprocessing, the spectra and spectral parameters of galaxies in this optically targeted sample can be used to complement data obtained at other wavelengths to characterize the properties of galaxies in the local universe and to explore the large scale structures in which they reside.Comment: 13 pages, 9 figures, 3 external online tables, accepted for publication in ApJ

Option pricing under stochastic volatility: the exponential Ornstein-Uhlenbeck model

We study the pricing problem for a European call option when the volatility of the underlying asset is random and follows the exponential Ornstein-Uhlenbeck model. The random diffusion model proposed is a two-dimensional market process that takes a log-Brownian motion to describe price dynamics and an Ornstein-Uhlenbeck subordinated process describing the randomness of the log-volatility. We derive an approximate option price that is valid when (i) the fluctuations of the volatility are larger than its normal level, (ii) the volatility presents a slow driving force toward its normal level and, finally, (iii) the market price of risk is a linear function of the log-volatility. We study the resulting European call price and its implied volatility for a range of parameters consistent with daily Dow Jones Index data.Comment: 26 pages, 6 colored figure

Detection and imaging in strongly backscattering randomly layered media

Abstract. Echoes from small reflectors buried in heavy clutter are weak and difficult to distinguish from the medium backscatter. Detection and imaging with sensor arrays in such media requires filtering out the unwanted backscatter and enhancing the echoes from the reflectors that we wish to locate. We consider a filtering and detection approach based on the singular value decomposition of the local cosine transform of the array response matrix. The algorithm is general and can be used for detection and imaging in heavy clutter, but its analysis depends on the model of the cluttered medium. This paper is concerned with the analysis of the algorithm in finely layered random media. We obtain a detailed characterization of the singular values of the transformed array response matrix and justify the systematic approach of the filtering algorithm for detecting and refining the time windows that contain the echoes that are useful in imaging

Extreme times for volatility processes

We present a detailed study on the mean first-passage time of volatility processes. We analyze the theoretical expressions based on the most common stochastic volatility models along with empirical results extracted from daily data of major financial indices. We find in all these data sets a very similar behavior that is far from being that of a simple Wiener process. It seems necessary to include a framework like the one provided by stochastic volatility models with a reverting force driving volatility toward its normal level to take into account memory and clustering effects in volatility dynamics. We also detect in data a very different behavior in the mean first-passage time depending whether the level is higher or lower than the normal level of volatility. For this reason, we discuss asymptotic approximations and confront them to empirical results with a good agreement, specially with the ExpOU model.Comment: 10, 6 colored figure

Pricing Exotic Options in a Path Integral Approach

In the framework of Black-Scholes-Merton model of financial derivatives, a path integral approach to option pricing is presented. A general formula to price European path dependent options on multidimensional assets is obtained and implemented by means of various flexible and efficient algorithms. As an example, we detail the cases of Asian, barrier knock out, reverse cliquet and basket call options, evaluating prices and Greeks. The numerical results are compared with those obtained with other procedures used in quantitative finance and found to be in good agreement. In particular, when pricing at-the-money and out-of-the-money options, the path integral approach exhibits competitive performances.Comment: 21 pages, LaTeX, 3 figures, 6 table