Multifrequency Jump-Diffusions: An Equilibrium Approach

This paper proposes that equilibrium valuation is a powerful method to generate endogenous jumps in asset prices, which provides a structural alternative to traditional reduced-form specifications with exogenous discontinuities. We specify an economy with continuous consumption and dividend paths, in which endogenous price jumps originate from the market impact of regime-switches in the drifts and volatilities of fundamentals. We parsimoniously incorporate shocks of heterogeneous durations in consumption and dividends while keeping constant the number of parameters. Equilibrium valuation creates an endogenous relation between a shock's persistence and the magnitude of the induced price jump. As the number of frequencies driving fundamentals goes to infinity, the price process converges to a novel stochastic process, which we call a multifractal jump-diffusion.

Multifrequency News and Stock Returns

Recent research documents that aggregate stock prices are driven by shocks with persistence levels ranging from daily intervals to several decades. Building on these insights, we introduce a parsimonious equilibrium model in which regime-shifts of heterogeneous durations affect the volatility of dividend news. We estimate tightly parameterized specifications with up to 256 discrete states on daily U.S. equity returns. The multifrequency equilibrium has significantly higher likelihood than the classic Campbell and Hentschel (1992) specification, while generating volatility feedback effects 6 to 12 times larger. We show in an extension that Bayesian learning about stochastic volatility is faster for bad states than good states, providing a novel source of endogenous skewness that complements the "uncertainty" channel considered in previous literature (e.g., Veronesi, 1999). Furthermore, signal precision induces a tradeoff between skewness and kurtosis, and economies with intermediate investor information best match the data.

Accretion Disks Around Young Objects. III. Grain Growth

We present detailed models of irradiated T Tauri disks including dust grain growth with power-law size distributions. The models assume complete mixing between dust and gas and solve for the vertical disk structure self-consistentlyincluding the heating effects of stellar irradiation as well as local viscous heating. For a given total dust mass, grain growth is found to decrease the vertical height of the surface where the optical depth to the stellar radiation becomes unit and thus the local irradiation heating, while increasing the disk emission at mm and sub-mm wavelengths. The resulting disk models are less geometrically thick than our previous models assuming interstellar medium dust, and agree better with observed spectral energy distributions and images of edge-on disks, like HK Tau/c and HH 30. The implications of models with grain growth for determining disk masses from long-wavelength emission are considered.Comment: 29 pages, including 11 figures and 1 table, APJ accepte

Constraining the Envelope Structure of L1527 IRS: Infrared Scattered Light Modeling

We model Spitzer Space Telescope observations of the Taurus Class 0 protostar L1527 IRS (IRAS 04368+2557) to provide constraints on its protostellar envelope structure. The nearly edge-on inclination of L1527 IRS, coupled with the highly spatially-resolved near to mid-infrared images of this object and the detailed IRS spectrum, enable us to constrain the outflow cavity geometry quite well, reducing uncertainties in the other derived parameters. The mid-infrared scattered light image shows a bright central source within a dark lane; the aspect ratio of this dark lane is such that it appears highly unlikely to be a disk shadow. In modeling this dark lane, we conclude that L1527 IRS is probably not described by a standard TSC envelope with simple bipolar cavities. We find it necessary to model the dark lane and central source as a modified inner envelope structure. This structure may be due either to a complex wind-envelope interaction or induced by the central binary. To fit the overall SED, we require the central source to have a large near to mid-infrared excess, suggesting substantial disk accretion. Our model reproduces the overall morphology and surface brightness distribution of L1527 IRS fairly well, given the limitations of using axisymmetric models to fit the non-axisymmetric real object, and the derived envelope infall rates are in reasonable agreement with some other investigations. IRAC observations of L1527 IRS taken 12 months apart show variability in total flux and variability in the opposing bipolar cavities, suggesting asymmetric variations in accretion. We also provide model images at high resolution for comparison to future observations with current ground-based instrumentation and future space-based telescopes.Comment: 50 pages, 14 figures 2 tables, accepted by the Astrophysical Journal. The manuscript with full resolution figures can be downloaded from http://astro.lsa.umich.edu/~jjtobin/L1527.pd

Volatility Comovement: A Multifrequency Approach

We implement a multifrequency volatility decomposition of three exchange rates and show that components with similar durations are strongly correlated across series. This motivates a bivariate extension of the Markov-Switching Multifractal (MSM) introduced in Calvet and Fisher (2001, 2004). Bivariate MSM is a stochastic volatility model with a closed-form likelihood. Estimation can proceed by ML for state spaces of moderate size, and by simulated likelihood via a particle filter in high-dimensional cases. We estimate the model and confirm its main assumptions in likelihood ratio tests. Bivariate MSM compares favorably to a standard multivariate GARCH both in- and out-of-sample. We extend the model to multivariate settings with a potentially large number of assets by proposing a parsimonious multifrequency factor structure.

Periodic variations in the colours of the classical T Tauri star RW Aur A

The classical T Tauri star RW Aur A is an irregular variable with a large amplitude in all photometric bands. In an extended series of photometric data we found small-amplitude periodic variations in the blue colours of the star, with a period of 2.64 days. The period was relatively stable over several years. The amplitude of the periodic signal is 0.21 mag in U-V, 0.07 mag in B-V, and about 0.02 mag in V-R and V-I. No periodicity was found in the V magnitude. The relevance of this photometric period to the recently discovered periodicity in spectral features of the star is discussed, and the hypothesis of a hot spot is critically considered.Comment: 5 pages, 8 figures, uses new aa.cls, accepted for publication in Astronomy and Astrophysic