Business Time and New Credit Risk Models

This paper examines a new model of credit risk measurement, the Variance Gamma- Merton one, which seems to be adequate for describing single default occurrence and default correlation in turbulent times. It is based on the notion of business time. Business time runs faster than calendar time when the market is very active and a lot of information arrives; it runs at a slower pace than calendar time when few information arrives. We report a calibration to USA spread data, which shows the accurateness of the model at the single default level; we also compare the perfeormance wrt a traditional structural model at the joint default level.

Evolution of coupled lives' dependency across generations and pricing impact

This paper studies the dependence between coupled lives - both within and across generations - and its effects on prices of reversionary annuities in the presence of longevity risk. Longevity risk is represented via a stochastic mortality intensity. Dependence is modelled through copula functions. We consider Archimedean single and multi-parameter copulas. We and that dependence decreases when passing from older generations to younger generations. Not only the level of dependence but also its features - as measured by the copula - change across generations: the best-fit Archimedean copula is not the same across generations. Moreover, for all the generations under exam the single-parameter copula is dominated by the two-parameter one. The independence assumption produces quantifiable mispricing of reversionary annuities. The misspecification of the copula produces different mispricing effects on different generations. The research is conducted using a well-known dataset of double life contracts

Geocoder: An Efficient Backscatter Map Constructor

The acoustic backscatter acquired by multibeam and sidescan sonars carries important information about the seafloor morphology and physical properties, providing valuable data to aid the difficult task of seafloor characterization, and important auxiliary information for a bathymetric survey. One necessary step towards this characterization is the assemblage of more consistent and more accurate mosaics of acoustic backscatter. For that, it is necessary to radiometrically correct the backscatter intensities registered by these sonars, to geometrically correct and position each acoustic sample in a projection coordinate system and to interpolate properly the intensity values into a final backscatter map. Geocoder is a software tool that implements the ideas discussed above. Initially, the original backscatter time series registered by the sonar is corrected for angle varying gains, for beam pattern and filtered for speckle removal. All samples of the time series are preserved during all the operations, ensuring that the full data resolution is used for the final mosaicking. The time serie s is then slant-range corrected based on a bathymetric model, in the case of sidescan, or based on beam bathymetry, in the case of the multibeam. Subsequently, each backscatter sample of the series is geocoded in a projected coordinate system in accordance to an interpolation scheme that resembles the acquisition geometry. An anti-aliasing algorithm is applied in parallel to the mosaicking procedure, which allows the assemblage of mosaics at any required resolution. Overlap among parallel lines is resolved by a priority table based on the distance of each sample from the ship track; a blending algorithm is applied to minimize the seams between overlapping lines. The final mosaic exhibits low noise, few artifacts, reduced seams between parallel acquisition lines and reduced clutter in the near-nadir region, while still preserving regional data continuity and local seafloor features

Experiments for multibeam Backscatter Adjustments on the NOAA Ship FAIRWEATHER

A series of experiments were conducted to adjust and normalize the acoustic backscatter acquired by Reson 8111 and 8160 systems. The dependency of the backscatter on the receiver gain, transmit power, pulse width and acquisition mode was analyzed. Empirical beam patterns are calculated as the difference between the backscatter measured by the sonars and the expected backscatter. Expected acoustic backscatter is estimated based on a mathematical model

Clustering Acoustic Backscatter in the Angular Response Space

Backscatter mosaicking is a necessary step in the analysis and interpretation of sidescan and multibeam sonar records. However, due to limitations intrinsic to the mosaicking technique, backscatter mosaics are restricted in their capacity to unambiguously discriminate seafloor properties. A more adequate technique to characterize the seafloor is the analysis of backscatter angular responses, since those responses are intrinsic properties of the seafloor. This technique sometimes lacks spatial resolution, however, as the analysis is limited to the swath width of the sonar. In this paper, we propose an approach to combine mosaicking and angular response analysis techniques in an attempt to take advantage of both the spatial resolution of the mosaic, and the angular resolution derived from the angular response analysis. In order to test these ideas, we used acoustic backscatter acquired by a Reson 8101 (240kHz) multibeam sonar during normal survey operations conducted on the NOAA Ship FAIRWEATHER around Cape Decision, Alaska in spring 2005. First, we defined parameters that uniquely described the angular responses, and treated those parameters as a feature vector in a multidimensional space. The parameters were then clustered with a simple unsupervised clustering algorithm. The result of the clustering analysis defined areas on the seafloor which had similar angular responses, which we called themes. We then used these themes to develop more robust indicators of angular response from their coverage areas, which were finally used as Angle Varying Gain correction tables to assemble an enhanced mosaic

Modeling High-Frequency Seafloor Backscattering of Gassy Sediments: The Eel River Margin Case

Models of acoustic backscatter typically take into account two different processes: interface scattering and volume scattering. What happens to these two contributions when the sediment is charged with gas bubbles? For the interface backscatter contribution we adopted the model developed by Jackson et al. (1986), but added modifications to accommodate gas bubbles, which when present, even in very small quantities, can dominate the acoustic characteristics of the sediment. The model parameters that are affected by gas content are the density ratio, the sound speed ratio and the loss parameter. To a first approximation, the model roughness parameters are not influenced by the presence of gas. For the volume backscatter contribution we developed a model based on the presence and distribution of gas in the sediment. We treat the bubbles as individual point scatters that sum to the bubble contribution. This bubble contribution is then added to the volume contribution of other scatters. A potential area to test the ideas outlined above is the highly sedimented, tectonically active, Eel River margin offshore Northern California. This continental margin reveals evidence of abundant subsurface gas and numerous seafloor expulsion features, where a large volume of marine data has been acquired as part of the STRATAFORM project. Two different sets of multibeam backscatter data acquired at 30kHz and 95kHz provide raw measurements for the backscatter as a function of grazing angle. These raw backscatter measurements are then radiometrically corrected in order to be compared with the results of the proposed model. Radiometric corrections include the removal of the time varying and angle varying gains applied during acquisition, calculation of the true grazing angle with respect to a bathymetric model, and correction for footprint size. Results of core data analysis at various sampling locations provide local measurements of gas content in the sediments that when compared to the model show general agreement

A Surprise Occurrence in Acoustic Bottom Backscatter Measurements Conducted in the Eastern Bering Sea

Acoustic backscatter measurements at different frequencies were made in the eastern Bering Sea in August 2006 from the NOAA Ship Fairweather. The measurements consisted of approximately 2,250 nm of trackline acoustic backscatter data from a 100 kHz RESON model 8111; 2,250 nm of trackline acoustic backscatter data from a 40 kHz Reson model 8160; 750 nm of trackline acoustic backscatter data from a 455 kHz Klein model 5410; and 750 nm of trackline acoustic backscatter data from a 180 kHz pre-production Klein model 7180. The two Klein systems were each towed SW-NE once along the same specified 750 nm of tracklines. The two RESON systems were each operated twice SW-NE and once NE-SW along the same tracklines as the Klein systems. The acoustic backscatter was typically what might be expected from a flat, featureless expanse of fine grained sediments. However, there was a chance encounter with an embedded community of gastropods that was documented both with bottom grab samples and video footage of the seabed. The presence of the embedded community of gastropods drastically changed the level and angle dependence of the backscatter. This paper presents a comparative analysis of the backscatter properties of the gastropod community that were observed at 40 kHz, 100 kHz, 180 kHz and 455 kHz

Quantum Monte Carlo study of a vortex in superfluid 4^4He and search for a vortex state in the solid

We have performed a microscopic study of a straight quantized vortex line in three dimensions in condensed $^4$He at zero temperature using the Shadow Path Integral Ground State method and the fixed-phase approximation. We have characterized the energy and the local density profile around the vortex axis in superfluid $^4$He at several densities, ranging from below the equilibrium density up to the overpressurized regime. For the Onsager-Feynman (OF) phase our results are exact and represent a benchmark for other theories. The inclusion of backflow correlations in the phase improves the description of the vortex with respect to the OF phase by a large reduction of the core energy of the topological excitation. At all densities the phase with backflow induces a partial filling of the vortex core and this filling slightly increases with density. The core size slightly decreases for increasing density and the density profile has well defined density dependent oscillations whose wave vector is closer to the wave vector of the main peak in the static density response function rather than to the roton wave vector. Our results can be applied to vortex rings of large radius $R$ and we find good agreement with the experimental value of the energy as function of $R$ without any free parameter. We have studied also $^4$He above the melting density in the solid phase using the same functional form for the phase as in the liquid. We found that off-diagonal properties of the solid are not qualitatively affected by the velocity field induced by the vortex phase, both with and without backflow correlations. Therefore we find evidence that a perfect $^4$He crystal is not a marginally stable quantum solid in which rotation would be able to induce off-diagonal long-range coherence.Comment: 15 pages, 8 figure