Three essays on liquidity risk

Preface In this thesis we study several questions related to transaction data measured at an individual level. The questions are addressed in three essays that will constitute this thesis. In the first essay we use tick-by-tick data to estimate non-parametrically the jump process of 37 big stocks traded on the Paris Stock Exchange, and of the CAC 40 index. We separate the total daily returns in three components (trading continuous, trading jump, and overnight), and we characterize each one of them. We estimate at the individual and index levels the contribution of each return component to the total daily variability. For the index, the contribution of jumps is smaller and it is compensated by the larger contribution of overnight returns. We test formally that individual stocks jump more frequently than the index, and that they do not respond independently to the arrive of news. Finally, we find that daily jumps are larger when their arrival rates are larger. At the contemporaneous level there is a strong negative correlation between the jump frequency and the trading activity measures. The second essay study the general properties of the trade- and volume-duration processes for two stocks traded on the Paris Stock Exchange. These two stocks correspond to a very illiquid stock and to a relatively liquid stock. We estimate a class of autoregressive gamma process with conditional distribution from the family of non-central gamma (up to a scale factor). This process was introduced by Gouriéroux and Jasiak and it is known as Autoregressive gamma process. We also evaluate the ability of the process to fit the data. For this purpose we use the Diebold, Gunther and Tay (1998) test; and the capacity of the model to reproduce the moments of the observed data, and the empirical serial correlation and the partial serial correlation functions. We establish that the model describes correctly the trade duration process of illiquid stocks, but have problems to adjust correctly the trade duration process of liquid stocks which present long-memory characteristics. When the model is adjusted to volume duration, it successfully fit the data. In the third essay we study the economic relevance of optimal liquidation strategies by calibrating a recent and realistic microstructure model with data from the Paris Stock Exchange. We distinguish the case of parameters which are constant through the day from time-varying ones. An optimization problem incorporating this realistic microstructure model is presented and solved. Our model endogenizes the number of trades required before the position is liquidated. A comparative static exercise demonstrates the realism of our model. We find that a sell decision taken in the morning will be liquidated by the early afternoon. If price impacts increase over the day, the liquidation will take place more rapidly.

How useful is satellite positioning system (GPS) to track gait parameters? A review.

Over the last century, numerous techniques have been developed to analyze the movement of humans while walking and running. The combined use of kinematics and kinetics methods, mainly based on high speed video analysis and forceplate, have permitted a comprehensive description of locomotion process in terms of energetics and biomechanics. While the different phases of a single gait cycle are well understood, there is an increasing interest to know how the neuro-motor system controls gait form stride to stride. Indeed, it was observed that neurodegenerative diseases and aging could impact gait stability and gait parameters steadiness. From both clinical and fundamental research perspectives, there is therefore a need to develop techniques to accurately track gait parameters stride-by-stride over a long period with minimal constraints to patients. In this context, high accuracy satellite positioning can provide an alternative tool to monitor outdoor walking. Indeed, the high-end GPS receivers provide centimeter accuracy positioning with 5-20 Hz sampling rate: this allows the stride-by-stride assessment of a number of basic gait parameters--such as walking speed, step length and step frequency--that can be tracked over several thousand consecutive strides in free-living conditions. Furthermore, long-range correlations and fractal-like pattern was observed in those time series. As compared to other classical methods, GPS seems a promising technology in the field of gait variability analysis. However, relative high complexity and expensiveness--combined with a usability which requires further improvement--remain obstacles to the full development of the GPS technology in human applications.

Sedation and analgesia for colonoscopy: patient tolerance, pain, and cardiorespiratory parameters.

BACKGROUND: Colonoscopy is generally performed with the patient sedated and receiving analgesics. However, the benefit of the most often used combination of intravenous midazolam and pethidine on patient tolerance and pain and its cardiorespiratory risk have not been fully defined. METHODS: In this double-blind prospective study, 150 outpatients undergoing routine colonoscopy were randomly assigned to receive either (1) low-dose midazolam (35 micrograms/kg) and pethidine (700 micrograms/kg in 48 patients, 500 micrograms/kg in 102 patients), (2) midazolam and placebo pethidine, or (3) pethidine and placebo midazolam. RESULTS: Tolerance (visual analog scale, 0 to 100 points: 0 = excellent; 100 = unbearable) did not improve significantly more in group 1 compared with group 2 (7 points; 95% confidence interval [-2-17]) and group 3 (2 points; 95% confidence interval [-7-12]). Similarly, pain was not significantly improved in group 1 as compared with the other groups. Male gender (p < 0.001) and shorter duration of the procedure (p = 0.004), but not amnesia, were associated with better patient tolerance and less pain. Patient satisfaction was similar in all groups. Oxygen desaturation and hypotension occurred in 33% and 11%, respectively, with a similar frequency in all three groups. CONCLUSIONS: In this study, the combination of low-dose midazolam and pethidine does not improve patient tolerance and lessen pain during colonoscopy as compared with either drug given alone. When applying low-dose midazolam, oxygen desaturation and hypotension do not occur more often after combined use of both drugs. For the individual patient, sedation and analgesia should be based on the endoscopist's clinical judgement.

Quantitative analysis of crystal/grain sizes and their distributions in 2D and 3D

We review methods to estimate the average crystal (grain) size and the crystal (grain) size distribution in solid rocks. Average grain sizes often provide the base for stress estimates or rheological calculations requiring the quantification of grain sizes in a rock's microstructure. The primary data for grain size data are either 1D (i.e. line intercept methods), 2D (area analysis) or 3D (e.g., computed tomography, serial sectioning). These data have been used for different data treatments over the years, whereas several studies assume a certain probability function (e.g., logarithm, square root) to calculate statistical parameters as the mean, median, mode or the skewness of a crystal size distribution. The finally calculated average grain sizes have to be compatible between the different grain size estimation approaches in order to be properly applied, for example, in paleo-piezometers or grain size sensitive flow laws. Such compatibility is tested for different data treatments using one- and two-dimensional measurements. We propose an empirical conversion matrix for different datasets. These conversion factors provide the option to make different datasets compatible with each other, although the primary calculations were obtained in different ways. In order to present an average grain size, we propose to use the area-weighted and volume-weighted mean in the case of unimodal grain size distributions, respectively, for 2D and 3D measurements. The shape of the crystal size distribution is important for studies of nucleation and growth of minerals. The shape of the crystal size distribution of garnet populations is compared between different 2D and 3D measurements, which are serial sectioning and computed tomography. The comparison of different direct measured 3D data; stereological data and direct presented 20 data show the problems of the quality of the smallest grain sizes and the overestimation of small grain sizes in stereological tools, depending on the type of CSD. (C) 2011 Published by Elsevier Ltd.

Diagnostic value of vestibulo-ocular reflex parameters in the detection and characterization of labyrinthine lesions.

OBJECTIVE: To evaluate the power of various parameters of the vestibulo-ocular reflex (VOR) in detecting unilateral peripheral vestibular dysfunction and in characterizing certain inner ear pathologies. STUDY DESIGN: Prospective study of consecutive ambulatory patients presenting with acute onset of peripheral vertigo and spontaneous nystagmus. SETTING: Tertiary referral center. PATIENTS: Seventy-four patients (40 females, 34 males) and 22 normal subjects (11 females, 11 males) were included in the study. Patients were classified in three main diagnoses: vestibular neuritis: 40; viral labyrinthitis: 22; Meniere's disease: 12. METHODS: The VOR function was evaluated by standard caloric and impulse rotary tests (velocity step). A mathematical model of vestibular function was used to characterize the VOR response to rotational stimulation. The diagnostic value of the different VOR parameters was assessed by uni- and multivariable logistic regression. RESULTS: In univariable analysis, caloric asymmetry emerged as the most powerful VOR parameter in identifying unilateral vestibular deficit, with a boundary limit set at 20%. In multivariable analysis, the combination of caloric asymmetry and rotational time constant asymmetry significantly improved the discriminatory power over caloric alone (p&lt;0.0001) and produced a detection score with a correct classification of 92.4%. In discriminating labyrinthine diseases, different combinations of the VOR parameters were obtained for each diagnosis (p&lt;0.003) supporting that the VOR characteristics differ between the three inner ear disorders. However, the clinical usefulness of these characteristics in separating the pathologies was limited. CONCLUSION: We propose a powerful logistic model combining the indices of caloric and time constant asymmetries to detect a peripheral vestibular loss, with an accuracy of 92.4%. Based on vestibular data only, the discrimination between the different inner ear diseases is statistically possible, which supports different pathophysiologic changes in labyrinthine pathologies.

Formule sanguine: intérêt des nouveaux paramètres [Complete blood counts: new parameters].

Performing a complete blood count analysis is a daily routine necessary for a good care of patients. Nowadays, modern blood analyzers provide on top of classical blood values, several additional parameters. In this paper, using short case presentations, we discuss how to interpret these results and integrate them in the clinical context.

Correlations between trabecular bone score, measured using anteroposterior dual-energy x-ray absorptiometry acquisition, and 3-dimensional parameters of bone microarchitecture: an experimental study on human cadaver vertebrae.

Developing a novel technique for the efficient, noninvasive clinical evaluation of bone microarchitecture remains both crucial and challenging. The trabecular bone score (TBS) is a new gray-level texture measurement that is applicable to dual-energy X-ray absorptiometry (DXA) images. Significant correlations between TBS and standard 3-dimensional (3D) parameters of bone microarchitecture have been obtained using a numerical simulation approach. The main objective of this study was to empirically evaluate such correlations in anteroposterior spine DXA images. Thirty dried human cadaver vertebrae were evaluated. Micro-computed tomography acquisitions of the bone pieces were obtained at an isotropic resolution of 93μm. Standard parameters of bone microarchitecture were evaluated in a defined region within the vertebral body, excluding cortical bone. The bone pieces were measured on a Prodigy DXA system (GE Medical-Lunar, Madison, WI), using a custom-made positioning device and experimental setup. Significant correlations were detected between TBS and 3D parameters of bone microarchitecture, mostly independent of any correlation between TBS and bone mineral density (BMD). The greatest correlation was between TBS and connectivity density, with TBS explaining roughly 67.2% of the variance. Based on multivariate linear regression modeling, we have established a model to allow for the interpretation of the relationship between TBS and 3D bone microarchitecture parameters. This model indicates that TBS adds greater value and power of differentiation between samples with similar BMDs but different bone microarchitectures. It has been shown that it is possible to estimate bone microarchitecture status derived from DXA imaging using TBS.

Regional specificity of MRI contrast parameter changes in normal ageing revealed by voxel-based quantification (VBQ).

Normal ageing is associated with characteristic changes in brain microstructure. Although in vivo neuroimaging captures spatial and temporal patterns of age-related changes of anatomy at the macroscopic scale, our knowledge of the underlying (patho)physiological processes at cellular and molecular levels is still limited. The aim of this study is to explore brain tissue properties in normal ageing using quantitative magnetic resonance imaging (MRI) alongside conventional morphological assessment. Using a whole-brain approach in a cohort of 26 adults, aged 18-85years, we performed voxel-based morphometric (VBM) analysis and voxel-based quantification (VBQ) of diffusion tensor, magnetization transfer (MT), R1, and R2* relaxation parameters. We found age-related reductions in cortical and subcortical grey matter volume paralleled by changes in fractional anisotropy (FA), mean diffusivity (MD), MT and R2*. The latter were regionally specific depending on their differential sensitivity to microscopic tissue properties. VBQ of white matter revealed distinct anatomical patterns of age-related change in microstructure. Widespread and profound reduction in MT contrasted with local FA decreases paralleled by MD increases. R1 reductions and R2* increases were observed to a smaller extent in overlapping occipito-parietal white matter regions. We interpret our findings, based on current biophysical models, as a fingerprint of age-dependent brain atrophy and underlying microstructural changes in myelin, iron deposits and water. The VBQ approach we present allows for systematic unbiased exploration of the interaction between imaging parameters and extends current methods for detection of neurodegenerative processes in the brain. The demonstrated parameter-specific distribution patterns offer insights into age-related brain structure changes in vivo and provide essential baseline data for studying disease against a background of healthy ageing.

The impact of navigator timing parameters and navigator spatial resolution on 3D coronary magnetic resonance angiography.

The impact of navigator spatial resolution and navigator evaluation time on image quality in free-breathing navigator-gated 3D coronary magnetic resonance angiography (MRA), including real-time motion correction, was investigated in a moving phantom. Objective image quality parameters signal-to-noise ratio (SNR) and vessel sharpness were compared. It was found that for improved mage quality a short navigator evaluation time is of crucial importance. Navigator spatial resolution showed minimal influence on image quality.

Evaluation of the caloric test by combining 3 response parameters.

The slow-phase velocity of nystagmus is one of the most sensitive parameters of vestibular function and is currently the standard for evaluating the caloric test. However, the assessment of this parameter requires recording the response by using nystagmography. The aim of this study was to evaluate whether frequency and duration of the caloric nystagmus, as measured by using a clinical test with Frenzel glasses, could predict the result of the recorded test. The retrospective analysis of 222 caloric test results recorded by means of electronystagmography has shown a good association between the 3 parameters for unilateral weakness. The asymmetry observed in the velocity can be predicted by a combination of frequency and duration. On the other hand, no relationship was observed between the parameters for directional preponderance. These results indicate that a clinical caloric test with frequency and duration as parameters can be used to predict the unilateral weakness, which would be obtained by use of nystagmography. We propose an evaluation of the caloric test on the basis of diagrams combining the 3 response parameters.

Estimating the apparent transverse relaxation time (R2(*)) from images with different contrasts (ESTATICS) reduces motion artifacts.

Relaxation rates provide important information about tissue microstructure. Multi-parameter mapping (MPM) estimates multiple relaxation parameters from multi-echo FLASH acquisitions with different basic contrasts, i.e., proton density (PD), T1 or magnetization transfer (MT) weighting. Motion can particularly affect maps of the apparent transverse relaxation rate R2(*), which are derived from the signal of PD-weighted images acquired at different echo times. To address the motion artifacts, we introduce ESTATICS, which robustly estimates R2(*) from images even when acquired with different basic contrasts. ESTATICS extends the fitted signal model to account for inherent contrast differences in the PDw, T1w and MTw images. The fit was implemented as a conventional ordinary least squares optimization and as a robust fit with a small or large confidence interval. These three different implementations of ESTATICS were tested on data affected by severe motion artifacts and data with no prominent motion artifacts as determined by visual assessment or fast optical motion tracking. ESTATICS improved the quality of the R2(*) maps and reduced the coefficient of variation for both types of data-with average reductions of 30% when severe motion artifacts were present. ESTATICS can be applied to any protocol comprised of multiple 2D/3D multi-echo FLASH acquisitions as used in the general research and clinical setting.