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.

COMMIT: Convex Optimization Modeling for Microstructure Informed Tractography.

Tractography is a class of algorithms aiming at in vivo mapping the major neuronal pathways in the white matter from diffusion magnetic resonance imaging (MRI) data. These techniques offer a powerful tool to noninvasively investigate at the macroscopic scale the architecture of the neuronal connections of the brain. However, unfortunately, the reconstructions recovered with existing tractography algorithms are not really quantitative even though diffusion MRI is a quantitative modality by nature. As a matter of fact, several techniques have been proposed in recent years to estimate, at the voxel level, intrinsic microstructural features of the tissue, such as axonal density and diameter, by using multicompartment models. In this paper, we present a novel framework to reestablish the link between tractography and tissue microstructure. Starting from an input set of candidate fiber-tracts, which are estimated from the data using standard fiber-tracking techniques, we model the diffusion MRI signal in each voxel of the image as a linear combination of the restricted and hindered contributions generated in every location of the brain by these candidate tracts. Then, we seek for the global weight of each of them, i.e., the effective contribution or volume, such that they globally fit the measured signal at best. We demonstrate that these weights can be easily recovered by solving a global convex optimization problem and using efficient algorithms. The effectiveness of our approach has been evaluated both on a realistic phantom with known ground-truth and in vivo brain data. Results clearly demonstrate the benefits of the proposed formulation, opening new perspectives for a more quantitative and biologically plausible assessment of the structural connectivity of the brain.

Strontium ranelate and alendronate have differing effects on distal tibia bone microstructure in women with osteoporosis.

The structural basis of the antifracture efficacy of strontium ranelate and alendronate is incompletely understood. We compared the effects of strontium ranelate and alendronate on distal tibia microstructure over 2 years using HR-pQCT. In this pre-planned, interim, intention-to-treat analysis at 12 months, 88 osteoporotic postmenopausal women (mean age 63.7 +/- 7.4) were randomized to strontium ranelate 2 g/day or alendronate 70 mg/week in a double-placebo design. Primary endpoints were changes in microstructure. Secondary endpoints included lumbar and hip areal bone mineral density (aBMD), and bone turnover markers. This trial is registered with http://www.controlled-trials.com, number ISRCTN82719233. Baseline characteristics of the two groups were similar. Treatment with strontium ranelate was associated with increases in mean cortical thickness (CTh, 5.3%), cortical area (4.9%) and trabecular density (2.1%) (all P < 0.001, except cortical area P = 0.013). No significant changes were observed with alendronate. Between-group differences in favor of strontium ranelate were observed for CTh, cortical area, BV/TV and trabecular density (P = 0.045, 0.041, 0.048 and 0.035, respectively). aBMD increased to a similar extent with strontium ranelate and alendronate at the spine (5.7% versus 5.1%, respectively) and total hip (3.3% versus 2.2%, respectively). No significant changes were observed in remodeling markers with strontium ranelate, while suppression was observed with alendronate. Within the methodological constraints of HR-pQCT through its possible sensitivity to X-ray attenuation of different minerals, strontium ranelate had greater effects than alendronate on distal tibia cortical thickness and trabecular volumetric density.

Venous cannula performance assessment in a realistic caval tree model.

OBJECTIVES: A new caval tree system was designed for realistic in vitro simulation. The objective of our study was to assess cannula performance for virtually wall-less versus standard percutaneous thin-walled venous cannulas in a setting of venous collapse in case of negative pressure. METHODS: For a collapsible caval model, a very flexible plastic material was selected, and a model with nine afferent veins was designed according to the anatomy of the vena cava. A flow bench was built including a lower reservoir holding the caval tree, built by taking into account the main afferent vessels and their flow provided by a reservoir 6 cm above. A cannula was inserted in this caval tree and connected to a centrifugal pump that, in turn, was connected to a reservoir positioned 83 cm above the second lower reservoir (after-load = 60 mmHg). Using the same pre-load, the simulated venous drainage for cardiopulmonary bypass was realized using a 24 F wall-less cannula (Smartcanula) and 25 F percutaneous cannula (Biomedicus), and stepwise increased augmentation (1500 RPM, 2000 and 2500 RPM) of venous drainage. RESULTS: For the thin wall and the wall-less cannulas, 36 pairs of flow and pressure measurements were realized for three different RPM values. The mean Q-values at 1500, 2000 and 2500 RPM were: 3.98 ± 0.01, 6.27 ± 0.02 and 9.81 ± 0.02 l/min for the wall-less cannula (P <0.0001), versus 2.74 ± 0.02, 3.06 ± 0.05, 6.78 ± 0.02 l/min for the thin-wall cannula (P <0.0001). The corresponding inlet pressure values were: -8.88 ± 0.01, -23.69 ± 0.81 and -70.22 ± 0.18 mmHg for the wall-less cannula (P <0.0001), versus -36.69 ± 1.88, -80.85 ± 1.71 and -101.83 ± 0.45 mmHg for the thin-wall cannula (P <0.0001). The thin-wall cannula showed mean Q-values 37% less and mean P values 26% more when compared with the wall-less cannula (P <0.0001). CONCLUSIONS: Our in vitro water test was able to mimic a negative pressure situation, where the wall-less cannula design performs better compared with the traditional thin-wall cannula.

Accelerated Microstructure Imaging via Convex Optimization (AMICO) from diffusion MRI data.

Microstructure imaging from diffusion magnetic resonance (MR) data represents an invaluable tool to study non-invasively the morphology of tissues and to provide a biological insight into their microstructural organization. In recent years, a variety of biophysical models have been proposed to associate particular patterns observed in the measured signal with specific microstructural properties of the neuronal tissue, such as axon diameter and fiber density. Despite very appealing results showing that the estimated microstructure indices agree very well with histological examinations, existing techniques require computationally very expensive non-linear procedures to fit the models to the data which, in practice, demand the use of powerful computer clusters for large-scale applications. In this work, we present a general framework for Accelerated Microstructure Imaging via Convex Optimization (AMICO) and show how to re-formulate this class of techniques as convenient linear systems which, then, can be efficiently solved using very fast algorithms. We demonstrate this linearization of the fitting problem for two specific models, i.e. ActiveAx and NODDI, providing a very attractive alternative for parameter estimation in those techniques; however, the AMICO framework is general and flexible enough to work also for the wider space of microstructure imaging methods. Results demonstrate that AMICO represents an effective means to accelerate the fit of existing techniques drastically (up to four orders of magnitude faster) while preserving accuracy and precision in the estimated model parameters (correlation above 0.9). We believe that the availability of such ultrafast algorithms will help to accelerate the spread of microstructure imaging to larger cohorts of patients and to study a wider spectrum of neurological disorders.

Effects of strontium ranelate and alendronate on bone microstructure in women with osteoporosis. Results of a 2-year study.

A Strontium ranelate appears to influence more than alendronate distal tibia bone microstructure as assessed by high-resolution peripheral quantitative computed tomography (HR-pQCT), and biomechanically relevant parameters as assessed by micro-finite element analysis (mu FEA), over 2 years, in postmenopausal osteoporotic women.Introduction Bone microstructure changes are a target in osteoporosis treatment to increase bone strength and reduce fracture risk.Methods Using HR-pQCT, we investigated the effects on distal tibia and radius microstructure of strontium ranelate (SrRan; 2 g/day) or alendronate (70 mg/week) for 2 years in postmenopausal osteoporotic women. This exploratory randomized, double-blind trial evaluated HR-pQCT and FEA parameters, areal bone mineral density (BMD), and bone turnover markers.Results In the intention-to-treat population (n = 83, age: 64 +/- 8 years; lumbar T-score: -2.8 +/- 0.8 [DXA]), distal tibia Cortical Thickness (CTh) and Density (DCort), and cancellous BV/TV increased by 6.3%, 1.4%, and 2.5%, respectively (all P < 0.005), with SrRan, but not with alendronate (0.9%, 0.4%, and 0.8%, NS) (P < 0.05 for all above between-group differences). Difference for CTh evaluated with a distance transformation method was close to significance (P = 0.06). The estimated failure load increased with SrRan (+2.1%, P < 0.005), not with alendronate (-0.6%, NS) (between-group difference, P < 0.01). Cortical stress was lower with SrRan (P < 0.05); both treatments decreased trabecular stress. At distal radius, there was no between-group difference other than DCort (P < 0.05). Bone turnover markers decreased with alendronate; bALP increased (+21%) and serum-CTX-I decreased (-1%) after 2 years of SrRan (between-group difference at each time point for both markers, P < 0.0001). Both treatments were well tolerated.Conclusions Within the constraints of HR-pQCT method, and while a possible artefactual contribution of strontium cannot be quantified, SrRan appeared to influence distal tibia bone microstructure and FEA-determined biomechanical parameters more than alendronate. However, the magnitude of the differences is unclear and requires confirmation with another method.

A realistic Computed Tomography simulator for small motion analysis of cerebral aneurysms.

This paper describes a realistic simulator for the Computed Tomography (CT) scan process for motion analysis. In fact, we are currently developing a new framework to find small motion from the CT scan. In order to prove the fidelity of this framework, or potentially any other algorithm, we present in this paper a simulator to simulate the whole CT acquisition process with a priori known parameters. In other words, it is a digital phantom for the motion analysis that can be used to compare the results of any related algorithm with the ground-truth realistic analytical model. Such a simulator can be used by the community to test different algorithms in the biomedical imaging domain. The most important features of this simulator are its different considerations to simulate the best the real acquisition process and its generality.

Widespread age-related differences in the human brain microstructure revealed by quantitative magnetic resonance imaging.

A pressing need exists to disentangle age-related changes from pathologic neurodegeneration. This study aims to characterize the spatial pattern and age-related differences of biologically relevant measures in vivo over the course of normal aging. Quantitative multiparameter maps that provide neuroimaging biomarkers for myelination and iron levels, parameters sensitive to aging, were acquired from 138 healthy volunteers (age range: 19-75 years). Whole-brain voxel-wise analysis revealed a global pattern of age-related degeneration. Significant demyelination occurred principally in the white matter. The observed age-related differences in myelination were anatomically specific. In line with invasive histologic reports, higher age-related differences were seen in the genu of the corpus callosum than the splenium. Iron levels were significantly increased in the basal ganglia, red nucleus, and extensive cortical regions but decreased along the superior occipitofrontal fascicle and optic radiation. This whole-brain pattern of age-associated microstructural differences in the asymptomatic population provides insight into the neurobiology of aging. The results help build a quantitative baseline from which to examine and draw a dividing line between healthy aging and pathologic neurodegeneration.

Modelling of iron-filled magneto-active polymers with a dispersed chain-like microstructure

Magneto-active polymers are a class of smart materials commonly manufactured by mixing micron-sized iron particles in a rubber-like matrix. When cured in the presence of an externally applied magnetic field, the iron particles arrange themselves into chain-like structures that lend an overall anisotropy to the material. It has been observed through electron micrographs and X-ray tomographs that these chains are not always perfect in structure, and may have dispersion due to the conditions present during manufacturing or some undesirable material properties. We model the response of these materials to coupled magneto-mechanical loading in this paper using a probability based structure tensor that accounts for this imperfect anisotropy. The response of the matrix material is decoupled from the chain phase, though still being connected through kinematic constraints. The latter is based on the definition of a 'chain deformation gradient' and a 'chain magnetic field'. We conclude with numerical examples that demonstrate the effect of chain dispersion on the response of the material to magnetoelastic loading.

En face optical coherence tomography of foveal microstructure in full-thickness macular hole: a model to study perifoveal müller cells.

PURPOSE: To characterize perifoveal intraretinal cavities observed around full-thickness macular holes (MH) using en face optical coherence tomography and to establish correlations with histology of human and primate maculae. DESIGN: Retrospective nonconsecutive observational case series. METHODS: Macular en face scans of 8 patients with MH were analyzed to quantify the areas of hyporeflective spaces, and were compared with macular flat mounts and sections from 1 normal human donor eye and 2 normal primate eyes (Macaca fascicularis). Immunohistochemistry was used to study the distribution of glutamine synthetase, expressed by Müller cells, and zonula occludens-1, a tight-junction protein. RESULTS: The mean area of hyporeflective spaces was lower in the inner nuclear layer (INL) than in the complex formed by the outer plexiform (OPL) and the Henle fiber layers (HFL): 5.0 × 10(-3) mm(2) vs 15.9 × 10(-3) mm(2), respectively (P < .0001, Kruskal-Wallis test). In the OPL and HFL, cavities were elongated with a stellate pattern, whereas in the INL they were rounded and formed vertical cylinders. Immunohistochemistry confirmed that Müller cells followed a radial distribution around the fovea in the frontal plane and a "Z-shaped" course in the axial plane, running obliquely in the OPL and HFL and vertically in the inner layers. In addition, zonula occludens-1 co-localized with Müller cells within the complex of OPL and HFL, indicating junctions in between Müller cells and cone axons. CONCLUSION: The dual profile of cavities around MHs correlates with Müller cell morphology and is consistent with the hypothesis of intra- or extracellular fluid accumulation along these cells.

Microstructure of the superior longitudinal fasciculus predicts stimulation-induced interference with on-line motor control.

A cortical visuomotor network, comprising the medial intraparietal sulcus (mIPS) and the dorsal premotor area (PMd), encodes the sensorimotor transformations required for the on-line control of reaching movements. How information is transmitted between these two regions and which pathways are involved, are less clear. Here, we use a multimodal approach combining repetitive transcranial magnetic stimulation (rTMS) and diffusion tensor imaging (DTI) to investigate whether structural connectivity in the 'reaching' circuit is associated to variations in the ability to control and update a movement. We induced a transient disruption of the neural processes underlying on-line motor adjustments by applying 1Hz rTMS over the mIPS. After the stimulation protocol, participants globally showed a reduction of the number of corrective trajectories during a reaching task that included unexpected visual perturbations. A voxel-based analysis revealed that participants exhibiting higher fractional anisotropy (FA) in the second branch of the superior longitudinal fasciculus (SLF II) suffered less rTMS-induced behavioral impact. These results indicate that the microstructural features of the white matter bundles within the parieto-frontal 'reaching' circuit play a prominent role when action reprogramming is interfered. Moreover, our study suggests that the structural alignment and cohesion of the white matter tracts might be used as a predictor to characterize the extent of motor impairments.

Accelerated Microstructure Imaging via Convex Optimization (AMICO) in crossing fibers

Mapping the microstructure properties of the local tissues in the brain is crucial to understand any pathological condition from a biological perspective. Most of the existing techniques to estimate the microstructure of the white matter assume a single axon orientation whereas numerous regions of the brain actually present a fiber-crossing configuration. The purpose of the present study is to extend a recent convex optimization framework to recover microstructure parameters in regions with multiple fibers.

Accelerated Microstructure Imaging via Convex Optimisation for regions with multiple fibres (AMICOx)

This paper reviews and extends our previous work to enable fast axonal diameter mapping from diffusion MRI data in the presence of multiple fibre populations within a voxel. Most of the existing mi-crostructure imaging techniques use non-linear algorithms to fit their data models and consequently, they are computationally expensive and usually slow. Moreover, most of them assume a single axon orientation while numerous regions of the brain actually present more complex configurations, e.g. fiber crossing. We present a flexible framework, based on convex optimisation, that enables fast and accurate reconstructions of the microstructure organisation, not limited to areas where the white matter is coherently oriented. We show through numerical simulations the ability of our method to correctly estimate the microstructure features (mean axon diameter and intra-cellular volume fraction) in crossing regions.