Estimation of jump-diffusion processes via empirical characteristic functions

Preface The starting point for this work and eventually the subject of the whole thesis was the question: how to estimate parameters of the affine stochastic volatility jump-diffusion models. These models are very important for contingent claim pricing. Their major advantage, availability T of analytical solutions for characteristic functions, made them the models of choice for many theoretical constructions and practical applications. At the same time, estimation of parameters of stochastic volatility jump-diffusion models is not a straightforward task. The problem is coming from the variance process, which is non-observable. There are several estimation methodologies that deal with estimation problems of latent variables. One appeared to be particularly interesting. It proposes the estimator that in contrast to the other methods requires neither discretization nor simulation of the process: the Continuous Empirical Characteristic function estimator (EGF) based on the unconditional characteristic function. However, the procedure was derived only for the stochastic volatility models without jumps. Thus, it has become the subject of my research. This thesis consists of three parts. Each one is written as independent and self contained article. At the same time, questions that are answered by the second and third parts of this Work arise naturally from the issues investigated and results obtained in the first one. The first chapter is the theoretical foundation of the thesis. It proposes an estimation procedure for the stochastic volatility models with jumps both in the asset price and variance processes. The estimation procedure is based on the joint unconditional characteristic function for the stochastic process. The major analytical result of this part as well as of the whole thesis is the closed form expression for the joint unconditional characteristic function for the stochastic volatility jump-diffusion models. The empirical part of the chapter suggests that besides a stochastic volatility, jumps both in the mean and the volatility equation are relevant for modelling returns of the S&P500 index, which has been chosen as a general representative of the stock asset class. Hence, the next question is: what jump process to use to model returns of the S&P500. The decision about the jump process in the framework of the affine jump- diffusion models boils down to defining the intensity of the compound Poisson process, a constant or some function of state variables, and to choosing the distribution of the jump size. While the jump in the variance process is usually assumed to be exponential, there are at least three distributions of the jump size which are currently used for the asset log-prices: normal, exponential and double exponential. The second part of this thesis shows that normal jumps in the asset log-returns should be used if we are to model S&P500 index by a stochastic volatility jump-diffusion model. This is a surprising result. Exponential distribution has fatter tails and for this reason either exponential or double exponential jump size was expected to provide the best it of the stochastic volatility jump-diffusion models to the data. The idea of testing the efficiency of the Continuous ECF estimator on the simulated data has already appeared when the first estimation results of the first chapter were obtained. In the absence of a benchmark or any ground for comparison it is unreasonable to be sure that our parameter estimates and the true parameters of the models coincide. The conclusion of the second chapter provides one more reason to do that kind of test. Thus, the third part of this thesis concentrates on the estimation of parameters of stochastic volatility jump- diffusion models on the basis of the asset price time-series simulated from various "true" parameter sets. The goal is to show that the Continuous ECF estimator based on the joint unconditional characteristic function is capable of finding the true parameters. And, the third chapter proves that our estimator indeed has the ability to do so. Once it is clear that the Continuous ECF estimator based on the unconditional characteristic function is working, the next question does not wait to appear. The question is whether the computation effort can be reduced without affecting the efficiency of the estimator, or whether the efficiency of the estimator can be improved without dramatically increasing the computational burden. The efficiency of the Continuous ECF estimator depends on the number of dimensions of the joint unconditional characteristic function which is used for its construction. Theoretically, the more dimensions there are, the more efficient is the estimation procedure. In practice, however, this relationship is not so straightforward due to the increasing computational difficulties. The second chapter, for example, in addition to the choice of the jump process, discusses the possibility of using the marginal, i.e. one-dimensional, unconditional characteristic function in the estimation instead of the joint, bi-dimensional, unconditional characteristic function. As result, the preference for one or the other depends on the model to be estimated. Thus, the computational effort can be reduced in some cases without affecting the efficiency of the estimator. The improvement of the estimator s efficiency by increasing its dimensionality faces more difficulties. The third chapter of this thesis, in addition to what was discussed above, compares the performance of the estimators with bi- and three-dimensional unconditional characteristic functions on the simulated data. It shows that the theoretical efficiency of the Continuous ECF estimator based on the three-dimensional unconditional characteristic function is not attainable in practice, at least for the moment, due to the limitations on the computer power and optimization toolboxes available to the general public. Thus, the Continuous ECF estimator based on the joint, bi-dimensional, unconditional characteristic function has all the reasons to exist and to be used for the estimation of parameters of the stochastic volatility jump-diffusion models.

Scale decisions can reverse conclusions on community assembly processes.

AIM: Phylogenetic diversity patterns are increasingly being used to better understand the role of ecological and evolutionary processes in community assembly. Here, we quantify how these patterns are influenced by scale choices in terms of spatial and environmental extent and organismic scales. LOCATION: European Alps. METHODS: We applied 42 sampling strategies differing in their combination of focal scales. For each resulting sub-dataset, we estimated the phylogenetic diversity of the species pools, phylogenetic α-diversities of local communities, and statistics commonly used together with null models in order to infer non-random diversity patterns (i.e. phylogenetic clustering versus over-dispersion). Finally, we studied the effects of scale choices on these measures using regression analyses. RESULTS: Scale choices were decisive for revealing signals in diversity patterns. Notably, changes in focal scales sometimes reversed a pattern of over-dispersion into clustering. Organismic scale had a stronger effect than spatial and environmental extent. However, we did not find general rules for the direction of change from over-dispersion to clustering with changing scales. Importantly, these scale issues had only a weak influence when focusing on regional diversity patterns that change along abiotic gradients. MAIN CONCLUSIONS: Our results call for caution when combining phylogenetic data with distributional data to study how and why communities differ from random expectations of phylogenetic relatedness. These analyses seem to be robust when the focus is on relating community diversity patterns to variation in habitat conditions, such as abiotic gradients. However, if the focus is on identifying relevant assembly rules for local communities, the uncertainty arising from a certain scale choice can be immense. In the latter case, it becomes necessary to test whether emerging patterns are robust to alternative scale choices.

The role of oxidative stress during inflammatory processes.

Abstract The production of various reactive oxidant species in excess of endogenous antioxidant defense mechanisms promotes the development of a state of oxidative stress, with significant biological consequences. In recent years, evidence has emerged that oxidative stress plays a crucial role in the development and perpetuation of inflammation, and thus contributes to the pathophysiology of a number of debilitating illnesses, such as cardiovascular diseases, diabetes, cancer, or neurodegenerative processes. Oxidants affect all stages of the inflammatory response, including the release by damaged tissues of molecules acting as endogenous danger signals, their sensing by innate immune receptors from the Toll-like (TLRs) and the NOD-like (NLRs) families, and the activation of signaling pathways initiating the adaptive cellular response to such signals. In this article, after summarizing the basic aspects of redox biology and inflammation, we review in detail the current knowledge on the fundamental connections between oxidative stress and inflammatory processes, with a special emphasis on the danger molecule high-mobility group box-1, the TLRs, the NLRP-3 receptor, and the inflammasome, as well as the transcription factor nuclear factor-κB.

Geochemical and H-O-Sr-Nd isotope evidence for magmatic processes and meteoric-water interactions in the basal complex of La Gomera, Canary Islands

The plutonic rocks of the Basal Complex of La Gomera, Canary Islands, Spain, were studied by means of major and trace element contents and by H-O-Sr-Nd isotope compositions in order to distinguish primary magmatic characteristics and late-stage alteration products. Deciphering the effects of alteration allowed us to determine primary, plume-related compositions that indicated D- and (18)O-depletion relative to normal upper mantle, supporting the conclusions of earlier studies on the plutonic rocks of Fuerteventura and La Palma. Late-stage alteration took place during the formation of the intrusive series induced by interaction with meteoric water. Inferred isotopic compositions of the meteoric water indicate that the water infiltrated into the rock edifice at a height of about 1500 m above sea level, suggesting the existence of a subaerial volcano which was active during the intrusive activity and that it has been either distroyed or remain buried by later volcanic and landslide events.

Unravelling the interaction between tectonic and sedimentary processes during lithospheric thinning in the Alpine Tethys margins

The discovery of exhumed continental mantle and hyper-extended crust in present-day magma-poor rifted margins is at the origin of a paradigm shift within the research field of deep-water rifted margins. It opened new questions about the strain history of rifted margins and the nature and composition of sedimentary, crustal and mantle rocks in rifted margins. Thanks to the benefit of more than one century of work in the Alps and access to world-class outcrops preserving the primary relationships between sediments and crustal and mantle rocks from the fossil Alpine Tethys margins, it is possible to link the subsidence history and syn-rift sedimentary evolution with the strain distribution observed in the crust and mantle rocks exposed in the distal rifted margins. In this paper, we will focus on the transition from early to late rifting that is associated with considerable crustal thinning and a reorganization of the rift system. Crustal thinning is at the origin of a major change in the style of deformation from high-angle to low-angle normal faulting which controls basin-architecture, sedimentary sources and processes and the nature of basement rocks exhumed along the detachment faults in the distal margin. Stratigraphic and isotopic ages indicate that this major change occurred in late Sinemurian time, involving a shift of the syn-rift sedimentation toward the distal domain associated with a major reorganization of the crustal structure with exhumation of lower and middle crust. These changes may be triggered by mantle processes, as indicated by the infiltration of MOR-type magmas in the lithospheric mantle, and the uplift of the Brianconnais domain. Thinning and exhumation of the crust and lithosphere also resulted in the creation of new paleogeographic domains, the Proto Valais and Liguria-Piemonte domains. These basins show a complex, 3D temporal and spatial evolution that might have evolved, at least in the case of the Liguria-Piemonte basin, in the formation of an embryonic oceanic crust. The re-interpretation of the rift evolution and the architecture of the distal rifted margins in the Alps have important implications for the understanding of rifted margins worldwide, but also for the paleogeographic reconstruction of the Alpine domain and its subsequent Alpine compressional overprint.

Weakening processes in thrust faults: insights from the Monte Perdido thrust fault (southern Pyrenees, Spain)

The Monte Perdido thrust fault (southern Pyrenees) consists of a 6-m-thick interval of intensely deformed clay-bearing rocks. The fault zone is affected by a pervasive pressure solution seam and numerous shear surfaces. Calcite extensional-shear veins are present along the shear surfaces. The angular relationships between the two structures indicate that shear surfaces developed at a high angle (70°) to the local principal maximum stress axis r1. Two main stages of deformation are present. The first stage corresponds to the development of calcite shear veins by a combination of shear surface reactivation and extensional mode I rupture. The second stage of deformation corresponds to chlorite precipitation along the previously reactivated shear surfaces. The pore fluid factor k computed for the two deformation episodes indicates high fluid pressures during the Monte Perdido thrust activity. During the first stage of deformation, the reactivation of the shear surface was facilitated by a suprahydrostatic fluid pressure with a pore fluid factor kv equal to 0.89. For the second stage, the fluid pressure remained still high (with a k value ranging between 0.77 and 0.84) even with the presence of weak chlorite along the shear surfaces. Furthermore, evidence of hydrostatic fluid pressure during calcite cement precipitation supports that incremental shear surface reactivations are correlated with cyclic fluid pressure fluctuations consis- tent with a fault-valve model.

Relaxivity of Gd-based contrast agents on X nuclei with long intrinsic relaxation times in aqueous solutions.

The relaxivity of commercially available gadolinium (Gd)-based contrast agents was studied for X-nuclei resonances with long intrinsic relaxation times ranging from 6 s to several hundred seconds. Omniscan in pure 13C formic acid had a relaxivity of 2.9 mM(-1) s(-1), whereas its relaxivity on glutamate C1 and C5 in aqueous solution was approximately 0.5 mM(-1) s(-1). Both relaxivities allow the preparation of solutions with a predetermined short T1 and suggest that in vitro substantial sensitivity gains in their measurement can be achieved. 6Li has a long intrinsic relaxation time, on the order of several minutes, which was strongly affected by the contrast agents. Relaxivity ranged from approximately 0.1 mM(-1) s(-1) for Omniscan to 0.3 for Magnevist, whereas the relaxivity of Gd-DOTP was at 11 mM(-1) s(-1), which is two orders of magnitude higher. Overall, these experiments suggest that the presence of 0.1- to 10-microM contrast agents should be detectable, provided sufficient sensitivity is available, such as that afforded by hyperpolarization, recently introduced to in vivo imaging.

Antagonism of neuromuscular blockade but not muscle relaxation affects depth of anaesthesia

RÉSUMÉ Introduction L'effet des agents myorelaxants ainsi que des anticholinestérases sur la profondeur d'anesthésie a été étudié avec des résultats contradictoires. C'est pourquoi nous avons évalué l'effet de l'atracurium et de la néostigmine sur le BIS (bispectral index) ainsi que sur les potentiels auditives évoqués (middle-latency auditory evoked potentials, A-Line® autoregressive index [AAI]). Méthodes Après avoir obtenu l'accord du comité d'éthique local, nous avons étudié 40 patients ayant donné leur consentement écrit, ASA I-II, âgé de 18-69 ans. L'anesthésie générale a consisté en anesthésie intra-veineuse à objectif de concentration avec du propofol et du remifentanil. La fonction de la jonction neuromusculaire était monitorée en continu au moyen d'un électromyographe. Le BIS et l'AAI ont été enregistrés en continu. Après avoir atteint des valeurs stables au niveau du BIS, les patients ont été attribués à deux groupes par randomisation. Les patients du groupe 1 ont reçu 0.4 mg kg-1 d'atracurium et 5 minutes plus tard le même volume de NaCI 0.9%, dans le groupe 2 la séquence d'injection était inversée, le NaCI 0.9% en premier et l'atracurium en deuxième. Au moment où le premier « twitch » d'un train de quatre atteignait 10% de l'intensité avant la relaxation, les patients ont été randomisés une deuxième fois. Les patients du groupe N ont reçu 0.04 mg kg-1 de néostigmine et 0.01 rn9 kg-1 de glycopyrrolate alors que le groupe contrôle (G) ne recevait que 0.01 mg kg-] de glycopyrrolate. Résultats : L 'injection d'atracurium ou de NaCI 0.9% n'a pas eu d'effet sur le BIS ou l'AAI. Après l'injection de néostigmine avec glycopyrrolate, le BIS et I `AAI a augmenté de manière significative (changement maximal moyen du BIS 7.1 ± 7.5, P< 0.001, de l'AAI 9.7 ± 10.5, P< 0.001). Suite à l'injection de glycopyrrolate seule, le BIS et l'AAI a augmenté également (changement maximal moyen du BIS 2.2 ± 3.4, P< 0.008, de l'AAI 3.5 ± 5.7, P< 0.012), mais cette augmentation était significativement moins importante que dans le groupe N (P< 0.012 pour le BIS, P< 0.027 pour l'AAI). Conclusion Ces résultats laissent supposer que la néostigmine peut altérer la profondeur de l'anesthésie. La diminution de la profondeur d'anesthésie enregistrée par le BIS et l'AAI correspond probablement à une réapparition brusque d'une stimulation centrale liée à la proprioception. Au contraire, lors de la curarisation, le tonus musculaire diminue de manière beaucoup plus progressive, pouvant ainsi expliquer l'absence d'effet sur la profondeur d'anesthésie. ABSTRACT Background. Conflicting effects of neuromuscular blocking drugs and anticholinesterases on depth of anaesthesia have been reported. Therefore we evaluated the effect of atracurium and neostigmine on bispectral index (BIS) and middle-latency auditory evoked potentials (AAI). Methods. We studied 40 patients (ASA I-II) aged 18-69 yr. General anaesthesia consisted of propofol and remifentanil by target-controlled infusion and neuromuscular function was monitored by electromyography. When BIS reached stable values, patients were randomly assigned to one of two groups. Group I received atracurium 0.4 mg kg-1 and, 5 min later, the same volume of NaCl 0.9%; group 2 received saline first and then atracurium. When the first twitch of a train of four reached 10% of control intensity, patients were again randomized: one group (N) received neostigmine 0.04 mg kg-1 and glycopyrrolate 0.01 mg kg-1, and the control group (G) received only glycopyrrolate. Results. Injection of atracurium or NaCl 0.9% had no effect on BIS or AAI. After neostigmine¬glycopyrrolate, BIS and AAI increased significantly (mean maximal change of BIS 7.1 [SD 7.5], P<0.001; mean maximal change of AAI 9.7 [10.5], P<0.001). When glycopyrrolate was injected alone BIS and AAI also increased (mean maximal change of BIS 2.2 [3.4], P=0.008; mean maximal change of AAI 3.5 [5.7], P=0.012), but this increase was significantly less than in group N (P=0.012 for BIS; P=0.027 for AAI). Conclusion. These data suggest that neostigmine alters the state of propofol-remifentanil anaesthesia and may enhance recovery.

Limites des procédés d'investigation de la fonction érectile dans le cadre d'expertises médicolégales [Limits of the processes of investigation of the erectile function in forensic expertises].

Résumé La responsabilité d'un expert chargé d'apprécier la capacité érectile d'un prévenu est importante, car la peine infligée par le tribunal peut dépendre de ses conclusions. Sa tâche est en plus ardue car les procédés d'investigations de la fonction érectile ont tous des limites. Malgré toutes ces limites qui sont décrites dans cet article, l'expert peut aider à la recherche de la vérité comme les auteurs le démontrent. Summary The responsability of the expert in charge to appreciate the erectile capacity of an accused is considerable, as the sentence inflicted by the Tribunal could depend directly on his conclusions. His duty is harder as all the investigation procedures of the erectile functions have limits. Despite these limits, described in this article, the expert can help to discover the truth, as demonstrated by the authors.

Early clarification processes in clients presenting with borderline personality disorder: Relations with symptom level and change

Clarification-Oriented Psychotherapy (COP), an integrative treatment form with a basis in process-experiential psychotherapy, is particularly relevant for clients with Personality Disorders (PDs). We argue here that two related core therapeutic COP principles, "dual action regulation" and "interactional games" have consequences for symptom severity and therapeutic outcome for clients with PDs. A high quality COP clarification process requires that client's interactional games may be quickly assessed and treated in all (preferably early) therapy sessions. These processes can be observed and measured using the observer-rated Bochum Process and Relationship Rating Scales (BPRRS) which measure both clients' and therapists' contributions to the quality of the clarification processes engaged in therapy. This measure has been successfully applied to COP-therapies, but not, as yet, to therapies other than experiential, nor to specific client populations such as borderline personality disorder. The present study is a first attempt to evaluate the application of COP processes to other therapies and populations. We measured action regulation and interactional games using the BPRRS during intake sessions of a 10-session psychodynamic treatment of borderline personality disorder for a total of N = 30 clients and N = 8 therapists. Significant relationships were found between the client's degree of interactional games and both pretherapy symptom level and symptom change across therapy. These results are discussed in the context of Clarification-Oriented Psychotherapy, and more generally Person-Centered and Process-Experiential Psychotherapies. The potential relevance of the findings for psychodynamic psychotherapists are explored as well as the potential usefulness of taking into account a detailed analysis of interactional games for the training of psychotherapists working with any model of therapy working with clients presenting with BPD.