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.

The long-term culture of porcine urothelial cells and induction of urothelial stratification.

OBJECTIVE: To assess porcine urothelial cell cultures and the in vitro induction of urothelial stratification in long-term cultures, to study their morphological, functional and genetic behaviour, and thus provide potential autologous urothelium for tissue-engineered substitutes for demucosalized gastric or colonic tissue. MATERIALS AND METHODS: Primary cultures of porcine urothelium were established and the cells passaged thereafter. Cell specificity was confirmed by cytokeratin analysis, cell membrane stability assessed using lactate dehydrogenase leakage, cell de-differentiation by gamma-glutamyl transferase activity and genomic stability by karyotype investigations. Histology and scanning electron microscopy were performed to study the cultured cells and the stratified constructs. Furthermore, collagen matrices were tested as cell scaffolds. RESULTS: The cells were cultured for 180 days; 10 subcultures were established during this period. Stratification was induced in a culture flask and on a collagen matrix. Cytokeratins 7, 8, 17 and 18 were expressed in all cultures, and cell membranes were stable, with no evident de-differentiation. The cultures were stable in their genotype and no chromosomal aberrations were found. The histology and immunohistochemistry of the stratified porcine constructs, and cell membrane stability and cell de-differentiation, were compared with those in the human system. CONCLUSION: Pig and human urothelial cells can be cultured over a long period with no signs of senescence. Urothelial stratification can be induced in vitro. The collagen matrix seems to be an excellent scaffold, allowing cell adherence and growth.

Very long half-life of paroxetine following intoxication in an extensive cytochrome P4502D6 metabolizer

A very long half-life of paroxetine (195 h instead of the usual value of around 16 h) was measured after an overdose with 2 g paroxetine and 1 g clorazepate in a patient who was an extensive cytochrome P4502D6 metabolizer. The patient recovered well without any clinically significant complications. A consequence of the close monitoring of paroxetine levels in this patient was that it was decided not to reintroduce any other antidepressant despite her suicide attempt, until normal levels of paroxetine had been reached, which took over 1 month.

Long-Term Safety of Canakinumab in Patients with Gouty Arthritis.

Background/Purpose: Gouty arthritis (GA) is a chronic inflammatory disease. Targeting the inflammatory pathway through IL-1_ inhibition with canakinumab (CAN) may provide significant long-term benefits. CAN safety versus triamcinolone acetonide (TA) over initial 24 weeks (blinded study) for patients (pts) with history of frequent attacks (_3 in year before baseline) was reported earlier from core (_-RELIEVED [_-REL] and _-REL-II) and first extension (E1) studies1. Herein we present full 18-month long-term CAN safety data, including open-label second extension (E2) studies. Methods: GA pts completing _-REL E1 and _-REL-II E1 studies1 were enrolled in these 1-year, open-label, E2 studies. All pts entering E2, whether randomized to CAN or TA, received CAN 150 mg sc on demand upon new attack. Data are presented only for pts randomized to CAN, and are reported cumulatively, i.e. including corresponding data from previously reported core and E1 studies. Long-term safety outcomes and safety upon re-treatment are presented as incidence rate per 100 patient-years (pyr) of study participation for AEs and SAEs. Deaths are reported for all pts (randomized to CAN or TA). Selected predefined notable laboratory abnormalities are shown (neutrophils, platelets, liver and renal function tests). Long-term attack rate per year is also provided. Results: In total, 69/115 (60%) and 72/112 (64.3%) of the pts randomized to CAN in the two core studies entered the two E2 studies, of which 68 and 64 pts, respectively completed the E2 studies. The 2 study populations had differing baseline comorbidity and geographic origin. Lab data (not time adjusted) for neutropenia appears worse after retreatment in _-REL E2, and deterioration of creatinine clearance appears worse after retreatment (Table 1). The time-adjusted incidence rates for AEs were 302.4/100 pyr and 360/100 pyr, and for SAEs were 27.9/100 pyr and 13.9/100 pyr in _-REL E2 and _-REL-II E2 respectively (Table 1). The time-adjusted incidence rates of any AEs, infection AEs, any SAEs, and selected SAEs before and after re-treatment are presented in Table 1. Incidence rates for AEs and SAEs declined after re-treatment, with the exception of SAEs in _-REL-II E2, which increased from 2.9/100 pyr to 10.9/100 pyr (no infection SAEs after retreatment in _-REL-II E2, and other SAEs fit no special pattern). In the total safety population (N_454, core and all extensions), there were 4 deaths, 2 in the core studies previously reported1 and 2 during the _-REL E2 study (one patient in the CAN group died from pneumonia; one patient in the TA group who never received CAN died of pneumococcal sepsis). None of the deaths was suspected by investigators to be study drug related. The mean rates of new attacks per year on CAN were 1.21 and 1.18 in _-REL E2 and in _-REL-II E2. Conclusion: The clinical safety profile of CAN upon re-treatment was maintained long-term with no new infection concerns

Long-term close follow-up of chorioretinal lesions in presumed ocular tuberculosis

Purpose: To evaluate the long-term outcome (up to 7 years) of presumed ocular tuberculosis (TB) when the therapeutic decision was based on WHO guidelines. Methods: Twelve out of 654 new uveitic patients (1998-2004) presented with choroiditis and positive tuberculosis skin test (TST) (skin lesion diameter >15 mm). Therapy was administered according to WHO recommendations after ophthalmic and systemic investigation. The area size of ocular lesions at presentation and after therapy, measured on fluorescein and indocyanine green angiographies, was considered the primary outcome. Relapse of choroiditis was considered a secondary outcome. The T-SPOTTB test was performed when it became available. Results: Visual acuity (VA) significantly improved after therapy (p=0.0357). The mean total surface of fluorescein lesions at entry was 44.8±20.9 (arbitrary units) and decreased to 32.5±16.9 after therapy (p=0.0165). The mean total surface of indocyanine green lesions at entry was 24.5±13.3 and decreased to 10.8±5.4 after therapy (p=0.0631). The T-SPOT TB revealed 2 false TST-positive results. The mean follow-up was 4.5±1.5 years. Two relapses out of 10 confirmed ocular TB was observed after complete lesion healing, 2.5 years and 4.5 years after therapy, respectively. Conclusions: A decrease of ocular lesion mean size and a mean improvement of VA were observed after antituberculous therapy. Our long-term follow-up of chorioretinal lesions demonstrated relapse of ocular tuberculosis in 10% of patients with confirmed ocular TB, despite complete initial retinal scarring.

Nurture versus nature: long-term impact of forced right-handedness on structure of pericentral cortex and basal ganglia.

Does a conflict between inborn motor preferences and educational standards during childhood impact the structure of the adult human brain? To examine this issue, we acquired high-resolution T1-weighted magnetic resonance scans of the whole brain in adult "converted" left-handers who had been forced as children to become dextral writers. Analysis of sulcal surfaces revealed that consistent right- and left-handers showed an interhemispheric asymmetry in the surface area of the central sulcus with a greater surface contralateral to the dominant hand. This pattern was reversed in the converted group who showed a larger surface of the central sulcus in their left, nondominant hemisphere, indicating plasticity of the primary sensorimotor cortex caused by forced use of the nondominant hand. Voxel-based morphometry showed a reduction of gray matter volume in the middle part of the left putamen in converted left-handers relative to both consistently handed groups. A similar trend was found in the right putamen. Converted subjects with at least one left-handed first-degree relative showed a correlation between the acquired right-hand advantage for writing and the structural changes in putamen and pericentral cortex. Our results show that a specific environmental challenge during childhood can shape the macroscopic structure of the human basal ganglia. The smaller than normal putaminal volume differs markedly from previously reported enlargement of cortical gray matter associated with skill acquisition. This indicates a differential response of the basal ganglia to early environmental challenges, possibly related to processes of pruning during motor development.

Association of ischaemic stroke subtype with long-term cardiovascular events.

BACKGROUND AND PURPOSE: There is no strong evidence that all ischaemic stroke types are associated with high cardiovascular risk. Our aim was to investigate whether all ischaemic stroke types are associated with high cardiovascular risk. METHODS: All consecutive patients with ischaemic stroke registered in the Athens Stroke Registry between 1 January 1993 and 31 December 2010 were categorized according to the TOAST classification and were followed up for up to 10 years. Outcomes assessed were cardiovascular and all-cause mortality, myocardial infarction, stroke recurrence, and a composite cardiovascular outcome consisting of myocardial infarction, angina pectoris, acute heart failure, sudden cardiac death, stroke recurrence and aortic aneurysm rupture. The Kaplan-Meier product limit method was used to estimate the probability of each end-point in each patient group. Cox proportional hazards models were used to determine the independent covariates of each end-point. RESULTS: Two thousand seven hundred and thirty patients were followed up for 48.1 ± 41.9 months. The cumulative probabilities of 10-year cardiovascular mortality in patients with cardioembolic stroke [46.6%, 95% confidence interval (CI) 40.6-52.8], lacunar stroke (22.1%, 95% CI 16.2-28.0) or undetermined stroke (35.2%, 95% CI 27.8-42.6) were either similar to or higher than those of patients with large-artery atherosclerotic stroke (LAA) (28.7%, 95% CI 22.4-35.0). Compared with LAA, all other TOAST types had a higher probability of 10-year stroke recurrence. In Cox proportional hazards analysis, compared with patients with LAA, patients with any other stroke type were associated with similar or higher risk for the outcomes of overall mortality, cardiovascular mortality, stroke recurrence and composite cardiovascular outcome. CONCLUSIONS: Large-artery atherosclerotic stroke and cardioembolic stroke are associated with the highest risk for future cardiovascular events, with the latter carrying at least as high a risk as LAA stroke.

Le QT long acquis [Acquired long QT syndrome].

The long QT syndrome may be acquired or genetically determined. The syndrome is characterized by a prolonged QT interval and is associated with an increased risk of cardiac arrhythmia such as a torsade de pointe and death. Electrolytes disorders such as hypomagnesemia and hypokaliemia and several drugs may increase the risk to develop a long QT syndrome. The epidemiology, the aetiology, the diagnostic approach as well as the management options of an acquired QT prolongation is discussed and reviewed herein.