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.

Native folding of aggregation-prone recombinant proteins in Escherichia coli by osmolytes, plasmid- or benzyl alcohol-overexpressed molecular chaperones.

When massively expressed in bacteria, recombinant proteins often tend to misfold and accumulate as soluble and insoluble nonfunctional aggregates. A general strategy to improve the native folding of recombinant proteins is to increase the cellular concentration of viscous organic compounds, termed osmolytes, or of molecular chaperones that can prevent aggregation and can actively scavenge and convert aggregates into natively refoldable species. In this study, metal affinity purification (immobilized metal ion affinity chromatography [IMAC]), confirmed by resistance to trypsin digestion, was used to distinguish soluble aggregates from soluble nativelike proteins. Salt-induced accumulation of osmolytes during induced protein synthesis significantly improved IMAC yields of folding-recalcitrant proteins. Yet, the highest yields were obtained with cells coexpressing plasmid-encoded molecular chaperones DnaK-DnaJ-GrpE, ClpB, GroEL-GroES, and IbpA/B. Addition of the membrane fluidizer heat shock-inducer benzyl alcohol (BA) to the bacterial medium resulted in similar high yields as with plasmid-mediated chaperone coexpression. Our results suggest that simple BA-mediated induction of endogenous chaperones can substitute for the more demanding approach of chaperone coexpression. Combined strategies of osmolyte-induced native folding with heat-, BA-, or plasmid-induced chaperone coexpression can be thought to optimize yields of natively folded recombinant proteins in bacteria, for research and biotechnological purposes.

Insight in protein S deficiency from mouse models

Protein S (ProS) is an important negative regulator of blood coagulation. Its physiological importance is evident in purpura fulminans and other life-threatening thrombotic disorders typical of ProS deficient patients. Our previous characterization of ProS deficiency in mouse models has shown similarities with the human phenotypes: heterozygous ProS-deficient mice (Pros+/-) had increased thrombotic risk whereas homozygous deficiency in ProS (Pros-/-) was incompatible with life (Blood 2009; 114:2307-2314). In tissues, ProS exerts cellular functions by binding to and activating tyrosine kinase receptors of the Tyro3 family (TAM) on the cell surface.To extend the analysis of coagulation defects beyond the Pros-/- phenotype and add new insights into the sites of synthesis ProS and its action, we generated mice with inactivated ProS in hepatocytes (Proslox/loxAlbCre+) as well as in endothelial and hematopoietic cells (Proslox/loxTie2Cre+). Both models resulted in significant reduction of circulating ProS levels and in a remarkable increased thrombotic risk in vivo. In a model of tissue factor (TF)-induced venous thromboembolism (VTE), only 17% of Proslox/loxAlbCre+ mice (n=12) and only 13% of Proslox/loxTie2Cre+ mice (n=14) survived, compared with 86% of Proslox/lox mice (n=14; P<0.001).To mimic a severe acquired ProS deficiency, ProS gene was inactivated at the adult stage using the polyI:C-inducible Mx1-Cre system (Proslox/loxMx1Cre+). Ten days after polyI:C treatment, Proslox/loxMx1Cre+ mice developed disseminated intravascular coagulation with extensive lung and liver thrombosis.It is worth noting that no skin lesions compatible with purpura fulminans were observed in any of the above-described models of partial ProS deficiency. In order to shed light on the pathogenesis of purpura fulminans, we exposed the different ProS-deficient mice to warfarin (0.2 mg/day). We observed that Pros+/-, Proslox/loxAlbCre+ and Proslox/loxTie2Cre+ mice developed retiform purpura (characterized by erythematous and necrotic lesions of the genital region and extremities) and died after 3 to 5 days after the first warfarin administration.In human, ProS is also synthesized by megakaryocytes and hence stored at high concentrations in circulating platelets (pProS). The role of pProS has been investigated by generating megakaryocyte ProS-deficient model using the PF4 promoter as Cre driver (Proslox/loxPf4Cre+). In the TF-induced VTE model, Proslox/loxPf4Cre+ (n=15) mice showed a significant increased risk of thrombosis compared to Proslox/lox controls (n=14; survival rate 47% and 86%, respectively; P<0.05). Furthermore, preliminary results suggest survival to be associated with higher circulating ProS levels. In order to evaluate the potential role of pProS in thrombus formation, we investigated the thrombotic response to intravenous injection of collagen-epinephrine in vivo and platelet function in vitro. Both in vivo and in vitro experiments showed similar results between Proslox/loxPf4Cre+ and Proslox/lox, indicating that platelet reactivity was not influenced by the absence of pProS. These data suggest that pProS is delivered at the site of thrombosis to inhibit thrombin generation.We further investigated the ability of ProS to function as a ligand of TAM receptors, by using homozygous and heterozygous deficient mice for both the TAM ligands ProS and Gas6. Gas6-/-Pros-/- mice died in utero and showed comparable dramatic bleeding and thrombotic phenotype as described for Pros-/- embryos.In conclusion, like complete ProS deficiency, double deficiency in ProS and Gas6 was lethal, whereas partial ProS deficiency was not. Mice partially deficient in ProS displayed a prothrombotic phenotype, including those with only deficiency in pProS. Purpura fulminans did not occur spontaneously in mice with partial Pros deficiency but developed upon warfarin administration.Thus, the use of different mice models of ProS deficiency can be instrumental in the study of its highly variable thrombotic phenotype and in the investigation of additional roles of ProS in inflammation and autoimmunity through TAM signaling.

Carleson Measures and Logvinenko-Sereda sets on compact manifolds

Given a compact Riemannian manifold $M$ of dimension $m \geq 2$, we study the space of functions of $L^2(M)$generated by eigenfunctions ofeigenvalues less than $L \geq 1$ associated to the Laplace-Beltrami operator on $M$. On these spaces we give a characterization of the Carleson measures and the Logvinenko-Sereda sets.

On the configuration of Herman rings of meromorphic functions

We prove some results concerning the possible configuration s of Herman rings for transcendental meromorphic functions. We show that one pole is enough to obtain cycles of Herman rings of arbitrary period a nd give a sufficient condition for a configuration to be realizable.

Hierarchy of interactive functions in father-mother-baby three-way games

In developmental research, the family has mainly been studied through dyadic interaction. Three-way interactions have received less attention, partly because of their complexity. This difficulty may be overcome by distinguishing between four hierarchically embedded functions in three-way interactions: (1) participation (inclusion of all participants), (2) organization (partners keeping to their roles), (3) focalization (sharing a common focus) and (4) affective contact (being in tune). We document this hierarchical model on a sample of 80 families observed in the Lausanne Trilogue Play situation across four different sites. Hierarchy between functions was demonstrated by means of Guttman scalability coefficient. Given the importance of the child's development in a threesome, the pertinence of this model for family assessment is discussed.

Epithelial sodium channel/degenerin family of ion channels: a variety of functions for a shared structure.

The recently discovered epithelial sodium channel (ENaC)/degenerin (DEG) gene family encodes sodium channels involved in various cell functions in metazoans. Subfamilies found in invertebrates or mammals are functionally distinct. The degenerins in Caenorhabditis elegans participate in mechanotransduction in neuronal cells, FaNaC in snails is a ligand-gated channel activated by neuropeptides, and the Drosophila subfamily is expressed in gonads and neurons. In mammals, ENaC mediates Na+ transport in epithelia and is essential for sodium homeostasis. The ASIC genes encode proton-gated cation channels in both the central and peripheral nervous system that could be involved in pain transduction. This review summarizes the physiological roles of the different channels belonging to this family, their biophysical and pharmacological characteristics, and the emerging knowledge of their molecular structure. Although functionally different, the ENaC/DEG family members share functional domains that are involved in the control of channel activity and in the formation of the pore. The functional heterogeneity among the members of the ENaC/DEG channel family provides a unique opportunity to address the molecular basis of basic channel functions such as activation by ligands, mechanotransduction, ionic selectivity, or block by pharmacological ligands.

Morphology and segregation in two-component diffusion-limited aggregation

A diffusion-limited-aggregation (DLA) model with two components (A and B species) is presented to investigate the structure of the composite deposits. The sticking probability PAB (=PBA) between the different species is introduced into the original DLA model. By using computer simulation it is shown that various patterns are produced with varying the sticking probabilities PAB (=PBA) and PAA (= PBB), where PAA (=PBB) is the sticking probability between the same species. Segregated patterns can be analyzed under the condition PAB < PAA, assumed throughout the paper. With decreasing sticking probability PAB, a clustering of the same species occurs. With sufficiently small values of both sticking probabilities PAB and PAA, the deposit becomes dense and the segregated patterns of the composite deposit show a striped structure. The effect of the concentration on the pattern morphology is also shown.

Calpastatin-mediated inhibition of calpains in the mouse brain prevents mutant ataxin 3 proteolysis, nuclear localization and aggregation, relieving Machado-Joseph disease.

Machado-Joseph disease is the most frequently found dominantly-inherited cerebellar ataxia. Over-repetition of a CAG trinucleotide in the MJD1 gene translates into a polyglutamine tract within the ataxin 3 protein, which upon proteolysis may trigger Machado-Joseph disease. We investigated the role of calpains in the generation of toxic ataxin 3 fragments and pathogenesis of Machado-Joseph disease. For this purpose, we inhibited calpain activity in mouse models of Machado-Joseph disease by overexpressing the endogenous calpain-inhibitor calpastatin. Calpain blockage reduced the size and number of mutant ataxin 3 inclusions, neuronal dysfunction and neurodegeneration. By reducing fragmentation of ataxin 3, calpastatin overexpression modified the subcellular localization of mutant ataxin 3 restraining the protein in the cytoplasm, reducing aggregation and nuclear toxicity and overcoming calpastatin depletion observed upon mutant ataxin 3 expression. Our findings are the first in vivo proof that mutant ataxin 3 proteolysis by calpains mediates its translocation to the nucleus, aggregation and toxicity and that inhibition of calpains may provide an effective therapy for Machado-Joseph disease.

Measures of ionicity of alkaline-earth oxides from the analysis of ab initio cluster wave functions

We present an analysis of the M-O chemical bonding in the binary oxides MgO, CaO, SrO, BaO, and Al2O3 based on ab initio wave functions. The model used to represent the local environment of a metal cation in the bulk oxide is an MO6 cluster which also includes the effect of the lattice Madelung potential. The analysis of the wave functions for these clusters leads to the conclusion that all the alkaline-earth oxides must be regarded as highly ionic oxides; however, the ionic character of the oxides decreases as one goes from MgO, almost perfectly ionic, to BaO. In Al2O3 the ionic character is further reduced; however, even in this case, the departure from the ideal, fully ionic, model of Al3+ is not exceptionally large. These conclusions are based on three measures, a decomposition of the Mq+-Oq- interaction energy, the number of electrons associated to the oxygen ions as obtained from a projection operator technique, and the analysis of the cation core-level binding energies. The increasing covalent character along the series MgO, CaO, SrO, and BaO is discussed in view of the existing theoretical models and experimental data.

Natural killer cell genes and functions after kidney transplantation

Natural Killer (NK) cells are of special interest in solid organ transplantation (SOT) because classical immunosuppressive drugs could enhance NK cells activity.We studied NK cells after kidney transplantation in three different situations. First, we analysed the peripheral repertoire reconstitution and function of NK cells after a polyclonal rabbit anti-thymocytes globulin (rATG) induction therapy, in 20 patients transplanted with living donor and with a low immunological risk. Second, we analysed the influence of KIR genes on the risk of CMV primo-infection or reactivation in 224 transplanted patients during the first year. Finally, we studied the risk of rejection and graft function during the first 5 years according to the KIR genes. Our study demonstrates that after an intial drop, NK cell reconstitution is fast with a ratio of CD56+/CD3− cells versus CD3+ cells that remains identical. The fraction of NK cells expressing the inhibitory receptor NKG2A significantly increases and the activating receptor NKG2D decreases after transplantation to retrieve the pretransplantation value after one year. The secretion of INF-f × and the cytotoxicity is maintained over time after transplantation. Then, we demonstrated that the presence of 2 KIR missing ligands and a large number of activating KIR gene protected against CMV primo-infection or reactivation during the first year post transplantation. Finally, the KIR genes and their HLA ligands do not influence the long term graft function after univariate and multivariate analysis. Our data suggest that despite the modification of the receptor repertoire, NK cell activity is preserved. NK cells are an important player of the immune response in the first year after transplantation mainly thanks to their anti-infectious activity.

Development of an aggregation assay to screen FimH antagonists.

Alpha-D-mannopyranosides are potent FimH antagonists, which inhibit the adhesion of Escherichia coli to highly mannosylated uroplakin Ia on the urothelium and therefore offer an efficient therapeutic opportunity for the treatment and prevention of urinary tract infection. For the evaluation of the therapeutic potential of FimH antagonists, their effect on the disaggregation of E. coli from Candida albicans and guinea pig erythrocytes (GPE) was studied. The mannose-specific binding of E. coli to yeast cells and erythrocytes is mediated by type 1 pili and can be monitored by aggregometry. Maximal aggregation of C. albicans or GPE to E. coli is reached after 600 s. Then the FimH antagonist was added and disaggregation determined by light transmission over a period of 1400 s. A FimH-deleted mutant of E. coli, which does not induce any aggregation, was used in a control experiment. The activities of FimH antagonists are expressed as IC(50)s, the half maximal inhibitory concentration of the disaggregation potential. n-Heptyl alpha-D-mannopyranoside (1) was used as a reference compound and exhibits an IC(50) of 77.14 microM , whereas methyl alpha-D-mannopyranoside (2) does not lead to any disaggregation at concentrations up to 800 microM. o-Chloro-p-[N-(2-ethoxy-3,4-dioxocyclobut-1-enyl)amino]phenyl alpha-D-mannopyranoside (3) shows a 90-fold and 2-chloro-4-nitrophenyl alpha-D-mannopyranoside (4) a 6-fold increased affinity compared to 1. Finally, 4-nitrophenyl alpha-D-mannopyranoside (5) exhibits an activity similar to 1. As negative control, D-galactose (6) was used. The standardized aggregation assay generates concentration-dependent, reproducible data allowing the evaluation of FimH antagonists according to their potency to inhibit E. coli adherence and can therefore be employed to select candidates for experimental and clinical studies for treatment and prevention of urinary tract infections.