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.

Molecular basis of leukocyte rolling on PSGL-1. Predominant role of core-2 O-glycans and of tyrosine sulfate residue 51.

Interactions between the leukocyte adhesion receptor L-selectin and P-selectin glycoprotein ligand-1 play an important role in regulating the inflammatory response by mediating leukocyte tethering and rolling on adherent leukocytes. In this study, we have examined the effect of post-translational modifications of PSGL-1 including Tyr sulfation and presentation of sialylated and fucosylated O-glycans for L-selectin binding. The functional importance of these modifications was determined by analyzing soluble L-selectin binding and leukocyte rolling on CHO cells expressing various glycoforms of PSGL-1 or mutant PSGL-1 targeted at N-terminal Thr or Tyr residues. Simultaneous expression of core-2 beta1,6-N-acetylglucosaminyltransferase and fucosyltransferase VII was required for optimal L-selectin binding to PSGL-1. Substitution of Thr-57 by Ala but not of Thr-44, strongly decreased L-selectin binding and leukocyte rolling on PSGL-1. Substitution of Tyr by Phe revealed that PSGL-1 Tyr-51 plays a predominant role in mediating L-selectin binding and leukocyte rolling whereas Tyr-48 has a minor role, an observation that contrasts with the pattern seen for the interactions between PSGL-1 and P-selectin where Tyr-48 plays a key role. Molecular modeling analysis of L-selectin and P-selectin interactions with PSGL-1 further supported these observations. Additional experiments showed that core-2 O-glycans attached to Thr-57 were also of critical importance in regulating the velocity and stability of leukocyte rolling. These observations pinpoint the structural characteristics of PSGL-1 that are required for optimal interactions with L-selectin and may be responsible for the specific kinetic and mechanical bond properties of the L-selectin-PSGL-1 adhesion receptor-counterreceptor pair.

Genetic basis and variable phenotypic expression of Kallmann syndrome: towards a unifying theory.

Idiopathic hypogonadotropic hypogonadism (IHH) is defined by absent or incomplete puberty and characterised biochemically by low levels of sex steroids, with low or inappropriately normal gonadotropin hormones. IHH is frequently accompanied by non-reproductive abnormalities, most commonly anosmia, which is present in 50-60% of cases and defines Kallmann syndrome. The understanding of IHH has undergone rapid evolution, both in respect of genetics and breadth of phenotype. Once considered in monogenic Mendelian terms, it is now more coherently understood as a complex genetic condition. Oligogenic and complex genetic-environmental interactions have now been identified, with physiological and environmental factors interacting in genetically susceptible individuals to alter the clinical course and phenotype. These potentially link IHH to ancient evolutionary pressures on the ancestral human genome.

Functional dissection of the ash2 and ash1 transcriptomes provides insights into the transcriptional basis of wing phenotypes and reveals conserved protein interactions

Background: The trithorax group (trxG) genes absent, small or homeotic discs 1 (ash1) and 2 (ash2) were isolated in a screen for mutants with abnormal imaginal discs. Mutations in either gene cause homeotic transformations but Hox genes are not their only targets. Although analysis of double mutants revealed that ash2 and ash1 mutations enhance each other's phenotypes, suggesting they are functionally related, it was shown that these proteins are subunits of distinct complexes.Results: The analysis of wing imaginal disc transcriptomes from ash2 and ash1 mutants showed that they are highly similar. Functional annotation of regulated genes using Gene Ontology allowed identification of severely affected groups of genes that could be correlated to the wing phenotypes observed. Comparison of the differentially expressed genes with those from other genome-wide analyses revealed similarities between ASH2 and Sin3A, suggesting a putative functional relationship. Coimmunoprecipitation studies and immunolocalization on polytene chromosomes demonstrated that ASH2 and Sin3A interact with HCF (host-cell factor). The results of nucleosome western blots and clonal analysis indicated that ASH2 is necessary for trimethylation of the Lys4 on histone 3 (H3K4).Conclusion: The similarity between the transcriptomes of ash2 and ash1 mutants supports a model in which the two genes act together to maintain stable states of transcription. Like in humans, both ASH2 and Sin3A bind HCF. Finally, the reduction of H3K4 trimethylation in ash2 mutants is the first evidence in Drosophila regarding the molecular function of this trxG gene.

Determinacy and Weakly Ramsey sets in Banach spaces

We give a sufficient condition for a set of block subspaces in an infinite-dimensional Banach space to be weakly Ramsey. Using this condition we prove that in the Levy-collapse of a Mahlo cardinal, every projective set is weakly Ramsey. This, together with a construction of W. H. Woodin, is used to show that the Axiom of Projective Determinacy implies that every projective set is weakly Ramsey. In the case of co we prove similar results for a stronger Ramsey property. And for hereditarily indecomposable spaces we show that the Axiom of Determinacy plus the Axiom of Dependent Choices imply that every set is weakly Ramsey. These results are the generalizations to the class of projective sets of some theorems from W. T. Gowers, and our paper "Weakly Ramsey sets in Banach spaces."

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 coincidence between the Shimomura's bargaining sets and the core

[cat] En l'article es dona una condició necessària per a que els conjunts de negociació definits per Shimomura (1997) i el nucli d'un joc cooperatiu amb utilitat transferible coincideixin. A tal efecte, s'introdueix el concepte de vectors de màxim pagament. La condició necessària consiteix a verificar que aquests vectors pertanyen al nucli del joc.

Comparative performance of supertree algorithms in large data sets using the soapberry family (Sapindaceae) as a case study.

For the last 2 decades, supertree reconstruction has been an active field of research and has seen the development of a large number of major algorithms. Because of the growing popularity of the supertree methods, it has become necessary to evaluate the performance of these algorithms to determine which are the best options (especially with regard to the supermatrix approach that is widely used). In this study, seven of the most commonly used supertree methods are investigated by using a large empirical data set (in terms of number of taxa and molecular markers) from the worldwide flowering plant family Sapindaceae. Supertree methods were evaluated using several criteria: similarity of the supertrees with the input trees, similarity between the supertrees and the total evidence tree, level of resolution of the supertree and computational time required by the algorithm. Additional analyses were also conducted on a reduced data set to test if the performance levels were affected by the heuristic searches rather than the algorithms themselves. Based on our results, two main groups of supertree methods were identified: on one hand, the matrix representation with parsimony (MRP), MinFlip, and MinCut methods performed well according to our criteria, whereas the average consensus, split fit, and most similar supertree methods showed a poorer performance or at least did not behave the same way as the total evidence tree. Results for the super distance matrix, that is, the most recent approach tested here, were promising with at least one derived method performing as well as MRP, MinFlip, and MinCut. The output of each method was only slightly improved when applied to the reduced data set, suggesting a correct behavior of the heuristic searches and a relatively low sensitivity of the algorithms to data set sizes and missing data. Results also showed that the MRP analyses could reach a high level of quality even when using a simple heuristic search strategy, with the exception of MRP with Purvis coding scheme and reversible parsimony. The future of supertrees lies in the implementation of a standardized heuristic search for all methods and the increase in computing power to handle large data sets. The latter would prove to be particularly useful for promising approaches such as the maximum quartet fit method that yet requires substantial computing power.

A common biological basis of obesity and nicotine addiction.

Smoking influences body weight such that smokers weigh less than non-smokers and smoking cessation often leads to weight increase. The relationship between body weight and smoking is partly explained by the effect of nicotine on appetite and metabolism. However, the brain reward system is involved in the control of the intake of both food and tobacco. We evaluated the effect of single-nucleotide polymorphisms (SNPs) affecting body mass index (BMI) on smoking behavior, and tested the 32 SNPs identified in a meta-analysis for association with two smoking phenotypes, smoking initiation (SI) and the number of cigarettes smoked per day (CPD) in an Icelandic sample (N=34,216 smokers). Combined according to their effect on BMI, the SNPs correlate with both SI (r=0.019, P=0.00054) and CPD (r=0.032, P=8.0 × 10(-7)). These findings replicate in a second large data set (N=127,274, thereof 76,242 smokers) for both SI (P=1.2 × 10(-5)) and CPD (P=9.3 × 10(-5)). Notably, the variant most strongly associated with BMI (rs1558902-A in FTO) did not associate with smoking behavior. The association with smoking behavior is not due to the effect of the SNPs on BMI. Our results strongly point to a common biological basis of the regulation of our appetite for tobacco and food, and thus the vulnerability to nicotine addiction and obesity.

Microbial influences on epithelial integrity and immune function as a basis for inflammatory diseases.

Certain autoimmune diseases as well as asthma have increased in recent decades, particularly in developed countries. The hygiene hypothesis has been the prevailing model to account for this increase; however, epidemiology studies also support the contribution of diet and obesity to inflammatory diseases. Diet affects the composition of the gut microbiota, and recent studies have identified various molecules and mechanisms that connect diet, the gut microbiota, and immune responses. Herein, we discuss the effects of microbial metabolites, such as short chain fatty acids, on epithelial integrity as well as immune cell function. We propose that dysbiosis contributes to compromised epithelial integrity and disrupted immune tolerance. In addition, dietary molecules affect the function of immune cells directly, particularly through lipid G-protein coupled receptors such as GPR43.

Estimation of soil nitrate in the spring as a basis for adjustment of nitrogen fertiliser rates

Selostus: Maassa olevan nitraattitypen arviointi simulointimallin avulla

Molecular basis of messenger RNA recognition by the specific bacterial repressing clamp RsmA/CsrA.

Proteins of the RsmA/CsrA family are global translational regulators in many bacterial species. We have determined the solution structure of a complex formed between the RsmE protein, a member of this family from Pseudomonas fluorescens, and a target RNA encompassing the ribosome-binding site of the hcnA gene. The RsmE homodimer with its two RNA-binding sites makes optimal contact with an 5'-A/UCANGGANGU/A-3' sequence in the mRNA. When tightly gripped by RsmE, the ANGGAN core folds into a loop, favoring the formation of a 3-base-pair stem by flanking nucleotides. We validated these findings by in vivo and in vitro mutational analyses. The structure of the complex explains well how, by sequestering the Shine-Dalgarno sequence, the RsmA/CsrA proteins repress translation.