A new look at the Heston characteristic function

A new expression for the characteristic function of log-spot in Heston model is presented. This expression more clearly exhibits its properties as an analytic characteristic function and allows us to compute the exact domain of the moment generating function. This result is then applied to the volatility smile at extreme strikes and to the control of the moments of spot. We also give a factorization of the moment generating function as product of Bessel type factors, and an approximating sequence to the law of log-spot is deduced.

Efficient estimation using the characteristic function : theory and applications with high frequency data

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The propensity to disrupt and the disruption nucleolus of a characteristic function game

Gately [1974] recently introduced the concept of an individual player's “propensity to disrupt” a payoff vector in a three-person characteristic function game. As a generalisation of this concept we propose the “disruption nucleolus” of ann-person game. The properties and computational possibilities of this concept are analogous to those of the nucleolus itself. Two numerical examples are given.

Commuting Nonselfadjoint Operators and their Characteristic Operator-Functions

* Partially supported by Grant MM-428/94 of MESC.

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.

Prevalence and clinical significance of small joint synovitis detected by ultrasonography in axial SpA

Objectives:¦The aim of this study was to estimate the prevalence of subclinical small joint synovitis detected by ultrasonography in patients with axial SpA, and to evaluate their relevance in terms of function or and disease activity.¦Methods:¦Forty axial SpA patients, 40 RA and 20 healthy subjects were evaluated by ultrasonography, using a reproducible semi-quantitative score by B-mode and Doppler, for synovitis, while disease activity and function were assessed using validated instruments (DAS28, BASDAI, BASFI, m-SACRAH and HAQ).¦Results:¦Median B-mode score were respectively 8.2 for axial SpA, 11.5 for RA and 6.0 for healthy subjects, corresponding to a prevalence of clinical significant synovitis of respectively 37.5%, 60% and 11% for a level of significance at > 8 chosen to¦classify as active > 75% of RA patient with DAS28 >2.6 and < 10% of controls. Addtionally, Doppler was positive in 8% of SpA, 30 % of RA and none of the healthy subjects. Echographic synovitis correlated with disease activity (DAS28) and function¦(HAQ, mSACRAH) in RA patients, but no correlation were found for SpA patients with disease activity (BASDAI) or function (BASFI, HAQ, mSACRAH). Cases of synovitis using classification by Doppler positivity were insufficient to allow any¦statistical analysis.¦Conclusions:¦B-mode ultrasonographic evaluation can demonstrate subclinical synovitis in almost 40% of SpA patients, but they do not appear to correlate with disease activity or function on the contrary to what is observed in RA patients, representing potentially different processes

Double generalized linear model for tissue culture proportion data: a Bayesian perspective

Joint generalized linear models and double generalized linear models (DGLMs) were designed to model outcomes for which the variability can be explained using factors and/or covariates. When such factors operate, the usual normal regression models, which inherently exhibit constant variance, will under-represent variation in the data and hence may lead to erroneous inferences. For count and proportion data, such noise factors can generate a so-called overdispersion effect, and the use of binomial and Poisson models underestimates the variability and, consequently, incorrectly indicate significant effects. In this manuscript, we propose a DGLM from a Bayesian perspective, focusing on the case of proportion data, where the overdispersion can be modeled using a random effect that depends on some noise factors. The posterior joint density function was sampled using Monte Carlo Markov Chain algorithms, allowing inferences over the model parameters. An application to a data set on apple tissue culture is presented, for which it is shown that the Bayesian approach is quite feasible, even when limited prior information is available, thereby generating valuable insight for the researcher about its experimental results.

Group theory and quasiprobability integrals of Wigner functions

The integral of the Wigner function of a quantum-mechanical system over a region or its boundary in the classical phase plane, is called a quasiprobability integral. Unlike a true probability integral, its value may lie outside the interval [0, 1]. It is characterized by a corresponding selfadjoint operator, to be called a region or contour operator as appropriate, which is determined by the characteristic function of that region or contour. The spectral problem is studied for commuting families of region and contour operators associated with concentric discs and circles of given radius a. Their respective eigenvalues are determined as functions of a, in terms of the Gauss-Laguerre polynomials. These polynomials provide a basis of vectors in a Hilbert space carrying the positive discrete series representation of the algebra su(1, 1) approximate to so(2, 1). The explicit relation between the spectra of operators associated with discs and circles with proportional radii, is given in terms of the discrete variable Meixner polynomials.

Efectividade de um programa de exercício aquático na osteoartrose do joelho

RESUMO: A osteoartrose do joelho é uma condição clínica cuja prevalência tem aumentado nos últimos anos na população idosa. Trata-se de uma condição que pode ser bastante incapacitante para o idoso, gerando um forte impacto social e económico. O exercício aquático tem sido identificado como um factor de promoção da melhoria do quadro clínico nesta população, mas a sua efectividade não está, ainda, determinada. Objectivo: investigar a efectividade, a curto e médio prazo, de um programa de exercício aquático, realizado em grupo, com a duração de 8 semanas, na amplitude articular, dor e rigidez do joelho, e na função física e qualidade de vida, em idosos com osteoartrose do joelho. Metodologia: Recorreu-se a um estudo quase-experimental, double-blind, controlado, sem aleatorização, cuja amostra, constituída por 43 sujeitos, foi selecionada por conveniência. Os sujeitos do grupo experimental (n=22) foram submetidos ao programa de exercício aquático e os do grupo de controlo (n=21) foram submetidos ao programa de exercício no solo. Ambos os programas foram definidos de acordo com as recomendações internacionais para a prática de exercício físico em idosos com osteoartrose (Arthritis Foundation, 2009a, 2009b). Todo o grupo foi avaliado no início do programa, no final do mesmo (8 semanas) e após 6 semanas de follow-up, nos seguintes indicadores: amplitude articular do joelho (através do goniómetro), dor, rigidez, função e qualidade de vida (através do KOOS). Resultados: A amostra deste estudo foi constituída por sujeitos maioritariamente do género feminino (76,7%), com uma média de 72,7 anos (DP=5,49). O programa de exercício aquático implementado demonstrou um aumento da amplitude articular passiva de flexão (p<0,0001) e extensão (p=0,016) do joelho, uma diminuição da dor e da rigidez articular (p<0,0001), um aumento da função nas AVD’s (p<0,0001) e no desporto/lazer (p=0,031), e ainda, um aumento da qualidade de vida (p<0,0001). Contudo, apenas os níveis de amplitude articular passiva de extensão do joelho (p=0,083) e de função no desporto/lazer (p=0,244) se mantiveram ao longo das seis semanas de follow-up. Conclusões: Apesar de algumas limitações, considera-se que este estudo é de grande importância para a comunidade científica e para os fisioterapeutas preocupados com a crescente prevalência da osteoartrose e dos custos associados. O exercício aquático parece ser uma estratégia importante na melhoria do estado de saúde dos idosos com osteoartrose do joelho.----------------- ABSTRACT: The osteoarthritis of the knee is a clinical condition that has been increasing among the elderly population over the past few years. It’s a condition that can be fairly disabling to the elderly individual, and which generates a strong social and economic impact. Aquatic exercise has been named as a promotional factor in the improvement of the clinical picture in this population, but its effectiveness is yet to be determined. Objective: To investigate the effectiveness, in a short and medium term, of an aquatic exercise program undertaken by a group over eight weeks, in the joint amplitude, pain and stiffness of the knee, and in the physical function and quality of life in elderly people who suffer from knee osteoarthritis. Methodology: was used a double-blind, quasi-experimental study with no randomization and its 43 subjects were selected as a matter of convenience. The subjects of the experimental group (n=22) were subjected to an aquatic exercise program and those of the control group (n=21) were subjected to a land-based exercise program. Both programs have followed international recommendations on the practice of physical exercise in elderly people who suffer from osteoarthritis (Arthritis Foundation, 2009a, 2009b). The entire group was evaluated in the beginning and at the end of the program (8 weeks later), and after a 6 week follow-up, in these parameters: knee range of motion (through a goniometer), pain, stiffness, function and quality of life (through KOOS). Results: This sample was predominantly female (76,7%) with a mean age of 72,7 years (SD=5,49). Aquatic exercise resulted in increase of passive joint flexion (p<0,0001) and knee extension (p=0,016), in the decline of pain and stiffness (p<0,0001), in the increase of function in the ADLs (p<0,0001). However, only the knee extension amplitude (p=0,083) and the function in sports/leisure (p=0,244) were kept through the six-week follow-up. Conclusions: Despite some limitations, this study is of great importance to the community and to the physiotherapists concerned with the growing prevalence of osteoarthritis and the associated costs. Aquatic exercise appears to be an important strategy in the improvement of the health condition of patients who suffer from knee osteoarthritis.

Three essays on the term structure of interest rates

A PhD Dissertation, presented as part of the requirements for the Degree of Doctor of Philosophy from the NOVA - School of Business and Economics

A comment on the Nash program and the theory of implementation

The mechanisms in the Nash program for cooperative games are madecompatible with the framework of the theory of implementation. This is donethrough a reinterpretation of the characteristic function that avoids feasibilityproblems, thereby allowing an analysis that focuses exclusively on the payoff space. In this framework, we show that the core is the only majorcooperative solution that is Maskin monotonic. Thus, implementation of mostcooperative solutions must rely on refinements of the Nash equilibrium concept(like most papers in the Nash program do). Finally, the mechanisms in theNash program are adapted into the model.

Integrated random processes exhibiting long tails, finite moments, and power-law spectra

A dynamical model based on a continuous addition of colored shot noises is presented. The resulting process is colored and non-Gaussian. A general expression for the characteristic function of the process is obtained, which, after a scaling assumption, takes on a form that is the basis of the results derived in the rest of the paper. One of these is an expansion for the cumulants, which are all finite, subject to mild conditions on the functions defining the process. This is in contrast with the Lévy distribution¿which can be obtained from our model in certain limits¿which has no finite moments. The evaluation of the spectral density and the form of the probability density function in the tails of the distribution shows that the model exhibits a power-law spectrum and long tails in a natural way. A careful analysis of the characteristic function shows that it may be separated into a part representing a Lévy process together with another part representing the deviation of our model from the Lévy process. This

Three essays in incomplete contracts

General Introduction These three chapters, while fairly independent from each other, study economic situations in incomplete contract settings. They are the product of both the academic freedom my advisors granted me, and in this sense reflect my personal interests, and of their interested feedback. The content of each chapter can be summarized as follows: Chapter 1: Inefficient durable-goods monopolies In this chapter we study the efficiency of an infinite-horizon durable-goods monopoly model with a fmite number of buyers. We find that, while all pure-strategy Markov Perfect Equilibria (MPE) are efficient, there also exist previously unstudied inefficient MPE where high valuation buyers randomize their purchase decision while trying to benefit from low prices which are offered once a critical mass has purchased. Real time delay, an unusual monopoly distortion, is the result of this attrition behavior. We conclude that neither technological constraints nor concern for reputation are necessary to explain inefficiency in monopolized durable-goods markets. Chapter 2: Downstream mergers and producer's capacity choice: why bake a larger pie when getting a smaller slice? In this chapter we study the effect of downstream horizontal mergers on the upstream producer's capacity choice. Contrary to conventional wisdom, we find anon-monotonic relationship: horizontal mergers induce a higher upstream capacity if the cost of capacity is low, and a lower upstream capacity if this cost is high. We explain this result by decomposing the total effect into two competing effects: a change in hold-up and a change in bargaining erosion. Chapter 3: Contract bargaining with multiple agents In this chapter we study a bargaining game between a principal and N agents when the utility of each agent depends on all agents' trades with the principal. We show, using the Potential, that equilibria payoffs coincide with the Shapley value of the underlying coalitional game with an appropriately defined characteristic function, which under common assumptions coincides with the principal's equilibrium profit in the offer game. Since the problem accounts for differences in information and agents' conjectures, the outcome can be either efficient (e.g. public contracting) or inefficient (e.g. passive beliefs).

An Abstract Algebraic Theory of L-Fuzzy Relations for Relational Databases

Classical relational databases lack proper ways to manage certain real-world situations including imprecise or uncertain data. Fuzzy databases overcome this limitation by allowing each entry in the table to be a fuzzy set where each element of the corresponding domain is assigned a membership degree from the real interval [0…1]. But this fuzzy mechanism becomes inappropriate in modelling scenarios where data might be incomparable. Therefore, we become interested in further generalization of fuzzy database into L-fuzzy database. In such a database, the characteristic function for a fuzzy set maps to an arbitrary complete Brouwerian lattice L. From the query language perspectives, the language of fuzzy database, FSQL extends the regular Structured Query Language (SQL) by adding fuzzy specific constructions. In addition to that, L-fuzzy query language LFSQL introduces appropriate linguistic operations to define and manipulate inexact data in an L-fuzzy database. This research mainly focuses on defining the semantics of LFSQL. However, it requires an abstract algebraic theory which can be used to prove all the properties of, and operations on, L-fuzzy relations. In our study, we show that the theory of arrow categories forms a suitable framework for that. Therefore, we define the semantics of LFSQL in the abstract notion of an arrow category. In addition, we implement the operations of L-fuzzy relations in Haskell and develop a parser that translates algebraic expressions into our implementation.

Cooperative of Noncooperative Behavior?

In an abstract two-agent model, we show that every deterministic joint choice function compatible with the hypothesis that agents act noncooperatively is also compatible with the hypothesis that they act cooperatively. the converse is false.