Dissertations / Theses on the topic 'Lely method'

We present the detailed study of the spin kinetics of the nitrogen (N) donor electrons in 6H SiC wafers grown by the Lely method and by the sublimation “sandwich method” (SSM) with a donor concentration of about 10 17cm-3 at T=10–40K. The donor electrons of the N donors substituting quasi-cubic “k1” and “k2” sites (Nk1,k2) in both types of the samples revealed the similar temperature dependence of the spin-lattice relaxation rate (T1 -1), which was described by the direct one-phonon and two-phonon processes induced by the acoustic phonons proportional to T and to T9, respectively. The character of the temperature dependence of the T1 -1 for the donor electrons of N substituting hexagonal (“h”) site (Nh) in both types of 6H SiC samples indicates that the donor electrons relax through the fast-relaxing centers by means of the cross-relaxation process. The observed enhancement of the phase memory relaxation rate (Tm -1) with the temperature increase for the Nh donors in both types of the samples, as well as for the Nk1,k2 donors in Lely grown 6H SiC, was explained by the growth of the free electron concentration with the temperature increase and their exchange scattering at the N donor centers. The observed significant shortening of the phase memory relaxation time Tm for the Nk1,k2 donors in the SSM grown sample with the temperature lowering is caused by hopping motion of the electrons between the occupied and unoccupied states of the N donors at Nh and Nk1,k2 sites. The impact of the N donor pairs, triads, distant donor pairs formed in n-type 6H SiC wafers on the spin relaxation times was discussed.

Spectral methods have been actively developed in the last decades. The main advantage of these methods is to yield exponential order of accuracy when the function is smooth. However, for discontinuous functions, their accuracy deteriorates due to the Gibbs phenomenon. When functions are contaminated with the Gibbs phenomenon, proper workarounds can be applied to recover their accuracy. In this dissertation, we review the spectral methods and their convergence remedies such as grid stretching, discontinuity inclusion and domain decomposition methods in pricing options. The basic functions of L´evy processes models are also reviewed. The main purpose of this dissertation is to show that high order of accuracy can be recovered from spectral approximations. We explored and designed numerical methods for solving PDEs and PIDEs that arise in finance. It is known that most standard numerical methods for solving financial PDEs and PIDEs are reduced to low order accurate results due to the discontinuity at strike prices in the initial condition. Firstly the Black Scholes (BS) PDE was solved numerically. The computation of the PDE is done by using barycentric spectral methods. Three different payoffs call options are used as initial and boundaries conditions. It appears that the grid stretching, the discontinuity inclusion and the domain decomposition methods provide efficient ways to remove Gibbs phenomenon. On the other hand, these methods restore the high accuracy of spectral methods in pricing financial options. The spectral domain decomposition method appears to be the most accurate workaround when we solve a BS PDE in this dissertation. Secondly, a financial PIDE was discretized and solved by using a barycen tric spectral domain decomposition method algorithm. The method is applied to two different options pricing problems under a class of infinite activity L´evy models. The use of barycentric spectral domain decomposition methods allows the computation of ODEs obtained from the discretization of the PIDE. The ODEs are solved by exponential time integration scheme. Several numerical tests for the pricing of European and butterfly options are given to illustrate the efficiency and accuracy of this algorithm. We also show that the option Greeks such as the Delta and Gamma sensitivity measures are computed with no spurious oscillation. The methods produce accurate results.
Dissertation (MSc)--University of Pretoria, 2017.
RidgeCape Capital company
Mathematics and Applied Mathematics
MSc
Unrestricted

Thesis(MSc)--Stellenbosch University, 2012.
ENGLISH ABSTRACT: The pricing of plain vanilla options, including early exercise options, such as Bermudan and American options, forms the basis for the calibration of financial models. As such, it is important to be able to price these options quickly and accurately. Empirical studies suggest that asset dynamics have jump components which can be modelled by exponential Lévy processes. As such models often have characteristic functions available in closed form, it is possible to use Fourier transform methods, and particularly, the Fast Fourier Transform, to price such options efficiently. In this dissertation we investigate and implement four such methods, dubbed the Carr- Madan method, the convolution method, the COS method and the Fourier spacetime stepping method. We begin by pricing European options using these Fourier methods in the Black-Scholes, Variance Gamma and Normal Inverse Gaussian models. Thereafter, we investigate the pricing of Bermudan and American options in the Black-Scholes and Variance Gamma models. Throughout, we compare the four Fourier pricing methods for accuracy and computational efficiency.
AFRIKAANSE OPSOMMING: Die prysbepaling van gewone vanilla opsies, insluitende opsies wat vroeg uitgeoefen kan word, soos Bermuda-en Amerikaanse opsies, is grondliggend vir die kalibrering van finansiële modelle. Dit is daarom belangrik dat die pryse van sulke opsies vinnig en akkuraat bepaal kan word. Empiriese studies toon aan dat batebewegings sprongkomponente besit, wat gemodelleer kan word met behulp van exponensiëele Lévyprosesse. Aangesien hierdie modelle dikwels karakteristieke funksies het wat beskikbaar is in geslote vorm, is dit moontlik om Fourier-transform metodes, en in besonders die vinnige Fourier-transform, te gebruik om opsiepryse doeltreffend te bepaal. In hierdie proefskrif ondersoek en implementeer ons vier sulke metodes, genaamd die Carr-Madan metode, die konvolusiemetode, die COS-metode en die Fourier ruimte-tydstap metode. Ons begin deur die pryse van Europese opsies in die Black-Scholes, Gammavariansie (Engels: Variance gamma) en Normaal Invers Gauss (Engels: Normal Inverse Gaussian)-modelle te bepaal met behulp van die vier Fourier-metodes. Daarna ondersoek ons die prysbepaling van Bermuda-en Amerikaanse opsies in die Black-Scholes en Gammavariansiemodelle. Deurlopend vergelyk ons die vier Fourier-metodes vir akkuraatheid en berekeningsdoeltreffendheid.

In this study, general geometric Levy market models are considered. Since these models are, in general, incomplete, that is, all contingent claims cannot be replicated by a self-financing portfolio consisting of investments in a risk-free bond and in the stock, it is suggested that the market should be enlarged by artificial assets based on the power-jump processes of the underlying Levy process. Then it is shown that the enlarged market is complete and the explicit hedging portfolios for claims whose payoff function depends on the prices of the stock and the artificial assets at maturity are derived. Furthermore, the portfolio optimization problem is considered in the enlarged market. The problem consists of choosing an optimal portfolio in such a way that the largest expected utility of the terminal wealth is obtained. It is shown that for particular choices of the equivalent martingale measure in the market, the optimal portfolio only consists of bonds and stocks. This corresponds to completing the market with additional assets in such a way that they are superfluous in the sense that the terminal expected utility is not improved by including these assets in the portfolio.

Thesis (MSc)--Stellenbosch University, 2013.
ENGLISH ABSTRACT: We study Monte Carlo methods for pricing American options where the stock price dynamics follow exponential pure jump L évy models. Only stock price dynamics for a single underlying are considered. The thesis begins with a general introduction to American Monte Carlo methods. We then consider two classes of these methods. The fi rst class involves regression - we briefly consider the regression method of Tsitsiklis and Van Roy [2001] and analyse in detail the least squares Monte Carlo method of Longsta and Schwartz [2001]. The variance reduction techniques of Rasmussen [2005] applicable to the least squares Monte Carlo method, are also considered. The stochastic mesh method of Broadie and Glasserman [2004] falls into the second class we study. Furthermore, we consider the dual method, independently studied by Andersen and Broadie [2004], Rogers [2002] and Haugh and Kogan [March 2004] which generates a high bias estimate from a stopping rule. The rules we consider are estimates of the boundary between the continuation and exercise regions of the option. We analyse in detail how to obtain such an estimate in the least squares Monte Carlo and stochastic mesh methods. These models are implemented using both a pseudo-random number generator, and the preferred choice of a quasi-random number generator with bridge sampling. As a base case, these methods are implemented where the stock price process follows geometric Brownian motion. However the focus of the thesis is to implement the Monte Carlo methods for two pure jump L évy models, namely the variance gamma and the normal inverse Gaussian models. We first provide a broad discussion on some of the properties of L évy processes, followed by a study of the variance gamma model of Madan et al. [1998] and the normal inverse Gaussian model of Barndor -Nielsen [1995]. We also provide an implementation of a variation of the calibration procedure of Cont and Tankov [2004b] for these models. We conclude with an analysis of results obtained from pricing American options using these models.
AFRIKAANSE OPSOMMING: Ons bestudeer Monte Carlo metodes wat Amerikaanse opsies, waar die aandeleprys dinamika die patroon van die eksponensiële suiwer sprong L évy modelle volg, prys. Ons neem slegs aandeleprys dinamika vir 'n enkele aandeel in ag. Die tesis begin met 'n algemene inleiding tot Amerikaanse Monte Carlo metodes. Daarna bestudeer ons twee klasse metodes. Die eerste behels regressie - ons bestudeer die regressiemetode van Tsitsiklis and Van Roy [2001] vlugtig en analiseer die least squares Monte Carlo metode van Longsta and Schwartz [2001] in detail. Ons gee ook aandag aan die variansie reduksie tegnieke van Rasmussen [2005] wat van toepassing is op die least squares Monte Carlo metodes. Die stochastic mesh metode van Broadie and Glasserman [2004] val in die tweede klas wat ons onder oë neem. Ons sal ook aandag gee aan die dual metode, wat 'n hoë bias skatting van 'n stop reël skep, en afsonderlik deur Andersen and Broadie [2004], Rogers [2002] and Haugh and Kogan [March 2004] bestudeer is. Die reëls wat ons bestudeer is skattings van die grense tussen die voortsettings- en oefenareas van die opsie. Ons analiseer in detail hoe om so 'n benadering in die least squares Monte Carlo en stochastic mesh metodes te verkry. Hierdie modelle word geï mplementeer deur beide die pseudo kansgetalgenerator en die verkose beste quasi kansgetalgenerator met brug steekproefneming te gebruik. As 'n basisgeval word hierdie metodes geï mplimenteer wanneer die aandeleprysproses 'n geometriese Browniese beweging volg. Die fokus van die tesis is om die Monte Carlo metodes vir twee suiwer sprong L évy modelle, naamlik die variance gamma en die normal inverse Gaussian modelle, te implimenteer. Eers bespreek ons in breë trekke sommige van die eienskappe van L évy prossesse en vervolgens bestudeer ons die variance gamma model soos in Madan et al. [1998] en die normal inverse Gaussian model soos in Barndor -Nielsen [1995]. Ons gee ook 'n implimentering van 'n variasie van die kalibreringsprosedure deur Cont and Tankov [2004b] vir hierdie modelle. Ons sluit af met die resultate wat verkry is, deur Amerikaanse opsies met behulp van hierdie modelle te prys.

Thesis (MSc)--Stellenbosch University, 2011.
ENGLISH ABSTRACT: Barrier options are options whose payoff depends on whether or not the underlying asset price hits a certain level - the barrier - during the life of the option. Closed-form solutions for the prices of these path-dependent options are available in the Black-Scholes framework. It is well{known, however, that the Black-Scholes model does not price even the so-called vanilla options correctly. There are a number of popular asset price models based on exponential Lévy dynamics which are all able to capture the volatility smile, i.e. reproduce market-observed prices of vanilla options. This thesis investigates the potential model risk associated with the pricing of barrier options in several exponential Lévy models. First, the Variance Gamma, Normal Inverse Gaussian and CGMY models are calibrated to market-observed vanilla option prices. Barrier option prices are then evaluated in these models using Monte Carlo methods. The prices obtained are then compared to each other, as well as the Black-Scholes prices. It is observed that the different exponential Lévy models yield barrier option prices which are quite close to each other, though quite different from the Black-Scholes prices. This suggests that the associated model risk is low.
AFRIKAANSE OPSOMMING: Versperring opsies is opsies met 'n afbetaling wat afhanklik is daarvan of die onderliggende bateprys 'n bepaalde vlak - die versperring - bereik gedurende die lewe van die opsie, of nie. Formules vir die pryse van sulke opsies is beskikbaar binne die Black-Scholes raamwerk. Dit is egter welbekend dat die Black-Scholes model nie in staat is om selfs die sogenaamde vanilla opsies se pryse korrek te bepaal nie. Daar bestaan 'n aantal populêre bateprysmodelle gebaseer op eksponensiële Lévy-dinamika, wat almal in staat is om die mark-waarneembare vanilla opsie pryse te herproduseer. Hierdie tesis ondersoek die potensiële modelrisiko geassosieer met die prysbepaling van versperring opsies in verskeie eksponseniële Lévy-modelle. Eers word die Variance Gamma{, Normal Inverse Gaussian- en CGMY-modelle gekalibreer op mark-waarneembare vanilla opsiepryse. Die pryse van versperring opsies in hierdie modelle word dan bepaal deur middel van Monte Carlo metodes. Hierdie pryse word dan met mekaar vergelyk, asook met die Black-Scholespryse. Dit word waargeneem dat die versperring opsiepryse in die verskillende eksponensiële Lévymodelle redelik na aan mekaar is, maar redelik verskil van die Black-Scholespryse. Dit suggereer dat die geassosieerde modelrisiko laag is.

The thesis deals with the valuation of real estates in the Czech Republic using statistical methods. The work focuses on a complex task based on data from an advertising web portal. The aim of the thesis is to create a prototype of the statistical predication model of the residential properties valuation in Prague and to further evaluate the dissemination of its possibilities. The structure of the work is conceived according to the CRISP-DM methodology. On the pre-processed data are tested the methods regression trees and random forests, which are used to predict the price of real estate.

>Magister Scientiae - MSc
This dissertation studies the computation methods of pricing of Asian options. Asian options are options in which the underlying variable is the average price over a period of time. Because of this, Asian options have a lower volatility and this render them cheaper relative to their European counterparts. Asian options belong to the so-called path-dependent derivatives; they are among the most difficult to price and hedge both analytically and numerically. In practice, it is only discrete Asian options that are traded, however continuous Asian options are used for studying purposes. Several approaches have been proposed in the literature, including Monte Carlo simulations, tree-based methods, Taylor’s expansion, partial differential equations, and analytical ap- proximations among others. When using partial differential equations for pricing of continuous time Asian options, the high dimensionality is problematic. In this dissertation we focus on the discrete time methods. We start off by explaining the binomial tree method, and our last chapter presents the very exciting and relatively simple method of Tsao and Huang, using Taylor approximations. The main papers that are used in this dissertation are articles by Jan Vecer (2001); LCG Rogers (1995); Eric Benhamou (2001); Gianluca Fusai (2007); Kamizono, Kariya and Nakatsuma (2006) and Tsao and Huang (2007). The author has provided computations, including graphs and tables dispersed over the different chapters, to demonstrate the utility of the methods. We observe various parameters of influence such as correlation, volatility, strike, etc. A further contribution by the author of this dissertation is, in particular, in Chapter 5, in the presentation of the work of Tsao et al. Here we have provided slightly more detailed explanations and again some further computational tables.

Mathematical and statistical modeling have been at the forefront of many significant advances in many disciplines in both the academic and industry sectors. From behavioral sciences to hard core quantum mechanics in physics, mathematical modeling has made a compelling argument for its usefulness and its necessity in advancing the current state of knowledge in the 21rst century. In Finance and Insurance in particular, stochastic modeling has proven to be an effective approach in accomplishing a vast array of tasks: risk management, leveraging of investments, prediction, hedging, pricing, insurance, and so on. However, the magnitude of the damage incurred in recent market crisis of 1929 (the great depression), 1937 (recession triggered by lingering fears emanating from the great depression), 1990 (one year recession following a decade of steady expansion) and 2007 (the great recession triggered by the sub-prime mortgage crisis) has suggested that there are certain aspects of financial markets not accounted for in existing modeling. Explanations have abounded as to why the market underwent such deep crisis and how to account for regime change risk. One such explanation brought forth was the existence of regimes in the financial markets. The basic idea of market regimes underscored the principle that the market was intrinsically subjected to many different states and can switch from one state to another under unknown and uncertain internal and external perturbations. Implementation of such a theory has been done in the simplifying case of Markov regimes. The mathematical simplicity of the Markovian regime model allows for semi-closed or closed form solutions in most financial applications while it also allows for economically interpretable parameters. However, there is a hefty price to be paid for such practical conveniences as many assumptions made on the market behavior are quite unreasonable and restrictive. One assumes for instance that each market regime has a constant propensity of switching to any other state irrespective of the age of the current state. One also assumes that there are no intermediate states as regime changes occur in a discrete manner from one of the finite states to another. There is therefore no telling how meaningful or reliable interpretation of parameters in Markov regime models are. In this thesis, we introduced a sound theoretical and analytic framework for Levy driven linear stochastic models under a semi Markov market regime switching process and derived It\'o formula for a general linear semi Markov switching model generated by a class of Levy It'o processes (1). It'o formula results in two important byproducts, namely semi closed form formulas for the characteristic function of log prices and a linear combination of duration times (2). Unlike Markov markets, the introduction of semi Markov markets allows a time varying propensity of regime change through the conditional intensity matrix. This is more in line with the notion that the market's chances of recovery (respectively, of crisis) are affected by the recession's age (respectively, recovery's age). Such a change is consistent with the notion that for instance, the longer the market is mired into a recession, the more improbable a fast recovery as the the market is more likely to either worsens or undergo a slow recovery. Another interesting consequence of the time dependence of the conditional intensity matrix is the interpretation of semi Markov regimes as a pseudo-infinite market regimes models. Although semi Markov regime assume a finite number of states, we note that while in any give regime, the market does not stay the same but goes through an infinite number of changes through its propensity of switching to other regimes. Each of those separate intermediate states endows the market with a structure of pseudo-infinite regimes which is an answer to the long standing problem of modeling market regime with infinitely many regimes. We developed a version of Girsanov theorem specific to semi Markov regime switching stochastic models, and this is a crucial contribution in relating the risk neutral parameters to the historical parameters (3). Given that Levy driven markets and regime switching markets are incomplete, there are more than one risk neutral measures that one can use for pricing derivative contracts. Although much work has been done about optimal choice of the pricing measure, two of them jump out of the current literature: the minimal martingale measure and the minimum entropy martingale measure. We first presented a general version of Girsanov theorem explicitly accounting for semi Markov regime. Then we presented Siu and Yang pricing kernel. In addition, we developed the conditional and unconditional minimum entropy martingale measure which minimized the dissimilarity between the historical and risk neutral probability measures through a version of Kulbach Leibler distance (4). Estimation of a European option price in a semi Markov market has been attempted before in the restricted case of the Black Scholes model. The problems encountered then were twofold: First, the author employed a Markov chain Monte Carlo methods which relied much on the tractability of the likelihood function of the normal random sequences. This tractability is unavailable for most Levy processes, hence the necessity of alternative pricing methods is essential. Second, the accuracy of the parameter estimates required tens of thousands of simulations as it is often the case with Metropolis Hasting algorithms with considerable CPU time demand. Both above outlined issues are resolved by the development of a semi-closed form expression of the characteristic function of log asset prices, and it opened the door to a Fourier transform method which is derived on the heels of Carr and Madan algorithm and the Fourier time stepping algorithm (5). A round of simulations and calibrations is performed to better capture the performance of the semi Markov model as opposed to Markov regime models. We establish through simulations that semi Markov parameters and the backward recurrence time have a substantial effect on option prices ( 6). Differences between Markov and Semi Markov market calibrations are quantified and the CPU times are reported. More importantly, interpretation of risk neutral semi Markov parameters offer more insight into the dynamic of market regimes than Markov market regime models ( 7). This has been systematically exhibited in this work as calibration results obtained from a set of European vanilla call options led to estimates of the shape and scale parameters of the Weibull distribution considered, offering a deeper view of the current market state as they determine the in-regime dynamic crucial to determining where the market is headed. After introducing semi Markov models through linear Levy driven models, we consider semi Markov markets with nonlinear multidimensional coupled asset price processes (8). We establish that the tractability of linear semi Markov market models carries over to multidimensional nonlinear asset price models. Estimating equations and pricing formula are derived for historical parameters and risk neutral parameters respectively (9). The particular case of basket of commodities is explored and we provide calibration formula of the model parameters to observed historical commodity prices through the LLGMM method. We also study the case of Heston model in a semi Markov switching market where only one parameter is subjected to semi Markov regime changes. Heston model is one the most popular model in option pricing as it reproduces many more stylized facts than Black Scholes model while retaining tractability. However, in addition to having a faster deceasing smiles than observed, one of the most damning shortcomings of most diffusion models such as Heston model, is their inability to accurately reproduce short term options prices. An avenue for solving these issues consists in generalizing Heston to account for semi Markov market regimes. Such a solution is implemented and a semi analytic formula for options is obtained.

This thesis introduces a novel theoretical option pricing ensemble framework to improve the bias and variance of option pricing models, especially those based on Levy Processes. In particular, we present a completely new, yet very general theoretical framework to calibrate and combine several option pricing models using ensemble methods. This framework has four main steps: general option pricing tasks, ensemble generation, ensemble pruning and ensemble integration. The modularity allows for a exible implementation in terms of asset classes, base models, pricing techniques and ensemble architecture.

Diese Dissertation untersucht Aspekte des Zusammenspiels von ergodischem Langzeitver- halten und der Glättungseigenschaft dynamischer Systeme, die von stochastischen Differen- tialgleichungen (SDEs) mit Sprüngen erzeugt sind. Im Speziellen werden SDEs getrieben von Lévy-Prozessen und der Marcusschen kanonischen Gleichung untersucht. Ein vari- ationeller Ansatz für den Malliavin-Kalkül liefert eine partielle Integration, sodass eine Variation im Raum in eine Variation im Wahrscheinlichkeitsmaß überführt werden kann. Damit lässt sich die starke Feller-Eigenschaft und die Existenz glatter Dichten der zuge- hörigen Markov-Halbgruppe aus einer nichtstandard Elliptizitätsbedingung an eine Kom- bination aus Gaußscher und Sprung-Kovarianz ableiten. Resultate für Sprungdiffusionen auf Untermannigfaltigkeiten werden aus dem umgebenden Euklidischen Raum hergeleitet. Diese Resultate werden dann auf zufällige dynamische Systeme angewandt, die von lin- earen stochastischen Differentialgleichungen erzeugt sind. Ruelles Integrierbarkeitsbedin- gung entspricht einer Integrierbarkeitsbedingung an das Lévy-Maß und gewährleistet die Gültigkeit von Oseledets multiplikativem Ergodentheorem. Damit folgt die Existenz eines Lyapunov-Spektrums. Schließlich wird der top Lyapunov-Exponent über eine Formel der Art von Furstenberg–Khasminsikii als ein ergodisches Mittel der infinitesimalen Wachs- tumsrate über die Einheitssphäre dargestellt.
The present thesis investigates certain aspects of the interplay between the ergodic long time behavior and the smoothing property of dynamical systems generated by stochastic differential equations (SDEs) with jumps, in particular SDEs driven by Lévy processes and the Marcus’ canonical equation. A variational approach to the Malliavin calculus generates an integration-by-parts formula that allows to transfer spatial variation to variation in the probability measure. The strong Feller property of the associated Markov semigroup and the existence of smooth transition densities are deduced from a non-standard ellipticity condition on a combination of the Gaussian and a jump covariance. Similar results on submanifolds are inferred from the ambient Euclidean space. These results are then applied to random dynamical systems generated by linear stochas- tic differential equations. Ruelle’s integrability condition translates into an integrability condition for the Lévy measure and ensures the validity of the multiplicative ergodic theo- rem (MET) of Oseledets. Hence the exponential growth rate is governed by the Lyapunov spectrum. Finally the top Lyapunov exponent is represented by a formula of Furstenberg– Khasminskii–type as an ergodic average of the infinitesimal growth rate over the unit sphere.

Mestrado em Matemática Financeira
Prices fluctuations in markets, both liquid and illiquid, exhibit discontinuous behaviour. Levy processes are a natural generalization for stochastic processes with jumps, since they comprehend simultaneously a deterministic component as well as continuous and discontinuous stochastic com¬ponents. As it is possible to model asset prices as exponential of Levy processes, in this work we set the model using two pure jump processes: variance gamma and generalized hyperbolic. While using this class of processes, some important economic characteristics change in relation to the usual Black-Scholes model. The market is no longer complete for a more general Levy model, with several sources of randomness. We start by introducing some important results about Levy processes and follow with a brief exposition on possible equivalent martingale measures. After this introduction, we estimate the parameters of the distributions, by using market data and the Fourier transform to calculate vanilla option prices, and then minimizing the error be¬tween the market and the model prices. With the models calibrated to market data, we use Monte Carlo simulation to price an exotic option on the underlying, with double barriers. The results are compared with the Black-Scholes model and the market prices, requested over the counter to some of the main liquidity providers for that kind of structures.
A flutuação de preços nos mercados, tanto líquidos como ilíquidos, evidenciam um compor¬tamento descontínuo. Os processos de Levy sao uma generalizacao natural para os processos estocsticos com saltos, uma vez que consideram simultaneamente uma componente determinística, tal como uma componente estocastica contínua e descontínua. Como e possível modelizar os precos dos activos como exponenciais de processos de Levy, neste trabalho definimos um modelo usando dois processos de saltos puros: o processo variance gamma e o processo hiperbólico generalizado. Aquando do uso desta classe de processos, algumas características econíomicas importantes mudam, em relacao ao modelo usual, de Black-Scholes. O mercado deixa de ser completo com um processo de Levy mais geral, com varias fontes de incerteza. Começamos por introduzir alguns resultados importantes sobre processos de Levy e seguida¬mente apresentamos uma breve exposição sobre as possíveis medidas equivalentes de martingala. Após esta introduçao, e feita a estimação de parametros das distribuicães, usando dados de mer¬cado e a transformada de Fourier para calcular os preços das opcoes mais simples, minimizando no fim o erro entre os precos de mercado e os precos do modelo. Com os modelos calibrados com os dados de mercado, usamos simulaçao de Monte Carlo para fazer o aprecamento de uma opcão exítica sobre o activo subjacente, com barreiras duplas. Os resultados sao comparados com o modelo de Black-Scholes e precços de mercado, solicitados a alguns dos maiores provedores de liquidez a este tipo de estruturas, transaccionadas fora de bolsa.

In the first section of the article, the two types of international double taxation, as well as the main mechanisms for its elimination, are reviewed. Subsequently, is analyzed the indirect tax credit in Peruvian tax law. The main section is devoted to the indirect tax credit set forth in the tax treaties concluded by Peru, including its practical application and the relation between such treaties and domestic legislation.
En las primeras secciones del artículo se revisan los dos tipos de doble imposición internacional, así como los principales mecanismos para su eliminación. Más adelante se analiza el crédito tributario indirecto en la ley tributaria peruana. La sección principal está dedicada al crédito indirecto previsto en los convenios tributarios suscritos por el Perú, incluyendo su aplicación práctica y la relación entre dichos convenios y la legislación doméstica.

The new Public Procurement Law introduces the Dispute Boards as a new settlement ofdisputes and contestations during the contractual execution of the work phase. The present article works, in the first place, the framework of public procurement and the controversies that are originated in the matter. Then, it will expose the development of the Dispute Boards in other countried and their characteristics. Finally, it concludes identifying the type of Dispute Boards that is being adopted in Peruvian law, showing his vantages and disadvantages.
La nueva Ley de Contrataciones del Estado, Ley N° 30225, incorpora la Junta de Resolución de Disputas, como un nuevo mecanismo de resolución de conflictos durante la fase de ejecución contractual de obras.En el artículo se desarrolla, en primer lugar, el marco de las contrataciones del Estado y las controversias que se originan en el mismo. Posteriormente, se expone el desarrollo de los Dispute Boards internacionalmente y sus características, y se concluye identificando el tipo de Dispute Boards adoptado en la legislación peruana, exponiendo sus fortalezas y debilidades.

Etude d'un algorithme pour le traitement d'un signal. Cet algorithme est composé de différents programmes indépendants permettant le calcul des polynômes orthonormaux, le calcul récursif, le calcul de la transformée de Fourier, de densité spectrale, réponse impulsionnelle d'un filtre numérique. Application à la reconnaissance des formes et simulation du processus de Lévy

[EN] The aim of the present Thesis is to develop models for the study of very high-frequency phenomena associated with the coupling dynamics of a railway vehicle with the track. Through these models, this Thesis intends to address squeal noise as a particular case of rolling noise when the train negotiates a small radius curve. Wheel/rail interaction is the predominant source of noise emission in railway operations. Rolling contact couples the wheel and the rail through a very small area, characterised by strongly non-linear and non-steady state dynamics that differentiates rolling noise from any other noise problem. Wheel/rail contact problem is studied based on Kalker's variational theory and the local falling behaviour of the coefficient of friction is introduced by means of a regularisation of Coulomb's law. Its implementation shows that the influence of the falling friction on the creep curves can be assumed negligible, thus rolling contact is finally modelled using a constant coefficient of friction. Flexibility is introduced in railway substructures through the Finite Element (FE) method in order to cover the high-frequency range. This work adopts a rotatory wheelset model that takes computational advantage of its rotational symmetry. It also develops a cyclic flexible rail model that fixes the translational contact force in a spatial point of the mesh through a technique called Moving Element (ME) method. A modal approach is used to reduce significantly the number of degrees of freedom of the global problem and a diagonalisation technique permits to decouple the resulting modal equations of motion in order to increase the computational velocity of the time integrator. Simulations in curving conditions in the time domain are carried out for constant friction conditions in order to study if the proposed interaction model can reproduce squeal characteristics for different curve radii and coefficients of friction.
[ES] El objetivo de la presente Tesis es desarrollar modelos para el estudio de fenómenos de muy alta frecuencia asociados a la dinámica acoplada de un vehículo ferroviario con la vía. A través de estos modelos, esta Tesis pretende abordar el fenómeno de los chirridos como un caso particular de ruido de rodadura en condiciones de curva cerrada. La interacción rueda/carril es la fuente predominante de ruido en las operaciones ferroviarias. El contacto es el responsable del acoplamiento entre la rueda y el carril a través de un área muy pequeña caracterizada por una dinámica fuertemente no lineal y no estacionaria. El problema de contacto rueda/carril se estudia mediante la teoría variacional de Kalker y la caída local del coeficiente de fricción se introduce por medio de una regularización de la ley de Coulomb, que muestra que su influencia sobre las curvas de fluencia se puede despreciar. Como consecuencia, el coeficiente de fricción se considera constante. La flexibilidad se introduce en las subestructuras ferroviarias a través del método de los Elementos Finitos (EF) para cubrir el rango de las altas frecuencias. La Tesis adopta un modelo de eje montado rotatorio que toma ventaja computacional de su simetría rotacional. También desarrolla un modelo de carril flexible y cíclico que fija la fuerza de contacto en un punto espacial de la malla mediante el método de los Elementos Móviles (EM). Se utiliza un enfoque modal para reducir significativamente el número de grados de libertad del problema global; las ecuaciones de movimiento resultantes en coordenadas modales se desacoplan mendiante una técnica de diagonalización para aumentar la velocidad computacional del integrador temporal. Las simulaciones en condiciones de curva en el dominio del tiempo se llevan a cabo en condiciones de fricción constante con el objetivo de estudiar si el modelo de interacción propuesto puede reproducir las características del chirrido en curva para diferentes radios de curva y coeficientes de fricción.
[CAT] L'objectiu de la present Tesi és desenvolupar models per a l'estudi de fenòmens de molt alta freqüència associats amb la dinàmica acoblada d'un vehicle ferroviari amb la via. Aquests models permeten simular el soroll de rodament encara que, en particular, aquest treball es proposa abordar el fenomen del soroll grinyolant produït quan el tren negocia un radi de curvatura estret. La interacció roda/carril és la font predominant de l'emissió de soroll en les operacions ferroviàries. El contacte acobla la roda i el carril a través d'una àrea molt reduïda que es caracteritza per una dinàmica fortament no lineal i no estacionària. El problema de contacte roda/carril s'estudia mitjançant la teoria variacional de Kalker i el descens local del coeficient de fricció s'introdueix per mitjà d'una regularització de la llei de Coulomb, què demostra que la seua influència en les corbes de fluència es pot suposar insignificant. Per tant, s'utilitza un coeficient de fricció constant per a modelar el contacte. La flexibilitat s'introdueix en les subestructures de ferrocarril a través del mètode d'Elements Finits (EF) per tal de cobrir el rang d'alta freqüència. La present tesi adopta un model d'eix muntat rotatori que s'aprofita de la seua la simetria rotacional per a augmentar la eficiència computacional. També desenvolupa un model de carril flexible i cíclic que fixa la força de contacte en un punt espacial de la malla a través del mètode dels Elements Mòbils (EM). S'empra un enfocament modal per reduir significativament el nombre de graus de llibertat del problema global, al temps que s'implementa una tècnica diagonalització que permet desacoblar les equacions modals de moviment per a augmentar la velocitat computacional de l'integrador temporal. Les simulacions en les condicions de corba en el domini del temps es duen a terme per a condicions de fricció constant per tal d'estudiar si el model d'interacció proposat pot reproduir les característiques del soroll grinyolant per a diferents radis de corba i coeficients de fricció.
Giner Navarro, J. (2017). Advances Techniques for Time-Domain Modelling of High-Frequency Train/Track Interaction [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/90637
TESIS

Manual debarking of logs in Thai mangrove forest is being implemented for the purpose of charcoal production. In the local conditions, workers debark the harvested logs with homemade mallets made from mangrove wood. The thesis compares this local accustomed method with two other imported methods known in Europe, drawknife debarking and peeling spud debarking. Two basic criteria saying about the effectivity of debarking, i.e. time of debarking particular logs and the difficulty were investigated. The difficulty was investigated with measuring the pulse rate and blood saturation with oxygen of the worker during debarking works. Measurements took place in mangrove forest in Thailand and were realized with the help of Department of Forest Engineering, Faculty of Forestry from the Kasetsart University.

碩士
國立屏東大學
體育學系碩士班
108
The purpose of this study is to explore the impact of different teaching methods on the skills of the national primary school children's baseball. To study the empirical research method, taking the fourth-grade children of Taichung City Zhongxiao National Primary School as the experimental object; 25 control groups (13 boys and 12 girls) perform instructional Lele baseball throwing skills teaching. The experimental group consisted of 25 students (13 boys and 12 girls) who taught the included Lele baseball throwing skills. Pre-testing before the course is involved, After the implementation of eight weeks and sixteen lessons, Forty minutes of teaching practice per lesson, After the completion of the course intervention, the post-test is implemented. The research tools are for the instructional Lele baseball throwing skill teaching and the inclusion of the Lele baseball throwing skill teaching. The test method is to develop and record the skill learning of Lele Baseball 7 meters. According to the data obtained from the experiment, The two-way variation analysis of the mixed design was tested. If the interactions are significantly different, Then carry out a simple main effect test. The statistical significance of this study was determined as α=.05. The research results indicate that: 1) here is no significant difference in the results of the Lele baseball throws in different groups. 2) There are significant differences in the results of different Lele baseball throws for different tests, and the post-test is better than the pre-test. 3) Both the same group and the different tests have a significant interaction effect on the Lele baseball throwing skill. in conclusion: After the different teaching methods are involved in the Lele baseball throwing skill course, they all have good effects on the Lele baseball throwing skill, and the inclusive teaching method is better than the command-based teaching method.

Analysing fertility developments in selected European countries between 1970 and 2014 using alternative methods Abstract Transversal fertility indices as the total fertility rate are distorted by tempo effect when timing of childbearing is changing. New indices as the tempo-adjusted total fertility rate remove this distortion and give another perspective on fertility trends in countries with present tempo effect. These countries are former Eastern Bloc countries and other European countries. This thesis uses the tempo-adjusted total fertility rate and data from Human Fertility Database to describe tempo distortion in fertility level in Sweden, Norway, Czechia, Slovakia, Estonia and Lithuania in period 1970-2014. A more detailed analysis by parity in Sweden and Czechia is conducted in the same period. Negative tempo effect has been present from 1970s in Sweden and Norway and then from 90s in the countries left with fertility postponement being very widespread. The tempo effect level in Sweden and Czechia was substantial at parity one and diminishing with higher parities. Keywords: fertility, timing, level, postponement, adjusted total fertility rate, tempo effect Number of characters without blank spaces: 138 653

The aim of this thesis is to introduce and summarize the process of scoring model development in general and then basic statistical approaches used to resolve this problem, which are in particular logistic regression, neural networks and decision trees (random forests). Application of described methods on a real dataset provided by PROFI CREDIT Czech, a.s. follows, including discussion of some implementation issues and their resolution. Obtained results are discussed and compared.

Activity of enzymes was investigated in the soils of Norway spruce forests in the Bohemian Forest. The aim of the study was the determintation of the impact of temperature and plants dominant in understorey on the activity of extracellular enzymes in the soils in the watershed of Plešné and Čertovo Lake. The measurement of enzymes activities was conducted using the fluorometric method with model substrates.

K. Kaprová (2019): Revealed preferences for outdoor recreation in natural areas - Czech and European perspective Abstract of the Doctoral Dissertation The dissertation thesis focuses on the investigation and synthesis of recreation welfare benefits associated with natural areas in the Czech Republic and in Europe. The dissertation thesis consists of five case studies. These represent various geographic levels of analysis: the level of one single recreation locality, the national level that takes into account large natural recreation sites in the Czech Republic (including protected areas), and a synthesis of results of studies on the European level. The methodological approach is based on the theory of environmental economics and employs non-market valuation techniques based on methods of revealed preferences, namely the hedonic pricing method and two types of travel cost modelling. In Study I, we examine how the presence and characteristics of urban greenery affect property prices in Prague. The results confirm that proximity to greenery and its area are important determinants of housing prices in Prague, which means that residents realize the positive values provided by urban greenery, including recreational ecosystem service. Benefits to residents differ with the type of greenery. Urban forests have the...

Dissertação de Mestrado em Matemática apresentada à Faculdade de Ciências e Tecnologia
O modelo de Black-Scholes foi um dos primeiros modelos de preços de opções europeias a ser aceite. Ainda hoje, este modelo desempenha um papel fundamental na previsão dos preços de uma opção, devido à facilidade que existe na sua implementação e ao facto da sua fórmula só depender de um único parâmetro não observável. No entanto, também apresenta algumas limitações, por causa de suposições estritas ou pouco realistas que lhe estão subjacentes. Daí que, foram desenvolvidos outros modelos que contornassem estas limitações, como é o caso do modelo de preços de opções baseado num processo de Lévy. Nesta dissertação, iremos deduzir equações diferencias representativas de cada um destes modelos e iremos estudar em pormenor a equação do modelo de preços de opções baseado num processo de Lévy. A equação diferencial representativa destes modelos baseados em processos de Lévy, é uma equação diferencial parcial fracionária por conter o operador fracionário de Riemann Liouville. As metodologias usadas na resolução desta equação, requerem que encontremos uma aproximação para este operador, de forma a que, possamos aplicar métodos numéricos. Assim, por um resultado teórico, que relaciona o operador fracionário de Riemann-Liouville com o operador fracionário de Grünwald-Letnikov, somos capazes de discretizar uma equação segundo o método implícito de Euler e segundo o método de Crank-Nicolson. De forma a que, possamos posteriormente, encontrar soluções numéricas para estes modelos de preços de opções de estilo europeu, tendo em conta determinadas condições de fronteira, e retirar conclusões quanto às propriedades de cada método numérico. Para além disso, pela introdução de um método de extrapolação, pretendemos diminuir os erros de aproximação e aumentar a ordem de convergência, obtendo resultados computacionais melhorados. Deste modo, este trabalho expressa bem como os diferentes ramos da matemática se conjugam, para solucionar problemas cada vez mais complexos, impostos pelos desafios dos mercados financeiros.
The Black-Scholes model was one of the first european-style option pricing models to be accepted. Even today, this model plays a fundamental role in predicting the prices of an option, due to the easiness that exists in its implementation and the fact that its formula only depends on a single unobservable parameter. However, it also has some limitations, because of the strict or unrealistic assumptions that underlie it. Hence, other models were developed to circumvent these limitations, such as the option pricing model based on a Lévy process. In this dissertation, we will deduce representative differential equations for each one of these models, and we will study, in detail, the equation of the option pricing model based on a Lévy process. The differential equation representing these models based on Lévy processes is a fractional partial differential equation because of the Riemann-Liouville fractional operator. The methodologies used in solving this equation, require us to find an approximation for this operator, so that we can apply numerical methods. Thus, by a theoretical result, which relates the Riemann-Liouville fractional operator with the Grünwald-Letnikov fractional operator, we are able to discretize an equation according to the implicit Euler method and according to the Crank-Nicolson method. So that we can later find numerical solutions for these european -style option pricing models, taking into account certain boundary conditions, and withdraw conclusions about the properties of each numerical method. Furthermore, by introducing an extrapolation method, we intend to reduce approximation errors and increase the order of convergence, obtaining improved computational results. In this way, this work expresses well how the different branches of mathematics come together to solve increasingly complex problems, imposed by the challenges of the financial markets.

Tesis (Doctor en Física)--Universidad Nacional de Córdoba, Facultad de Matemática, Astronomía, Física y Computación, 2018.
Estudios recientes realizados en una base de datos de Ajedrez cronológicamente ordenada, han mostrado que la distribución de popularidades de líneas de juego de Ajedrez se ajusta a una ley de Zipf. La ley de Zipf es común a muchos sistemas y es usualmente observada en conjunto con efectos de memoria tales como correlaciones de largo alcance y burstiness. Sin embargo los modelos existentes que estudian estos fenómenos no dan cuenta simultáneamente con la ley de Zipf y los efectos de memoria. En este trabajo de tesis, mediante una variante del modelo de crecimiento preferencial de Yule-Simon, introducido por Cattuto et al., se provee una explicación de la aparición simultanea de la ley de Zipf y los efectos de memoria en forma de correlaciones de largo alcance en la base de datos de Ajedrez. Se encuentra que el modelo de Cattuto et al. es capaz de reproducir ambos fenómenos, la ley de Zipf y las correlaciones de largo alcance, incluyendo además los efectos de tamaño del exponente de Hurst de las correspondientes series temporales. Más aún, se encuentra burstiness en la actividad de los grupos de jugadores más activos, aunque la actividad agregada del conjunto completo de jugadores presenta una distribución de tiempos entre eventos sin burstiness. Dado que el modelo de Cattuto et al. no es capaz de producir series temporales con comportamiento ’bursty ’, se realiza una modificación al núcleo de memoria que permite lograr una dinámica bursty. Introduciendo un núcleo de memoria finito, se mantiene el comportamiento de ley de potencia en la distribución de popularidades y, al mismo tiempo se obtienen series temporales que presentan burstiness como consecuencia de una transición de fase, en la cual, en el estado crítico, la dinámica está dominada por las fluctuaciones.
Recent works studying a chronologically sorted chess database have shown that the popularity distribution of opening lines in the game of chess follow a Zipf law. Zipf law is common to many systems and is usually observed together with memory effects, such as long-range correlations and burstiness. Nevertheless, existing models that study these phenomena do not account for the Zipf’s law and memory effects simultaneously. In this thesis, using a variant of the Yule-Simon preferential growth model, introduced by Cattuto et al., we provide an explanation of the simultaneous emergence of Zipf’s law and memory effects in the form of long-range correlations in the chess database. We find that Cattuto’s model is able to reproduce both phenomena, Zipf’s law and the long-range correlations., including the size effects displayed by the Hurst exponent of the corresponding time series. Furthermore, we find burstiness in the activity of the most active players, although the aggregated activity of all players in the database presents an interevent time distribution without burstiness. Since Cattuto’s model is not able to generate times series with a bursty behavior, we made a modification to the memory kernel that allows a bursty dynamics. By introducing a finite memory kernel, we keep the power-law behavior in the popularity distribution and, at the same time, we obtain time series that present burstiness as a consequence of a phase transition in which, at the critical point, the dynamic is ruled by fluctuations.