The main contribution of this thesis is to derive the properties and present a closed from solution of the exotic options under some specific types of Levy processes, such as American put options, American call options, British put options, British call options and American knock-out put options under either double exponential jump-diffusion processes or one-sided exponential jump-diffusion processes. Compared to the geometric Brownian motion, exponential jump-diffusion processes can better incorporate the asymmetric leptokurtic features and the volatility smile observed from the market. Pricing the option with early exercise feature is the optimal stopping problem to determine the optimal stopping time to maximize the expected options payoff. Due to the Markovian structure of the underlying process, the optimal stopping problem is related to the free-boundary problem consisting of an integral differential equation and suitable boundary conditions. By the local time-space formula for semi-martingales, the closed form solution for the options value can be derived from the free-boundary problem and we characterize the optimal stopping boundary as the unique solution to a nonlinear integral equation arising from the early exercise premium (EEP) representation. Chapter 2 and Chapter 3 discuss American put options and American call options respectively. When pricing options with early exercise feature under the double exponential jump-diffusion processes, a non-local integral term will be found in the infinitesimal generator of the underlying process. By the local time-space formula for semi-martingales, we show that the value function and the optimal stopping boundary are the unique solution pair to the system of two integral equations. The significant contributions of these two chapters are to prove the uniqueness of the value function and the optimal stopping boundary under less restrictive assumptions compared to previous literatures. In the degenerate case with only one-sided jumps, we find that the results are in line with the geometric Brownian motion models, which extends the analytical tractability of the Black-Scholes analysis to alternative models with jumps. In Chapter 4 and Chapter 5, we examine the British payoff mechanism under one-sided exponential jump-diffusion processes, which is the first analysis of British options for process with jumps. We show that the optimal stopping boundaries of British put options with only negative jumps or British call options with only positive jumps can also be characterized as the unique solution to a nonlinear integral equation arising from the early exercise premium representation. Chapter 6 provides the study of American knock-out put options under negative exponential jump-diffusion processes. The conditional memoryless property of the exponential distribution enables us to obtain an analytical form of the arbitrage-free price for American knock-out put options, which is usually more difficult for many other jump-diffusion models.

A high resolution speedy delivery time domain reflectometer (SD/TDR) has been developed in the Electrical Engineering department at The University of Texas at Austin. The SD/TDR uses a novel non-sinusoidal signal that does not undergo dispersion during transmission in a lossy media. SD/TDR is used to estimate the length and detect the location of faults in the transmission lines. Time of flight (TOF) is one of the critical parameters of SD/TDR and a function of several temperature dependent factors. Given the TOF and length of a transmission line, signal delay can be computed. This research presents an empirical study of the effect of temperature on the TOF in a plenum grade coaxial cable for temperatures ranging from -3 °C to 60 °C. We also study the effect of temperature on characteristic impedance of the coaxial cable. Finally, a SD double exponential waveform is used to estimate TOF for calibrated short and open terminations. / text

Economic stringencies have compelled Canadian hospitals to examine their administrative effectiveness critically. Improved supplies and inventory procedures adopted by leading industrial corporations, suggest that hospitals might benefit from such systems. Lack of the profit incentive, and the high ratio of wages to total expenses in hospitals, have delayed adoption of modern inventory management techniques. This study examined the economic status of Canadian hospitals, and endeavoured to discover whether a computer-based inventory management system, incorporating short-term statistical demand forecasting, would be feasible and advantageous. Scientific forecasting for inventory management is not used by hospitals. The writer considered which technique would be most suited to their needs, taking account of benefits claimed by industrial users. Samples of demand data were subjected to a variety of simple forecasting methods, including moving averages, exponentially smoothed averages and the Box-Jenkins method. Comparisons were made in terms of relative size of forecast errors; ease of data maintenance, and demands upon hospital clerical staffs. The computer system: BRUFICH facilitated scrutiny of the effect of each technique upon major components of the system. It is concluded that either of two methods would be appropriate: moving averages and double exponential smoothing. The latter, when combined with adaptive control through tracking signals, is easily incorporated within the total inventory system. It requires only a short run of data, tracks trend satisfactorily, and demands little operator intervention. The original system designed by this writer was adopted by the Hospital for Sick Children, Toronto, and has significantly improved their inventory management.

Η παρούσα διπλωματική διατριβή εντάσσεται ερευνητικά στη περιοχή της Στατιστικής Θεωρίας Αποφάσεων, καθώς ασχολούμαστε με τη μελέτη της κατανομής Laplace CL(θ,s), όπου με θ και s συμβολίζονται αντίστοιχα οι παράμετροι θέσεως και κλίμακος, και η οποία θεωρείται ως ιδανικό μοντέλο κατανομής οικονομικής φύσεως δεδομένων. / This thesis is part of research in the area of Statistical Decision Theory, as it deals with the study of the distribution Laplace CL (θ, s), where θ and s respectively symbolized the position and scale parameters, which is considered as an ideal model of distribution of economic kind of data.

<p>The purpose of this study is to identify an impact on an option pricing within NASDAQ OMX Stockholm Market, if the underlying</p><p>asset prices include jumps. The current financial crisis, when jumps are much more evident than ever, makes this issue very actual and important in the global sense for the portfolio hedging and other risk management applications for example for the banking sector. Therefore, an investigation is based on OMXS30 Index and SEB A Bank. To detect jumps the Barndorff-Nielsen and Shephard non-parametric bipower variation test is used. First it is examined on simulations, to be finally implemented on the real data. An affirmation of a jumps occurrence requires to apply an appropriate model for the option pricing. For this purpose the Kou model, a double exponential jump-diffusion one, is proposed, as it incorporates essential stylized facts not available for another models. Th parameters in the model are estimated by a new approach - a combined cumulant matching with lambda taken from the Barrndorff-Nielsen and Shephard test. To evaluate how the Kou model manages on the option pricing, it is compared to the Black-Scholes model and to the real prices of European call options from the Stockholm Stock Exchange. The results show that the Kou model outperforms the latter.</p>

The purpose of this study is to identify an impact on an option pricing within NASDAQ OMX Stockholm Market, if the underlying asset prices include jumps. The current financial crisis, when jumps are much more evident than ever, makes this issue very actual and important in the global sense for the portfolio hedging and other risk management applications for example for the banking sector. Therefore, an investigation is based on OMXS30 Index and SEB A Bank. To detect jumps the Barndorff-Nielsen and Shephard non-parametric bipower variation test is used. First it is examined on simulations, to be finally implemented on the real data. An affirmation of a jumps occurrence requires to apply an appropriate model for the option pricing. For this purpose the Kou model, a double exponential jump-diffusion one, is proposed, as it incorporates essential stylized facts not available for another models. Th parameters in the model are estimated by a new approach - a combined cumulant matching with lambda taken from the Barrndorff-Nielsen and Shephard test. To evaluate how the Kou model manages on the option pricing, it is compared to the Black-Scholes model and to the real prices of European call options from the Stockholm Stock Exchange. The results show that the Kou model outperforms the latter.

AssociaÃÃo TÃcnico-CientÃfica Eng. Paulo de Frontin / This paper presents the study and development of a voltage impulse generator using a cascaded boost converter topology operating in Discontinuous Conduction Mode (DCM) which will be used for the inspection of grounding systems used by electric power companies. The output voltage of the converter is applied to the grounding system which behaves as a load. The signal applied to the ground was measured by the data acquisition system and analyzed by an intelligent algorithms software. The voltage has the characteristics of a double exponential waveform which is a mathematical model used for study of lightning. Furthermore, the impulse generator has the option to produce a square waveform output voltage. Unlike, the traditional impulse generator with spark gaps, which was disadvantages of poor lifetime and the need of external system to operating the same, the developed generator uses only semiconductor devices in its construction. A theoretical study was carried out through qualitative and quantitative analyzes moreover, the switching process and the losses in the converter components were studied. In this work was performed the design of a cascaded boost converter for evaluating grounding systems with approximated 156 W, input voltage of 110 Vac rms and an output peak voltage of approximately 880 VDC, which correspond to the sum each voltage capacitor of the boost converter, when they are connected in series. A prototype with the indicated specifications was implemented and experimentally tested in the laboratory and real conditions using four grounding systems configurations. Tests were performed considering that the grounding impedance is resistive. The obtained experimental and simulation results are used to validate the theoretical analysis and the designed converter. / Este trabalho apresenta o estudo e desenvolvimento de um gerador de impulsos de tensÃo usando a topologia de um conversor boost em cascata operando em Modo de ConduÃÃo DescontÃnua (MCD) que serà utilizado para inspeÃÃo de sistemas de aterramentos usados pelas concessionÃrias de energia elÃtrica. A tensÃo obtida na saÃda do conversor à aplicada ao sistema de aterramento que se comporta como uma carga. O sinal aplicado ao aterramento à medido pelo sistema de aquisiÃÃo de dados e analisado pelo software por algoritmos inteligentes. A tensÃo aplicada tem as caracterÃsticas de uma onda tipo dupla exponencial que à um modelo matemÃtico para estudo de descargas atmosfÃricas. AlÃm disso, o gerador poderà gerar tensÃes com caracterÃsticas de uma onda quadrada. O gerador de impulsos desenvolvido utiliza apenas dispositivos semicondutores na sua construÃÃo que apresentam as vantagens de possuir uma longa vida Ãtil, podem operar em altas frequÃncias, sÃo acionados com baixa tensÃo e possuem uma baixa queda de tensÃo ao contrÃrio dos tradicionais geradores de impulsos que utilizam os spark gaps para chaveamento que apresentam como desvantagens a baixa vida Ãtil e a necessidade de um sistema externo para funcionamento da mesma. Um estudo teÃrico foi realizado atravÃs das anÃlises qualitativa e quantitativa, alÃm das anÃlises do processo de comutaÃÃo e das perdas nos componentes do conversor. Neste trabalho foi realizado o projeto do conversor boost em cascata para inspeÃÃo de sistemas de aterramento com uma potÃncia aproximada de 156 W, tensÃo de entrada eficaz de 110 Vca e tensÃo de pico de aproximadamente 880 Vcc que corresponde à soma da tensÃo dos capacitores do conversor boost quando estÃo dispostos em sÃrie. Um protÃtipo com as especificaÃÃes indicadas foi construÃdo e testado experimentalmente em laboratÃrio e em campo utilizando quatro topologias de sistemas de aterramento. Foram realizados testes considerando que a impedÃncia de aterramento era puramente resistiva. Os resultados de simulaÃÃo e experimentais obtidos sÃo utilizados para validar a anÃlise teÃrica e o projeto realizado.

Cette thèse montre la possibilité d’une application rigoureuse de la méthode d’intégrationnumérique double-exponentielle introduite par Takahasi et Morien 1974, et sa pertinence pour lescalculs à grande précision en théorie des nombres. Elle contient en particulier une étude détailléede cette méthode, des critères simples sur son champ d’application, et des estimations rigoureusesdes termes d’erreur.Des paramètres explicités et précis permettent de l’employer aisément pour le calcul garantide fonctions définies par des intégrales.Cette méthode est également appliquée en détail au calcul de transformées de Mellin inversesde facteurs gamma intervenant dans les calculs numériques de fonctions L. Par une étude unifiée,ce travail démontre la complexité d’un algorithme de M. Rubinstein et permet de proposer desalgorithmes de calcul de valeurs de fonctions L quelconques dont le résultat est garanti et dont lacomplexité est meilleure en la précision. / This thesis contains a detailed study of the so-called double exponential integration formulasintroduced by Takahasi and Moriin 1974,and provides explicit bounds forarigorous applicationof the method in number theory.Accurate parameters are given, which makes it possible to use it as a blackbox for the rigorouscomputation of functions defined by integrals.It also deals with numerical computations of L functions. The complexity of analgorithm dueto M. Rubinstein is proven. In the context of double-exponential transformation, a new algorithmis provided whose complexity is low in terms of precision.

Electronics for automotive needs to be able to handle different situations that can occur on the power line, such as high voltage transients. ISO16750 and ISO-7637 describes different pulses and tests a system needs to be able to handle. This report compares three different protection circuits that can output +5V and +12V built for low power devices. The circuits use different techniques for protection, one that uses TVS diodes, another that uses a voltage regulator IC with built in protection. The last protection uses P-channel MOSFET’s for protection. The circuits are compared against protection, price and leakage current. The most relevant transients to test a system against are decided to be pulse1, pulse 2a and load dump. A pulse generator consisting of a pulse shaping network and a common drain amplifier is used to create the test pulses. The result shows that all the circuits could protect against pulse 2a and load dump. However, all the circuits did fail against pulse 1 due to an undersized diode for negative voltage protection. The leakage current did not exceed 4µA for two of the circuits in the temperature interval of -40°C to +100°C. All the circuits started to have high leakage current when the temperature got up to +150°C. The price for the circuits didn’t differ that much, all the circuits cost below 3 US-dollar per circuit when making 10 000 circuits. The conclusions that could be made of the results are that all the circuits could protect against pulse 1, pulse 2a and load dump if correct diode is used for negative voltage protection. The protection that builds on Pchannel MOSFET’s should be the best choice for low power devices due to its low leakage current and potential for low cost. The disadvantage is the complexity and number of components needed for the circuit. The TVS diodes should be used if low complexity and low number of components is preferred. The disadvantage is that TVS diodes gets hot if a load dump is applied and the interval between stand-off voltage and maximum clamping voltage is quite high. The study also shows that there are cheaper solutions than using TVS diodes.

<p>In this thesis the double exponential jump-diffusion model is considered and the Laplace transform is used as a method for pricing both plain vanilla and path-dependent options. The evolution of the underlying stock prices are assumed to follow a double exponential jump-diffusion model. To invert the Laplace transform, the Euler algorithm is used. The thesis includes the programme code for European options and the application to the real data. The results show how the Kou model performs on the NASDAQ OMX Stockholm Market in the case of the SEB stock.</p>