Academic literature on the topic 'Levy model'

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Journal articles on the topic "Levy model"

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BEIKIRCH, MAXIMILIAN, SIMON CRAMER, MARTIN FRANK, PHILIPP OTTE, EMMA PABICH, and TORSTEN TRIMBORN. "ROBUST MATHEMATICAL FORMULATION AND PROBABILISTIC DESCRIPTION OF AGENT-BASED COMPUTATIONAL ECONOMIC MARKET MODELS." Advances in Complex Systems 23, no. 06 (September 2020): 2050017. http://dx.doi.org/10.1142/s0219525920500174.

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In science and especially in economics, agent-based modeling has become a widely used modeling approach. These models are often formulated as a large system of difference equations. In this study, we discuss two aspects, numerical modeling and the probabilistic description for two agent-based computational economic market models: the Levy–Levy–Solomon model and the Franke–Westerhoff model. We derive time-continuous formulations of both models, and in particular, we discuss the impact of the time-scaling on the model behavior for the Levy–Levy–Solomon model. For the Franke–Westerhoff model, we proof that a constraint required in the original model is not necessary for stability of the time-continuous model. It is shown that a semi-implicit discretization of the time-continuous system preserves this unconditional stability. In addition, this semi-implicit discretization can be computed at cost comparable to the original model. Furthermore, we discuss possible probabilistic descriptions of time-continuous agent-based computational economic market models. Especially, we present the potential advantages of kinetic theory in order to derive mesoscopic descriptions of agent-based models. Exemplified, we show two probabilistic descriptions of the Levy–Levy–Solomon and Franke–Westerhoff model.
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Rhee, Joon Hee, and Soo Chun Park. "The Term Structure Model under the α-Stable Levy Process." Journal of Derivatives and Quantitative Studies 18, no. 1 (February 28, 2010): 77–100. http://dx.doi.org/10.1108/jdqs-01-2010-b0003.

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This paper derives the analytic solutions of the pure discount bond price under the various types of -stable Levy process. It is well-known that only a few cases in-stable Levy process have the moment generating function. This paper extends the model to damped-stable Levy processes, which have artificial stable process with the moment generating function. This paper also extends models to stochastic volatility by time change method of Levy process.
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Cafiero, R., P. De Los Rios, A. Valleriani, and J. L. Vega. "Levy-nearest-neighbors Bak-Sneppen model." Physical Review E 60, no. 2 (August 1, 1999): R1111—R1114. http://dx.doi.org/10.1103/physreve.60.r1111.

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Chechkin, A. V., and V. Yu Gonchar. "A model for persistent Levy motion." Physica A: Statistical Mechanics and its Applications 277, no. 3-4 (March 2000): 312–26. http://dx.doi.org/10.1016/s0378-4371(99)00392-1.

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Lee, Jun Hui, and Kook Hyun Chang. "Volatility Smile Surface for Levy Option Pricing Model." Journal of Derivatives and Quantitative Studies 12, no. 1 (May 30, 2004): 73–86. http://dx.doi.org/10.1108/jdqs-01-2004-b0004.

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This paper discusses theoretical extensions of the implied volatility method of Dupire (1994) when the stock prices follow the Geometric Levy process. For the extensions of Kolmogorov forward equation for Levy process, this paper uses adjoint operator in L² spaces. This paper obtains similar results of Dupire (1994) and Andersen and Andreasan (2001). However, our results can be applied to more general semi-martingale processes such as well-known VG (Variance Gamma) model and NIG (Normal Inverse Gaussian) model with diffusion processes. This paper also applies the approach to the case of stochastic time changed Levy process, which generates the stochastic volatility models.
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Zschischang, Elmar, and Thomas Lux. "Some new results on the Levy, Levy and Solomon microscopic stock market model." Physica A: Statistical Mechanics and its Applications 291, no. 1-4 (March 2001): 563–73. http://dx.doi.org/10.1016/s0378-4371(00)00609-9.

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Zhang, Yang, Hai Lin, and Lian-shou Liu. "Levy Stability Analysis of Random Cascade Model." Communications in Theoretical Physics 24, no. 1 (July 30, 1995): 85–90. http://dx.doi.org/10.1088/0253-6102/24/1/85.

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Kohl, R. "The Influence of the Number of Different Stocks on the Levy–Levy–Solomon Model." International Journal of Modern Physics C 08, no. 06 (December 1997): 1309–16. http://dx.doi.org/10.1142/s0129183197001168.

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The stock market model of Levy, Levy, Solomon is simulated for more than one stock to analyze the behavior for a large number of investors. Small markets can lead to realistic looking prices for one and more stocks. A large number of investors leads to a semi-regular fashion simulating one stock. For many stocks, three of the stocks are semi-regular and dominant, the rest is chaotic. Aside from that we changed the utility function and checked the results.
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BAXTER, MARTIN. "LÉVY SIMPLE STRUCTURAL MODELS." International Journal of Theoretical and Applied Finance 10, no. 04 (June 2007): 593–606. http://dx.doi.org/10.1142/s021902490700438x.

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This paper considers credit portfolio models based on Levy processes in general, and the gamma model in particular. It describes both single-name and multi-name situations using the gamma model, along with calibration fits and a comparison of various simple Levy models. There is also extensive historical data, including the May 2005 Auto crisis, which can be described in terms of the model. Parameter-based risk management using the gamma model is also discussed along with implementation details.
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Levy, Sheri, Ashley Lytle, Jamie Macdonald, and MaryBeth Apriceno. "Reducing Ageism: PEACE (Positive Education about Aging and Contact Experiences) Model." Innovation in Aging 4, Supplement_1 (December 1, 2020): 647. http://dx.doi.org/10.1093/geroni/igaa057.2226.

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Abstract Drawing on interdisciplinary theorizing and research, the PEACE (Positive Education about Aging and Contact Experiences) model points to two interrelated factors that reduce ageism: providing education about aging and positive intergenerational contact experiences with older adults (Levy 2016). Evidence supporting the model will be discussed including a semester-long pre-posttest intervention with undergraduates (non-gerontology course) who learned about aging and had face-to-face and Instagram contact with older adults (Lytle, Nowacek, & Levy, 2020), brief online pre-post test experimental-control group studies with undergraduates and a community sample who learned about aging and positive intergenerational contact experiences (Lytle & Levy, 2017), and an online experimental-control group study with undergraduates who viewed brief videos addressing PEACE model components (Lytle, Macdonald, Apriceno, & Levy, under review). Across studies, PEACE model interventions promoted increased aging knowledge as well as reduced negative stereotyping of older adults, aging anxiety, and concerns about aging. Future directions will be discussed.
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Dissertations / Theses on the topic "Levy model"

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Walljee, Raabia. "The Levy-LIBOR model with default risk." Thesis, Stellenbosch : Stellenbosch University, 2015. http://hdl.handle.net/10019.1/96957.

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Thesis (MSc)--Stellenbosch University, 2015
ENGLISH ABSTRACT : In recent years, the use of Lévy processes as a modelling tool has come to be viewed more favourably than the use of the classical Brownian motion setup. The reason for this is that these processes provide more flexibility and also capture more of the ’real world’ dynamics of the model. Hence the use of Lévy processes for financial modelling is a motivating factor behind this research presentation. As a starting point a framework for the LIBOR market model with dynamics driven by a Lévy process instead of the classical Brownian motion setup is presented. When modelling LIBOR rates the use of a more realistic driving process is important since these rates are the most realistic interest rates used in the market of financial trading on a daily basis. Since the financial crisis there has been an increasing demand and need for efficient modelling and management of risk within the market. This has further led to the motivation of the use of Lévy based models for the modelling of credit risky financial instruments. The motivation stems from the basic properties of stationary and independent increments of Lévy processes. With these properties, the model is able to better account for any unexpected behaviour within the market, usually referred to as "jumps". Taking both of these factors into account, there is much motivation for the construction of a model driven by Lévy processes which is able to model credit risk and credit risky instruments. The model for LIBOR rates driven by these processes was first introduced by Eberlein and Özkan (2005) and is known as the Lévy-LIBOR model. In order to account for the credit risk in the market, the Lévy-LIBOR model with default risk was constructed. This was initially done by Kluge (2005) and then formally introduced in the paper by Eberlein et al. (2006). This thesis aims to present the theoretical construction of the model as done in the above mentioned references. The construction includes the consideration of recovery rates associated to the default event as well as a pricing formula for some popular credit derivatives.
AFRIKAANSE OPSOMMING : In onlangse jare, is die gebruik van Lévy-prosesse as ’n modellerings instrument baie meer gunstig gevind as die gebruik van die klassieke Brownse bewegingsproses opstel. Die rede hiervoor is dat hierdie prosesse meer buigsaamheid verskaf en die dinamiek van die model wat die praktyk beskryf, beter hierin vervat word. Dus is die gebruik van Lévy-prosesse vir finansiële modellering ’n motiverende faktor vir hierdie navorsingsaanbieding. As beginput word ’n raamwerk vir die LIBOR mark model met dinamika, gedryf deur ’n Lévy-proses in plaas van die klassieke Brownse bewegings opstel, aangebied. Wanneer LIBOR-koerse gemodelleer word is die gebruik van ’n meer realistiese proses belangriker aangesien hierdie koerse die mees realistiese koerse is wat in die finansiële mark op ’n daaglikse basis gebruik word. Sedert die finansiële krisis was daar ’n toenemende aanvraag en behoefte aan doeltreffende modellering en die bestaan van risiko binne die mark. Dit het verder gelei tot die motivering van Lévy-gebaseerde modelle vir die modellering van finansiële instrumente wat in die besonder aan kridietrisiko onderhewig is. Die motivering spruit uit die basiese eienskappe van stasionêre en onafhanklike inkremente van Lévy-prosesse. Met hierdie eienskappe is die model in staat om enige onverwagte gedrag (bekend as spronge) vas te vang. Deur hierdie faktore in ag te neem, is daar genoeg motivering vir die bou van ’n model gedryf deur Lévy-prosesse wat in staat is om kredietrisiko en instrumente onderhewig hieraan te modelleer. Die model vir LIBOR-koerse gedryf deur hierdie prosesse was oorspronklik bekendgestel deur Eberlein and Özkan (2005) en staan beken as die Lévy-LIBOR model. Om die kredietrisiko in die mark te akkommodeer word die Lévy-LIBOR model met "default risk" gekonstrueer. Dit was aanvanklik deur Kluge (2005) gedoen en formeel in die artikel bekendgestel deur Eberlein et al. (2006). Die doel van hierdie tesis is om die teoretiese konstruksie van die model aan te bied soos gedoen in die bogenoemde verwysings. Die konstruksie sluit ondermeer in die terugkrygingskoers wat met die wanbetaling geassosieer word, sowel as ’n prysingsformule vir ’n paar bekende krediet afgeleide instrumente.
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Turkvatan, Aysun. "Completion Of A Levy Market Model And Portfolio Optimization." Master's thesis, METU, 2008. http://etd.lib.metu.edu.tr/upload/12609904/index.pdf.

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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.
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Yilmaz, Busra Zeynep. "Completion, Pricing And Calibration In A Levy Market Model." Master's thesis, METU, 2010. http://etd.lib.metu.edu.tr/upload/12612598/index.pdf.

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In this thesis, modelling with Lé
vy processes is considered in three parts. In the first part, the general geometric Lé
vy market model is examined in detail. As such markets are generally incomplete, it is shown that the market can be completed by enlarging with a series of new artificial assets called &ldquo
power-jump assets&rdquo
based on the power-jump processes of the underlying Lé
vy process. The second part of the thesis presents two different methods for pricing European options: the martingale pricing approach and the Fourier-based characteristic formula method which is performed via fast Fourier transform (FFT). Performance comparison of the pricing methods led to the fact that the fast Fourier transform produces very small pricing errors so the results of both methods are nearly identical. Throughout the pricing section jump sizes are assumed to have a particular distribution. The third part contributes to the empirical applications of Lé
vy processes. In this part, the stochastic volatility extension of the jump diffusion model is considered and calibration on Standard&
Poors (S&
P) 500 options data is executed for the jump-diffusion model, stochastic volatility jump-diffusion model of Bates and the Black-Scholes model. The model parameters are estimated by using an optimization algorithm. Next, the effect of additional stochastic volatility extension on explaining the implied volatility smile phenomenon is investigated and it is found that both jumps and stochastic volatility are required. Moreover, the data fitting performances of three models are compared and it is shown that stochastic volatility jump-diffusion model gives relatively better results.
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West, Lydia. "American Monte Carlo option pricing under pure jump levy models." Thesis, Stellenbosch : Stellenbosch University, 2013. http://hdl.handle.net/10019.1/79994.

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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.
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Gong, Ruoting. "Small-time asymptotics and expansions of option prices under Levy-based models." Diss., Georgia Institute of Technology, 2012. http://hdl.handle.net/1853/44798.

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This thesis is concerned with the small-time asymptotics and expansions of call option prices, when the log-return processes of the underlying stock prices follow several Levy-based models. To be specific, we derive the time-to-maturity asymptotic behavior for both at-the-money (ATM), out-of-the-money (OTM) and in-the-money (ITM) call-option prices under several jump-diffusion models and stochastic volatility models with Levy jumps. In the OTM and ITM cases, we consider a general stochastic volatility model with independent Levy jumps, while in the ATM case, we consider the pure-jump CGMY model with or without an independent Brownian component. An accurate modeling of the option market and asset prices requires a mixture of a continuous diffusive component and a jump component. In this thesis, we first model the log-return process of a risk asset with a jump diffusion model by combining a stochastic volatility model with an independent pure-jump Levy process. By assuming smoothness conditions on the Levy density away from the origin and a small-time large deviation principle on the stochastic volatility model, we derive the small-time expansions, of arbitrary polynomial order, in time-t, for the tail distribution of the log-return process, and for the call-option price which is not at-the-money. Moreover, our approach allows for a unified treatment of more general payoff functions. As a consequence of our tail expansions, the polynomial expansion in t of the transition density is also obtained under mild conditions. The asymptotic behavior of the ATM call-option prices is more complicated to obtain, and, in general, is given by fractional powers of t, which depends on different choices of the underlying log-return models. Here, we focus on the CGMY model, one of the most popular tempered stable models used in financial modeling. A novel second-order approximation for ATM option prices under the pure-jump CGMY Levy model is derived, and then extended to a model with an additional independent Brownian component. The third-order asymptotic behavior of the ATM option prices as well as the asymptotic behavior of the corresponding Black-Scholes implied volatilities are also addressed.
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Mbakwe, Chidinma. "Model risk for barrier options when priced under different lévy dynamics." Thesis, Stellenbosch : Stellenbosch University, 2011. http://hdl.handle.net/10019.1/17810.

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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.
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Zhang, Bing. "A new levy based short-rate model for the fixed income market and its estimation with particle filter." College Park, Md. : University of Maryland, 2006. http://hdl.handle.net/1903/3664.

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Thesis (Ph. D.) -- University of Maryland, College Park, 2006.
Thesis research directed by: Mathematics. Title from t.p. of PDF. Includes bibliographical references. Published by UMI Dissertation Services, Ann Arbor, Mich. Also available in paper.
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Steinki, Oliver. "An investigation of ensemble methods to improve the bias and/or variance of option pricing models based on Lévy processes." Thesis, University of Manchester, 2015. https://www.research.manchester.ac.uk/portal/en/theses/an-investigation-of-ensemble-methods-to-improve-the-bias-andor-variance-of-option-pricing-models-based-on-levy-processes(8c4f1c41-2b87-4138-a6d6-91e8292b0f23).html.

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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.
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Enes, Diana Catarina Gonçalves. "Lévy processes in exotic options pricing." Master's thesis, Instituto Superior de Economia e Gestão, 2011. http://hdl.handle.net/10400.5/4324.

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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.
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Ellanskaya, Anastasia. "Utility maximisation and utility indifference pricing for exponential semimartingale models." Thesis, Angers, 2015. http://www.theses.fr/2015ANGE0061.

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Dans cette thèse nous considérons le problème de la maximisation d’utilité et de la formation des prix d’indifférence pour les modèles semimartingales exponentiels dépendant d’un facteur aléatoire ξ. L’enjeu est de résoudre le problème des prix d’indifférence en utilisant le grossissement de l’espace et de la filtration. Nous réduisons le problème de maximisation dans la filtration élargie au problème conditionnel, sachant {ξ = v}, que nous résolvons en utilisant une approche duale. Pour HARA-utilités nous introduisons les informations telles que les entropies relatives et les intégrales de type Hellinger, ainsi que les processus d’information correspondants, enfin d’exprimer, via ces processus, l’utilité maximal. En particulier, nous étudions les modèles de Lévy exponentiels, où les processus d’information sont déterministes ce que simplifie considèrablement les calculs des prix d’indiffrence. Enfin, nous appliquons les rèsultats au modèle du mouvement brownien géométrique et au modèle de diffusion-sauts qui inclut le mouvement brownien et les processus de Poisson. Dans les cas d’utilité logarithmique, de puissance et exponentielle, nous fournissons les formules explicites des informations, et puis, en utilisant les méthodes numériques, nous résolvons les équations pour obtenir les prix d’indifférence en cas de vente d’une option européenne
This thesis explores the utility maximisation problem and indifference pricing for exponential semimartingale models depending on a random factor ξ. The main idea to solve indifference pricing problem consists in the enlargement of the space and filtration. We reduce the maximization problem on the enlarged filtration to the conditional one, given {ξ = v}, which we solve using dual approach. For HARA-utilities we introduce the information quantities such that the relative entropies, Hellinger type integrals, and the corresponding information processes, and we express the maximal utility via these processes. As a particular case, we study exponential Levy models, where the information processes are deterministic and this fact simplify very much indifference price calculus. Finally, we apply the results to Geometric Brownian motion model and jump-diffusion model which incorporates Brownian motion and Poisson process. In the cases of logarithmic, power and exponential utilities, we provide the explicit formulae of information quantities and using the numerical methods we solve the equations for the seller’s and buyer’s indifference prices of European put option
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Books on the topic "Levy model"

1

Saez, Emmanuel. Optimal progressive capital income taxes in the infinite horizon model. Cambridge, MA: National Bureau of Economic Research, 2002.

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Gravelle, Jane. Does the Harberger Model greatly understate the excess burden of the corporate tax?: Another model says yes. Cambridge, MA: National Bureau of Economic Research, 1988.

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Financial models with Levy processes and volatility clustering. Hoboken, N.J: Wiley, 2011.

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Organisation for Economic Co-operation and Development. Committee on Fiscal Affairs. OECD model tax convention on income and on capital 2003: Condensed version. Edited by Végh Perla Gyöngyi. Amsterdam, Netherlands: International Bureau of Fiscal Documentation, 2003.

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Organisation for Economic Co-operation and Development, ed. "Taxes covered": A study of Article 2 of the OECD Model Tax Conventions. Amsterdam: IBFD, 2011.

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Organisation for Economic Co-operation and Development. Committee on Fiscal Affairs. OECD model tax convention on income and on capital: Condensed version 2010 ; and Key tax features of member countries 2010. Amsterdam: IBFD, 2010.

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Heijdra, Ben J. The dynamic macroeconomic effects of tax policy in an overlapping generation model. [Washington, D.C.]: International Monetary Fund, Fiscal Affairs Department, 1998.

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Farhi, Emmanuel. Capital taxation and ownership when markets are incomplete. Cambridge, MA: National Bureau of Economic Research, 2007.

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Farhi, Emmanuel. Capital taxation and ownership when markets are incomplete. Cambridge, Mass: National Bureau of Economic Research, 2007.

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Jessica, Cariboni, ed. Levy processes in credit risk. [Hoboken, NJ]: John Wiley & Sons, 2009.

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Book chapters on the topic "Levy model"

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Zhang, Huiming, and Junzo Watada. "Building Fuzzy Levy-GJR-GARCH American Option Pricing Model." In Lecture Notes in Computer Science, 197–209. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-14815-7_17.

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Bishwal, Jaya P. N. "Maximum Quasi-Likelihood Estimation in Fractional Levy Stochastic Volatility Model." In Parameter Estimation in Stochastic Volatility Models, 351–58. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-03861-7_8.

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Shekhawat, Shalini, Akash Saxena, Rajesh Kumar, and Vinay Pratap Singh. "Levy Flight Opposition Embedded BAT Algorithm for Model Order Reduction." In Springer Tracts in Nature-Inspired Computing, 103–18. Singapore: Springer Singapore, 2020. http://dx.doi.org/10.1007/978-981-15-5097-3_6.

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Arestis, Philip, and Malcolm Sawyer. "The Effectiveness of Fiscal Policy in the Levy Institute’s Stock-flow Model." In Contributions in Stock-flow Modeling, 300–320. London: Palgrave Macmillan UK, 2012. http://dx.doi.org/10.1057/9780230367357_13.

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Wu, Benbin, Jing Yang, and Liang He. "Parallel Social Influence Model with Levy Flight Pattern Introduced for Large-Graph Mining on Weibo.com." In Algorithms and Architectures for Parallel Processing, 102–11. Cham: Springer International Publishing, 2013. http://dx.doi.org/10.1007/978-3-319-03889-6_12.

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Gayathri, T., and D. Lalitha Bhaskari. "A Novel Cuckoo Search with Levy Distribution-Optimized Density-Based Clustering Model on MapReduce for Big Data Environment." In Lecture Notes in Electrical Engineering, 371–81. Singapore: Springer Singapore, 2022. http://dx.doi.org/10.1007/978-981-16-8554-5_35.

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Bishwal, Jaya P. N. "Fractional Ornstein–Uhlenbeck Processes, Levy–Ornstein–Uhlenbeck Processes, and Fractional Levy– Ornstein–Uhlenbeck Processes." In Parameter Estimation in Stochastic Volatility Models, 169–272. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-03861-7_4.

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Zhang, Huiming, and Junzo Watada. "Building Fuzzy Variance Gamma Option Pricing Models with Jump Levy Process." In Intelligent Decision Technologies 2017, 105–16. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-59424-8_10.

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Barbieri, Samuel, Katja Hofele, Karl-Heinz Wiederhold, Alphonse Probst, Claudia Mistl, Simone Danner, Sabine Kauffmann, et al. "Mouse Models of α-Synucleinopathy and Lewy Pathology." In Advances in Experimental Medicine and Biology, 147–67. Boston, MA: Springer US, 2001. http://dx.doi.org/10.1007/978-1-4615-1249-3_13.

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Barany, Ernest, and Maria Pia Beccar Varela. "Stochastic Differential Equations and Levy Models with Applications to High Frequency Data." In Handbook of Modeling High-Frequency Data in Finance, 327–46. Hoboken, NJ, USA: John Wiley & Sons, Inc., 2011. http://dx.doi.org/10.1002/9781118204580.ch12.

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Conference papers on the topic "Levy model"

1

Chen, Yunbo. "Research and simulation on Levy flight model for DTN." In 2010 3rd International Congress on Image and Signal Processing (CISP). IEEE, 2010. http://dx.doi.org/10.1109/cisp.2010.5647905.

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Cao, Lijuan, and Michael Grabchak. "Smoothly truncated levy walks: Toward a realistic mobility model." In 2014 IEEE International Performance Computing and Communications Conference (IPCCC). IEEE, 2014. http://dx.doi.org/10.1109/pccc.2014.7017071.

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Pereyra, Marcelo A., and Hadj Batatia. "A levy flight model for ultrasound in skin tissues." In 2010 IEEE Ultrasonics Symposium (IUS). IEEE, 2010. http://dx.doi.org/10.1109/ultsym.2010.5935579.

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Yuan, Yuchen, and Wanqing Song. "Degradation Prediction Of Tool Based On Fractional Levy Prediction Model." In 2022 Global Reliability and Prognostics and Health Management (PHM-Yantai). IEEE, 2022. http://dx.doi.org/10.1109/phm-yantai55411.2022.9942217.

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Xing, Jie, Toby Berger, and Terrence J. Sejnowski. "A Berger-Levy energy efficient neuron model with unequal synaptic weights." In 2012 IEEE International Symposium on Information Theory - ISIT. IEEE, 2012. http://dx.doi.org/10.1109/isit.2012.6284081.

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Painter, Scott, and Lincoln Paterson. "Levy Stochastic Model for the Variations in the Properties of Sedimentary Rock." In ECMOR IV - 4th European Conference on the Mathematics of Oil Recovery. European Association of Geoscientists & Engineers, 1994. http://dx.doi.org/10.3997/2214-4609.201411150.

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Benner, Peter, and Martin Redmann. "Approximation and model order reduction for second order systems with Levy-noise." In The 10th AIMS Conference on Dynamical Systems, Differential Equations and Applications (Madrid, Spain). American Institute of Mathematical Sciences, 2015. http://dx.doi.org/10.3934/proc.2015.0945.

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Lin, Shih-Kuei, and Te-Cheng Lin. "The Application of Levy Process with Stochastic Interest Rate in Structural Model." In 2008 3rd International Conference on Innovative Computing Information and Control. IEEE, 2008. http://dx.doi.org/10.1109/icicic.2008.539.

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Kiouach, Driss, and Yassine Sabbar. "Threshold Analysis of the Stochastic Hepatitis B Epidemic Model with Successful Vaccination and Levy Jumps." In 2019 4th World Conference on Complex Systems (WCCS). IEEE, 2019. http://dx.doi.org/10.1109/icocs.2019.8930709.

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Hong, Seongik, Injong Rhee, Seong Joon Kim, Kyunghan Lee, and Song Chong. "Routing performance analysis of human-driven delay tolerant networks using the truncated levy walk model." In Proceeding of the 1st ACM SIGMOBILE workshop. New York, New York, USA: ACM Press, 2008. http://dx.doi.org/10.1145/1374688.1374694.

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Reports on the topic "Levy model"

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Соловйов, В. М., В. В. Соловйова, and Д. М. Чабаненко. Динаміка параметрів α-стійкого процесу Леві для розподілів прибутковостей фінансових часових рядів. ФО-П Ткачук О. В., 2014. http://dx.doi.org/10.31812/0564/1336.

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Modem market economy of any country cannot successfully behave without the existence of the effective financial market. In the conditions of growing financial market, it is necessary to use modern risk-management methods, which take non-gaussian distributions into consideration. It is known, that financial and economic time series return’s distributions demonstrate so-called «heavy tails», which interrupts the modeling o f these processes with classical statistical methods. One o f the models, that is able to describe processes with «heavy tails», are the а -stable Levi processes. They can slightly simulate the dynamics of the asset prices, because it consists o f two components: the Brownian motion component and jump component. In the current work the usage of model parameters estimation procedure is proposed, which is based on the characteristic functions and is applied for the moving window for the purpose of financial-economic system’ s state monitoring.
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Gafni, Yedidya, and Vitaly Citovsky. Molecular interactions of TYLCV capsid protein during assembly of viral particles. United States Department of Agriculture, April 2007. http://dx.doi.org/10.32747/2007.7587233.bard.

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Tomato yellow leaf curl geminivirus (TYLCV) is a major pathogen of cultivated tomato, causing up to 100% crop loss in many parts of the world. The present proposal, a continuation of a BARD-funded project, expanded our understanding of the molecular mechanisms by which CP molecules, as well as its pre-coat partner V2, interact with each other (CP), with the viral genome, and with cellular proteins during assembly and movement of the infectious virions. Specifically, two major objectives were proposed: I. To study in detail the molecular interactions between CP molecules and between CP and ssDNA leading to assembly of infectious TYLCV virions. II. To study the roles of host cell factors in TYLCV assembly. Our research toward these goals has produced the following major achievements: • Characterization of the CP nuclear shuttling interactor, karyopherin alpha 1, its pattern of expression and the putative involvement of auxin in regulation of its expression. (#1 in our list of publication, Mizrachy, Dabush et al. 2004). • Identify a single amino acid in the capsid protein’s sequence that is critical for normal virus life-cycle. (#2 in our list of publications, Yaakov, Levy et al. in preparation). • Development of monoclonal antibodies with high specificity to the capsid protein of TYLCV. (#3 in our list of publications, Solmensky, Zrachya et al. in press). • Generation of Tomato plants resistant to TYLCV by expressing transgene coding for siRNA targeted at the TYLCV CP. (#4 in our list of publications, Zrachya, Kumar et al. in press). •These research findings provided significant insights into (i) the molecular interactions of TYLCV capsid protein with the host cell nuclear shuttling receptor, and (ii) the mechanism by which TYLCV V2 is involved in the silencing of PTGS and contributes to the virus pathogenicity effect. Furthermore, the obtained knowledge helped us to develop specific strategies to attenuate TYLCV infection, for example, by blocking viral entry into and/or exit out of the host cell nucleus via siRNA as we showed in our publication recently (# 4 in our list of publications). Finally, in addition to the study of TYLCV nuclear import and export, our research contributed to our understanding of general mechanisms for nucleocytoplasmic shuttling of proteins and nucleic acids in plant cells. Also integration for stable transformation of ssDNA mediated by our model pathogen Agrobacterium tumefaciens led to identification of plant specific proteins involved.
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Clark, Ximena, Danielle Zaror, and José Antonio Mejía-Guerra. Marcos legales estadísticos en América Latina: Realidades, mejores prácticas y recomendaciones. Inter-American Development Bank, December 2020. http://dx.doi.org/10.18235/0002938.

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Este trabajo hace un análisis comparativo de los marcos legales que rigen las Oficinas Nacionales de Estadística (ONEs) de 18 países de América Latina, contrastándolos con las recomendaciones internacionales existentes. Concluye que los marcos son en muchos casos obsoletos, debilitando la institucionalidad y el nivel técnico de las oficinas e impidiendo su habilidad para comunicar sus productos. En casi todos los países, el marco no reúne por lo menos una de las condiciones necesarias para facilitar la producción, el intercambio y la difusión de información, la transparencia, la confidencialidad y protección de datos, o contener las presiones externas que busquen influir en la información producida por la ONE. Un marco legal obsoleto puede ser el canal de conducción de políticas de debilitamiento institucional. No hay leyes perfectas y la legislación requiere ser actualizada para ajustarse a los tiempos, pero está claro que la estabilidad institucional de una ONE no puede estar sujeta a usos y costumbres, sino que debe estar propiamente legislada. El documento identifica áreas de oportunidad y mejores prácticas, y ofrece propuestas concretas en la forma de una ley modelo alineada con las recomendaciones internacionales. La investigación también explora la interacción de la legislación estadística con las legislaciones de acceso a la información pública y de protección de datos personales.
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