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1
Conforti, Giovanni, Pra Paolo Dai, and Sylvie Roelly. "Reciprocal class of jump processes." Universität Potsdam, 2014. http://opus.kobv.de/ubp/volltexte/2014/7077/.
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Processes having the same bridges as a given reference Markov process
constitute its reciprocal class. In this paper we study the reciprocal class
of compound Poisson processes whose jumps belong to a finite set A in R^d.
We propose a characterization of the reciprocal class as the unique set of
probability measures on which a family of time and space transformations
induces the same density, expressed in terms of the reciprocal invariants.
The geometry of A plays a crucial role in the design of the transformations,
and we use tools from discrete geometry to obtain an optimal characterization.
We deduce explicit conditions for two Markov jump processes to belong to the same class. Finally, we provide a natural interpretation of the invariants as short-time asymptotics for the probability that the reference process makes a cycle around its current state.
2
Ornthanalai, Chayawat. "Asset pricing with Lévy jump processes." Thesis, McGill University, 2009. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=66745.
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This thesis comprises of three essays that explore the theoretical development as well as the empirical applications of asset pricing models with Lévy jump processes. The first essay presents a new discrete-time framework that combines heteroskedastic processes with rich specifications of jumps in returns and volatility. Our models can be estimated with ease using standard maximum likelihood techniques. We evaluate the models by fitting a long sample of S&P500 index returns, and by valuing a large sample of options. We find strong empirical support for time-varying jump intensities. A model with jump intensity that is affine in the conditional variance performs particularly well both in return fitting and option valuation. In the second essay, we develop a new class of asset pricing model that combines the flexibility of Lévy processes with the ease of implementation of affine GARCH dynamics. This framework produces a large class of asset return processes that have analytical solutions for their pricing transform, and lead to a simple valuation of derivatives. We apply this newly proposed framework to various two-factor models consisting of a normal and a pure jump Lévy component. The results from joint estimation of options and returns on the market index reveal the important economic role of jumps. We find that models without jumps cannot reconcile the difference between market-realized returns and investors' ex-ante expectations of returns with an economically justifiable equity premium level. In the third essay, we provide evidence that the market crash risk is priced in individual equity options. We proceed by developing a factor model for equity returns and option pricing that takes into account the market's systematic risk factors, namely the market volatility and jump risks. The probability of large negative jumps in the market return produces the "crash fear" effect. In addition to the market risk factors, weCette thèse comporte trois essais qui explorent le développement théorique ainsi que les applications empiriques des modèles d'évaluation d'actifs avec des processus de saut de Lévy. Le premier essai présente un nouveau cadre d'évaluation en temps discret qui combine à la fois des processus heteroskedastic ainsi qu'une large famille de spécifications à base des sauts dans les processus de rendement et de la volatilité. Nos modèles peuvent être facilement estimés en utilisant des techniques standard de maximum de vraisemblance. Nous évaluons les modèles proposés en les adaptant à un long échantillon de rendement sur l'indice S&P500, et en évaluant un grand échantillon d'options. Nous trouvons un fort soutien empirique pour l'existence des sauts avec intensités à temps-variables. Un modèle à saut dont l'intensité est affine avec la variance conditionnelle performe particulièrement bien a la fois pour les rendements ainsi que pour l'évaluation des options. Dans le deuxième essai, nous développons une nouvelle famille de modèles d'évaluations d'actif qui combine la flexibilité des processus de Lévy avec la facilité d'implémentations des modèles affines GARCH. Ce cadre résulte à une grande classe des processus de rendement des actifs qui ont des solutions analytiques pour leur «transforme», et mène à une évaluation simple des produits dérivés. Nous appliquons ce cadre nouvellement proposé à de divers modèles à deux-facteurs-une composante normale et une autre a base du processus à saut de Lévy. Les résultats de l'évaluation commune des options et des rendements sur l'indice du marché indiquent le rôle économique important des sauts. Nous constatons que les modèles sans sauts ne peuvent pas réconcilier la différence entre les rendements réalisés du marché et les espérances des investisseurs concernant les rendements avec un niveau de prime de risque économiquemen
3
Xia, Yuan. "Multilevel Monte Carlo for jump processes." Thesis, University of Oxford, 2013. http://ora.ox.ac.uk/objects/uuid:7bc8e98a-0216-4551-a1f3-1b318e514ee8.
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This thesis consists of two parts. The first part (Chapters 2-4) considers multilevel Monte Carlo for option pricing in finite activity jump-diffusion models. We use a jump-adapted Milstein discretisation for constant rate cases and with the thinning method for bounded state-dependent rate cases. Multilevel Monte Carlo estimators are constructed for Asian, lookback, barrier and digital options. The computational efficiency is numerically demonstrated and analytically justified. The second part (Chapter 5) deals with option pricing problems in exponential Lévy models where the increments of the underlying process can be directly simulated. We discuss several examples: Variance Gamma, Normal Inverse Gaussian and alpha-stable processes and present numerical experiments of multilevel Monte Carlo for Asian, lookback, barrier options, where the running maximum of the Lévy process involved in lookback and barrier payoffs is approximated using discretely monitored maximum. To analytically verify the computational complexity of multilevel method, we also prove some upper bounds on Lp convergence rate of discretely monitored error for a broad class of Lévy processes.
4
Skoog, Daniel. "Jump processes and the implied volatility curve." Thesis, Uppsala University, Department of Mathematics, 2008. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-120040.
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Saeedi, Ardavan. "Nonparametric Bayesian models for Markov jump processes." Thesis, University of British Columbia, 2012. http://hdl.handle.net/2429/42963.
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Markov jump processes (MJPs) have been used as models in various fields such as
disease progression, phylogenetic trees, and communication networks. The main
motivation behind this thesis is the application of MJPs to data modeled as having
complex latent structure. In this thesis we propose a nonparametric prior, the
gamma-exponential process (GEP), over MJPs. Nonparametric Bayesian models
have recently attracted much attention in the statistics community, due to their flexibility,
adaptability, and usefulness in analyzing complex real world datasets. The
GEP is a prior over infinite rate matrices which characterize an MJP; this prior can
be used in Bayesian models where an MJP is imposed on the data but the number of
states of the MJP is unknown in advance. We show that the GEP model we propose
has some attractive properties such as conjugacy and simple closed-form predictive
distributions. We also introduce the hierarchical version of the GEP model;
sharing statistical strength can be considered as the main motivation behind the hierarchical
model. We show that our hierarchical model admits efficient inference
algorithms. We introduce two inference algorithms: 1) a “basic” particle Markov
chain Monte Carlo (PMCMC) algorithm which is an MCMC algorithm with sequences
proposed by a sequential Monte Carlo (SMC) algorithm; 2) a modified
version of this PMCPC algorithm with an “improved” SMC proposal. Finally, we
demonstrate the algorithms on the problems of estimating disease progression in
multiple sclerosis and RNA evolutionary modeling. In both domains, we found
that our model outperformed the standard rate matrix estimation approach.
6
Bu, Tianren. "Option pricing under exponential jump diffusion processes." Thesis, University of Manchester, 2018. https://www.research.manchester.ac.uk/portal/en/theses/option-pricing-under-exponential-jump-diffusion-processes(0dab0630-b8f8-4ee8-8bf0-8cd0b9b9afc0).html.
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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.
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Mina, Francesco. "On Markovian approximation schemes of jump processes." Thesis, Imperial College London, 2014. http://hdl.handle.net/10044/1/48049.
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The topic of this thesis is the study of approximation schemes of jump processes whose driving noise is a Levy process. In the first part of our work we study properties of the driving noise. We present a novel approximation method for the density of a Levy process. The scheme makes use of a continuous time Markov chain defined through a careful analysis of the generator. We identify the rate of convergence and carry out a detailed analysis of the error. We also analyse the case of multidimensional Levy processes in the form of subordinate Brownian motion. We provide a weak scheme to approximate the density that does not rely on discretising the Levy measure and results in better convergence rates. The second part of the thesis concerns the analysis of schemes for BSDEs driven by Brownian motion and a Poisson random measure. Such equations appear naturally in hedging problems, stochastic control and they provide a natural probabilistic approach to the solution of certain semi linear PIDEs. While the numerical approximation of the continuous case has been studied in the literature, there has been relatively little progress in the study of such equations with a discontinuous driver. We present a weak Monte Carlo scheme in this setting based on Picard iterations. We discuss its convergence and provide a numerical illustration.
8
Wong, Wee Chin. "Estimation and control of jump stochastic systems." Diss., Atlanta, Ga. : Georgia Institute of Technology, 2009. http://hdl.handle.net/1853/31775.
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Thesis (Ph.D)--Chemical Engineering, Georgia Institute of Technology, 2010.Committee Chair: Jay H. Lee; Committee Member: Alexander Gray; Committee Member: Erik Verriest; Committee Member: Magnus Egerstedt; Committee Member: Martha Grover; Committee Member: Matthew Realff. Part of the SMARTech Electronic Thesis and Dissertation Collection.
9
Dursun, Havva Ozlem. "Jump Detection With Power And Bipower Variation Processes." Master's thesis, METU, 2007. http://etd.lib.metu.edu.tr/upload/12608940/index.pdf.
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In this study, we show that realized bipower variation which is an extension of realized power variation is an alternative method that estimates integrated variance like realized variance. It is seen that realized bipower variation is robust to rare jumps. Robustness means that if we add rare jumps to a stochastic volatility process, realized bipower variation process continues to estimate integrated variance although realized variance estimates integrated variance plus the quadratic variation of the jump component. This robustness is crucial since it separates the discontinuous component of quadratic variation which comes from the jump part of the logarithmic price process. Thus, we demonstrate that if the logarithmic price process is in the class of stochastic volatility plus rare jumps processes then the difference between realized variance and realized bipower variation process estimates the discontinuous component of the quadratic variation. So, quadratic variation of the jump component can be estimated and jump detection can be achieved.
10
El-Bachir, Naoufel. "Stochastic default intensity modeling with dependent jump processes." Thesis, University of Reading, 2008. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.515698.
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Düvelmeyer, Dana, and Bernd Hofmann. "Ill-posedness of parameter estimation in jump diffusion processes." Universitätsbibliothek Chemnitz, 2004. http://nbn-resolving.de/urn:nbn:de:swb:ch1-200401199.
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In this paper, we consider as an inverse problem the simultaneous estimation
of the five parameters of a jump diffusion process from return observations of a
price trajectory. We show that there occur some ill-posedness phenomena in the
parameter estimation problem, because the forward operator fails to be injective
and small perturbations in the data may lead to large changes in the solution. We
illustrate the instability effect by a numerical case study. To overcome the difficulty
coming from ill-posedness we use a multi-parameter regularization approach that
finds a trade-off between a least-squares approach based on empircal densities and
a fitting of semi-invariants. In this context, a fixed point iteration is proposed that
provides good results for the example under consideration in the case study.
12
Hosking, John Joseph Absalom. "Malliavin calculus for functionals of pure jump Levy processes." Thesis, Imperial College London, 2009. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.502116.
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Klein, Markus, Christian Léonard, and Elke Rosenberger. "Agmon-type estimates for a class of jump processes." Universität Potsdam, 2012. http://opus.kobv.de/ubp/volltexte/2012/5699/.
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In the limit we analyze the generators of families of reversible jump processes in the n-dimensional space associated with a class of symmetric non-local Dirichlet forms and show exponential decay of the eigenfunctions. The exponential rate function is a Finsler distance, given as solution of certain eikonal equation. Fine results are sensitive to the rate functions being twice differentiable or just Lipschitz. Our estimates are similar to the semiclassical Agmon estimates for differential operators of second order. They generalize and strengthen previous results on the lattice.
14
Lee, Sanghoon. "Econometrics of jump-diffusion processes : approximation, estimation and forecasting." Thesis, University of Southampton, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.364734.
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Chatzipanagou, Eleftheria. "Computational option pricing under jump diffusion and Lévy processes." Thesis, University of Greenwich, 2015. http://gala.gre.ac.uk/18087/.
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The shortcomings of diffusion models in representing the risk related to large market movements have led to the development of various option pricing models with jumps. These models allow for a more realistic representation of price dynamics and greater flexibility in modelling and have therefore been the focus of much recent work. In this thesis the development of a robust finite difference method for the option pricing under jump-diffusion and Lévy processes is presented and its effectiveness is demonstrated on a range of pricing models.
16
Landwehr, Sandra. "On the geometry related to jump processes : investigating transition functions of Levy and Levy-type processes." Thesis, Swansea University, 2010. https://cronfa.swan.ac.uk/Record/cronfa42253.
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In this thesis, we study some geometrical aspects of metric measure spaces (Rn, psi1/2 , mu)where mu is a locally finite regular Borel measure and a metric on psi1/2 which arises from a continuous negative definite function psi : Rn → R which satisfies psi(xi) ≥ 0 with psi(xi) = 0. This study is motivated by the investigation of a transition density estimate for pure jump processes on a general metric measure space. To gain a better insight into the behaviour of transition functions of symmetric Levy processes in this general setting, it seems desirable to understand geometrical properties of their underlying state spaces. More precisely, we show completeness of the metric spaces (Rn, psi1/2) and study under which circumstances open balls Bpsi(x,r), x ∈ Rn, r > 0, with respect to this metric are convex. Moreover, we focus on conditions of the metric measure spaces (Rn,psi1/2 ,mu) for the balls to satisfy the volume growth property [equation] for mu-almost all x ∈ Rn, 0 < r < R and a constant Cpsi(x,R)≥1. Finally, we show that the homogeneity property of a metric measure space can be applied to our case and provide some results associated with the construction of a Hajlasz-Sobolc space over (Rn,psi1/2, lambda(n)),where lambda(n) denotes the n-dirnensional Lebesgue measure.
17
Winter, Jens. "Optimal control of Markovian jump processes with different information structures." [S.l. : s.n.], 2008. http://nbn-resolving.de/urn:nbn:de:bsz:289-vts-65458.
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Kim, Panki. "Potential theory for stable processes /." Thesis, Connect to this title online; UW restricted, 2004. http://hdl.handle.net/1773/5746.
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Ocone, Andrea. "Variational inference for Gaussian-jump processes with application in gene regulation." Thesis, University of Edinburgh, 2013. http://hdl.handle.net/1842/8280.
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In the last decades, the explosion of data from quantitative techniques has revolutionised our understanding of biological processes. In this scenario, advanced statistical methods and algorithms are becoming fundamental to decipher the dynamics of biochemical mechanisms such those involved in the regulation of gene expression. Here we develop mechanistic models and approximate inference techniques to reverse engineer the dynamics of gene regulation, from mRNA and/or protein time series data. We start from an existent variational framework for statistical inference in transcriptional networks. The framework is based on a continuous-time description of the mRNA dynamics in terms of stochastic differential equations, which are governed by latent switching variables representing the on/off activity of regulating transcription factors. The main contributions of this work are the following. We speeded-up the variational inference algorithm by developing a method to compute a posterior approximate distribution over the latent variables using a constrained optimisation algorithm. In addition to computational benefits, this method enabled the extension to statistical inference in networks with a combinatorial model of regulation. A limitation of this framework is the fact that inference is possible only in transcriptional networks with a single-layer architecture (where a single or couples of transcription factors regulate directly an arbitrary number of target genes). The second main contribution in this work is the extension of the inference framework to hierarchical structures, such as feed-forward loop. In the last contribution we define a general structure for transcription-translation networks. This work is important since it provides a general statistical framework to model complex dynamics in gene regulatory networks. The framework is modular and scalable to realistically large systems with general architecture, thus representing a valuable alternative to traditional differential equation models. All models are embedded in a Bayesian framework; inference is performed using a variational approach and compared to exact inference where possible. We apply the models to the study of different biological systems, from the metabolism in E. coli to the circadian clock in the picoalga O. tauri.
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Saize, Stefane. "Analytical Valuation of American-Style Asian Options under Jump-Diffusion Processes." Thesis, Uppsala universitet, Analys och sannolikhetsteori, 2014. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-224885.
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Koskela, Jere. "Consistency and intractable likelihood for jump diffusions and generalised coalescent processes." Thesis, University of Warwick, 2016. http://wrap.warwick.ac.uk/88065/.
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This thesis has two related aims: establishing tractable conditions for posterior consistency of statistical inference from non-IID data with an intractable likelihood, and developing Monte Carlo methodology for conducting such inference. Two prominent classes of models, jump diffusions and generalised coalescent processes, are considered throughout. Both are motivated by population genetics applications. Posterior consistency of nonparametric inference is established for joint inference of drift and compound Poisson jump components of unit volatility jump diffusions in arbitrary dimension under an identifiability assumption. This assumption is straightforward to verify in the diffusion case, but difficult to check in general for jump diffusions. A similar consistency result is established under somewhat weaker conditions for Λ-coalescent processes whenever time series data is available. I also show that Λ-coalescent inference cannot be consistent if observations are contemporaneous, in stark contrast to the more classical case of the Kingman coalescent. I also introduce the notion of reverse time sequential Monte Carlo (SMC), which has previously been applied to Kingman and Λ-coalescents. Here, reverse time SMC is presented as a generic algorithm, and general conditions under which it is effective are developed. In brief, it is well suited to integration over paths which begin at a mode of the target distribution, and terminate in the tails. These innovations are used to design new SMC algorithms for generalised coalescent processes, as well as non-coalescent examples including evaluating a containment probability of the hyperbolic diffusion, an overflow probability in a queueing model and finding an initial infection in an epidemic network model.
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Merino, Fernández Raúl. "Option Price Decomposition for Local and Stochastic Volatility Jump Diffusion Models." Doctoral thesis, Universitat de Barcelona, 2021. http://hdl.handle.net/10803/671682.
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In this thesis, an option price decomposition for local and stochastic volatility jump diffusion models is studied. On the one hand, we generalise and extend the Alòs decomposition to be used in a wide variety of models such as a general stochastic volatility model, a stochastic volatility jump dffusion model with finite activity or a rough volatility model.
Furthermore, we note that in the case of local volatility models, speci_cally, spot-dependent models, a new decomposition formula must be used to obtain good numerical results. In particular, we study the CEV model. On the other hand, we observe that the approximation formula can be improved by using the decomposition formula recursively. Using this decomposition method, the call price can be transformed into a Taylor type formula containing an infinite series with stochastic terms. New approximation formulae are obtained in the Heston model case, finding better approximations.En aquesta tesi, s'estudia una descomposició del preu d'una opció per a models de volatilitat local i volatilitat estocàstica amb salts. D'una banda, generalitzem i estenem la descomposició d'Alòs per a ser utilitzada en una àmplia varietat de models com, per exemple, un model de volatilitat estocàstica general, un model de volatilitat estocàstica amb salts d'activitat finita o un model de volatilitat 'rough'. A més a més, veiern que en el cas dels models de volatilitat local, en particular, els models dependents del 'spot' s'ha d'utilitzar una nova fórmula de descomposició per a obtenir bons resultats numèrics. En particular, estudiem el model CEV. D'altra banda, observem que la fórmula d'aproximació es pot millorar utilitzant la formula de descomposició de forma recursiva. Mitjançant aquesta tècnica de descomposició, el preu d'una opció de compra es pot transformar en una formula tipus Taylor que conté una sèrie infinita de termes estocàstics. S'obtenen noves fórmules d'aproximació en el cas del model de Heston, trobant una millor aproximació.
En esta tesis, se estudia una descomposición del precio de una opción para los modelos de volatilidad local y volatilidad estocástica con saltos. Por un lado, generalizamos y ampliamos la descomposición de Alòs para ser utilizada en una amplia variedad de modelos como, por ejemplo, un modelo de volatilidad estocástica general, un modelo de volatilidad estocástica con saltos de actividad finita o un modelo de volatilidad 'rough'. Además, vemos que en el caso de los modelos de volatilidad local, en particular, los modelos dependientes del 'spot', se debe utilizar una nueva fórmula de descomposición para obtener buenos resultados numéricos. En particular, estudiamos el modelo CEV. Por otro lado, observamos que la fórmula de aproximación se puede mejorar utilizando la fórmula de descomposición de forma recursiva. Mediante esta técnica de descomposición, el precio de una opción de compra se puede transformar en una fórmula tipo Taylor que contiene una serie infinita de términos estocásticos. Se obtienen nuevas fórmulas de aproximación en el caso del modelo de Heston, encontrando una mejor aproximación.
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Altay, Suhan. "On Forward Interest Rate Models: Via Random Fields And Markov Jump Processes." Master's thesis, METU, 2007. http://etd.lib.metu.edu.tr/upload/12608342/index.pdf.
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The essence of the interest rate modeling by using Heath-Jarrow-Morton framework is to find the drift condition of the instantaneous forward rate dynamics so that the entire term structure is arbitrage free. In this study, instantaneous forward interest rates are modeled using random fields and Markov Jump processes and the drift conditions of the forward rate dynamics are given. Moreover, the methodology presented in this study is extended to certain financial settings and instruments such as multi-country interest rate models, term structure of defaultable bond prices and forward measures. Also a general framework for bond prices via nuclear space valued semi-martingales is introduced.
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Iles, R. J. "Financial modelling and derivative pricing in the energy markets with jump processes." Thesis, Imperial College London, 2008. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.543458.
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Bambe, Moutsinga Claude Rodrigue. "Transform analysis of affine jump diffusion processes with applications to asset pricing." Diss., Pretoria : [s.n.], 2008. http://upetd.up.ac.za/thesis/available/etd-06112008-162807.
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Zhuang, Yuanying. "Some geometric considerations related to transition densities of jump-type Markov processes." Thesis, Swansea University, 2012. https://cronfa.swan.ac.uk/Record/cronfa42956.
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CALVIA, ALESSANDRO. "Optimal control of pure jump Markov processes with noise-free partial observation." Doctoral thesis, Università degli Studi di Milano-Bicocca, 2018. http://hdl.handle.net/10281/199013.
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La presente tesi tratta un problema di controllo ottimo su orizzonte temporale infinito per un processo di puro salto Markoviano e con osservazione parziale di tipo noise-free. È definita una coppia di processi stocastici, detti processo non osservato o segnale e processo osservato o dei dati. Il segnale è un processo di puro salto Markoviano a tempo continuo, a valori in uno spazio metrico completo e separabile, di cui è nota la misura controllata dei tassi di transizione. Il processo osservato prende valori in un ulteriore spazio metrico completo e separabile ed è di tipo noise-free. Con questa espressione si intende che i suoi valori a ogni tempo t sono funzione dei corrispondenti valori al tempo t del processo non osservato. Si fa l’ipotesi che tale funzione sia un’applicazione deterministica e, senza perdita di generalità, suriettiva tra gli spazi di stato dei processi non osservato e osservato. L’obiettivo è controllare la dinamica del processo non osservato, ossia la sua misura controllata dei tassi di transizione, attraverso un processo di controllo, il quale prende valori nell’insieme delle misure di probabilità di Borel su uno spazio metrico compatto, detto spazio delle azioni di controllo. I controlli ammissibili per il nostro problema sono i processi appena descritti che siano anche prevedibili rispetto alla filtrazione naturale del processo osservato. Il processo di controllo è scelto in questa classe al fine di minimizzare un funzionale costo con fattore di sconto su orizzonte temporale infinito. L’estremo inferiore di tale funzionale costo tra tutti i controlli ammissibili è la funzione valore.
Per studiare la funzione valore è necessario un passo preliminare. Il problema di controllo ottimo a osservazione parziale deve essere espresso come problema a osservazione completa. Ciò è possibile grazie allo studio del processo di filtraggio, un processo a valori in misure che fornisce a ogni istante t la legge condizionale del processo non osservato data l’osservazione disponibile fino al tempo t (rappresentata dalla filtrazione naturale del processo osservato al tempo t). Si dimostra che il processo di filtraggio soddisfa un’equazione differenziale stocastica esplicita e si caratterizza tale processo come Piecewise Deterministic Markov Process, nel senso di Davis.
Allo scopo di trattare il processo di filtraggio come variabile di stato, si studia un problema di controllo separato. Questo è definito come problema a tempo discreto e si mostra che è equivalente a quello originario, nel senso che le rispettive funzioni valore sono legate da una formula esplicita. Si dimostra, inoltre, che i controlli ammissibili per il problema originario e le strategie ammissibili di quello separato hanno una ben precisa struttura ed esiste una specifica relazione tra di essi.
Si caratterizza, quindi, la funzione valore del problema di controllo separato (dunque, indirettamente, la funzione valore del problema originario) come unico punto fisso di un operatore di contrazione, il quale agisce dallo spazio delle funzioni continue e limitate sullo spazio di stato del processo di filtraggio in sé. Di conseguenza, si dimostra che la funzione valore è continua e limitata.
Si studia anche il caso di un processo non osservato dato da una catena di Markov a stati finiti. In questo contesto, si mostra che la funzione valore del problema di controllo separato è uniformemente continua sullo spazio di stato del processo di filtraggio e che è l’unica soluzione viscosa vincolata (nel senso di Soner) di un’equazione di Hamilton-Jacobi-Bellman. Si dimostra, inoltre, che esiste un controllo ottimo ordinario, ossia un processo di controllo che prende valori nell’insieme delle azioni di controllo, e che tale processo è un piecewise open-loop control nel senso di Vermes.This thesis is concerned with an infinite horizon optimal control problem for a pure jump Markov process with noise-free partial observation. We are given a pair of stochastic processes, named unobserved or signal process and observed or data process. The signal process is a continuous-time pure jump Markov process, taking values in a complete and separable metric space, whose controlled rate transition measure is known. The observed process takes values in another complete and separable metric space and is of noise-free type. With this we mean that its values at each time t are given as a function of the corresponding values at time t of the unobserved process. We assume that this function is a deterministic and, without loss of generality, surjective map between the state spaces of the signal and data processes. The aim is to control the dynamics of the unobserved process, i.e. its controlled rate transition measure, through a control process, taking values in the set of Borel probability measures on a compact metric space, named set of control actions. We take as admissible controls for our problem all the processes of this kind that are also predictable with respect to the natural filtration of the data process. The control process is chosen in this class to minimize a discounted cost functional on infinite time horizon. The infimum of this cost functional among all admissible controls is the value function. In order to study the value function a preliminary step is required. We need to recast our optimal control problem with partial observation into a problem with complete observation. This is done studying the filtering process, a measure-valued stochastic process providing at each time t the conditional law of the unobserved process given the available observations up to time t (represented by the natural filtration of the data process at time t). We show that the filtering process satisfies an explicit stochastic differential equation and we characterize it as a Piecewise Deterministic Markov Process, in the sense of Davis. To treat the filtering process as a state variable, we study a separated optimal control problem. We introduce it as a discrete-time one and we show that it is equivalent to the original one, i.e. their respective value functions are linked by an explicit formula. We also show that admissible controls of the original problem and admissible policies of the separated one have a specific structure and there is a precise relationship between them. Next, we characterize the value function of the separated control problem (hence, indirectly, the value function of the original control problem) as the unique fixed point of a contraction mapping, acting from the space of bounded continuous function on the state space of the filtering process into itself. Therefore, we prove that the value function is bounded and continuous. The special case of a signal process given by a finite-state Markov chain is also studied. In this setting, we show that the value function of the separated control problem is uniformly continuous on the state space of the filtering process and that it is the unique constrained viscosity solution (in the sense of Soner) of a Hamilton-Jacobi-Bellman equation. We also prove that an optimal ordinary control exists, i.e. a control process taking values in the set of control actions, and that this process is a piecewise open-loop control in the sense of Vermes.
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Basna, Rani. "Mean Field Games for Jump Non-Linear Markov Process." Doctoral thesis, Linnéuniversitetet, Institutionen för matematik (MA), 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-55852.
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The mean-field game theory is the study of strategic decision making in very large populations of weakly interacting individuals. Mean-field games have been an active area of research in the last decade due to its increased significance in many scientific fields. The foundations of mean-field theory go back to the theory of statistical and quantum physics. One may describe mean-field games as a type of stochastic differential game for which the interaction between the players is of mean-field type, i.e the players are coupled via their empirical measure. It was proposed by Larsy and Lions and independently by Huang, Malhame, and Caines. Since then, the mean-field games have become a rapidly growing area of research and has been studied by many researchers. However, most of these studies were dedicated to diffusion-type games. The main purpose of this thesis is to extend the theory of mean-field games to jump case in both discrete and continuous state space. Jump processes are a very important tool in many areas of applications. Specifically, when modeling abrupt events appearing in real life. For instance, financial modeling (option pricing and risk management), networks (electricity and Banks) and statistics (for modeling and analyzing spatial data). The thesis consists of two papers and one technical report which will be submitted soon: In the first publication, we study the mean-field game in a finite state space where the dynamics of the indistinguishable agents is governed by a controlled continuous time Markov chain. We have studied the control problem for a representative agent in the linear quadratic setting. A dynamic programming approach has been used to drive the Hamilton Jacobi Bellman equation, consequently, the optimal strategy has been achieved. The main result is to show that the individual optimal strategies for the mean-field game system represent 1/N-Nash equilibrium for the approximating system of N agents. As a second article, we generalize the previous results to agents driven by a non-linear pure jump Markov processes in Euclidean space. Mathematically, this means working with linear operators in Banach spaces adapted to the integro-differential operators of jump type and with non-linear partial differential equations instead of working with linear transformations in Euclidean spaces as in the first work. As a by-product, a generalization for the Koopman operator has been presented. In this setting, we studied the control problem in a more general sense, i.e. the cost function is not necessarily of linear quadratic form. We showed that the resulting unique optimal control is of Lipschitz type. Furthermore, a fixed point argument is presented in order to construct the approximate Nash Equilibrium. In addition, we show that the rate of convergence will be of special order as a result of utilizing a non-linear pure jump Markov process. In a third paper, we develop our approach to treat a more realistic case from a modelling perspective. In this step, we assume that all players are subject to an additional common noise of Brownian type. We especially study the well-posedness and the regularity for a jump version of the stochastic kinetic equation. Finally, we show that the solution of the master equation, which is a type of second order partial differential equation in the space of probability measures, provides an approximate Nash Equilibrium. This paper, unfortunately, has not been completely finished and it is still in preprint form. Hence, we have decided not to enclose it in the thesis. However, an outlook about the paper will be included.
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Sedova, Ada. "Conditions for deterministic limits of markov jump processes| The Kurtz theorem in chemistry." Thesis, State University of New York at Albany, 2015. http://pqdtopen.proquest.com/#viewpdf?dispub=1588003.
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A theorem by Kurtz on convergence of Markov jump processes is presented as it relates to the use of the chemical master equation. Necessary mathematical background in the theory of stochastic processes is developed, as well as requirements of the mathematical model necessitated by results in the physical sciences. Applicability and usefulness of the master equation for this type of combinatorial model in chemistry is discussed, as well as analytical connections and modern applications in multiple research fields.
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Erbar, Matthias [Verfasser]. "Ricci curvature and gradient flows of the entropy for jump processes / Matthias Erbar." Bonn : Universitäts- und Landesbibliothek Bonn, 2013. http://d-nb.info/1044869372/34.
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Chaker, Jamil [Verfasser], and Moritz [Akademischer Betreuer] KaßMann. "Analysis of anisotropic nonlocal operators and jump processes / Jamil Chaker ; Betreuer: Moritz Kaßmann." Bielefeld : Universitätsbibliothek Bielefeld, 2017. http://d-nb.info/1150181672/34.
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Mattioli, Mauro. "Estimates on degenerate jump-diffusion processes and regularity of the related valuation equation." Doctoral thesis, Luiss Guido Carli, 2011. http://hdl.handle.net/11385/200886.
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Many risk-neutral pricing problems proposed in the finance literature require
to be dealt with by solving the corresponding Partial Integro-Differential Equation. Unfortunately, neither the standard Sobolev spaces theory, or the present literature on viscosity
solution theory is able to deal with some problems of interest in finance. A recent result presented by Costantini, Papi and D’Ippoliti accepted for pubblication on Finance and
Stochastics [17], shows that, under general conditions on the coefficients of the stochastic
integro-differential equation, whenever a Lyapunov-type condition is satisfied, the stochastic process does not reach the boundary of the domain where is defined. Furthermore, in
the same work it has been proved that there exists a unique viscosity solution to the pricing
problem when we deal with the corresponding pricing problem for European-type derivatives. The viscosity solution theory ensures just the continuity of the solution, when data
are continuous, but does not guarantees that such a solution has some additional regularity.
The aim of this work is to improve, for the pure differential case, the results existing in
literature dealing with the regularity of both the solutions X of the underlying stochastic
differential equations, and the solutions of the corresponding PDE. In particular we will
provide some estimates related to dependence with respect to the initial data for the process
X. Furthermore, dealing with the pricing problem, we improve our understanding on the
assumptions that ensure the viscosity solution to have additional regularity properties beside
the mere continuity.
A Lipschitz-type dependence result with respect to initial data, until a stopping time τ ,
is shown whenever the coefficients are locally Lipschitz continuous, and a Lyapunov-type
condition is satisfied. Such a result can be improved if a suitable weight function is put in
place.
A standard result in PDE theory ensures that, if the assumptions we assume in our work are
satisfied, then in each compact subset where the diffusion matrix is positive defined, there
exists a unique classical solution to the localized problem if initial data are continuous (see
e.g. [35] or [9]). We make use of such a result in order to prove that this classical solution
coincides, in the same subset, with the unique viscosity solution found in [17].
We give an application of such results, applying our evidences to the stochastic volatility
model proposed by Ekstrom and Tysk in [29]. In such a case all the hypotheses we are ¨
currently assuming are satisfied, and the expression of the Lyapunov function can be explicitely provided for different final payoff. As a consequence, we are able to get the results
of the existence and uniqueness of a classical solution to the pricing problem presented in[29] in an independent way. Furthermore it is possible to consider weakened assumptions
on the final payoff. On the other hand we try to consider a generalization of the model,
allowing the process exhibits sudden jumps provided that the jump measure satisfies some
suitable properties. In such a case, the expression for the Lyapunov function is provided as
well, hence we are able to state that the considered valuation problem admits one and only
one viscosity solution.
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CASELLA, BRUNO. "Exact Monte Carlo simulation of diffusion and jump diffusion processes with financial applications." Doctoral thesis, Università Bocconi, 2006. http://hdl.handle.net/11565/4050232.
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Qian, Kun. "Asymptotics of the first hitting times of Markov jump processes with applications to ATM." Thesis, University of Ottawa (Canada), 1993. http://hdl.handle.net/10393/6907.
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This dissertation has three parts. The first part (Chapter 2) is about the asymptotics of the distribution of the first hitting time of a forbidden set by a Markov jump process. Explicit error bounds for the departure of the hitting time distribution from exponentiality are provided. The second part (Chapter 3 and Chapter 4, joint with Ian Iscoe and David McDonald) discusses the capacity of an ATM multiplexor in terms of the probability distribution of the time until the first occurrence of an excessive demand for bandwidth. In the third part (Chapter 5), the problem of the buffer overflow of an ATM multiplexor is studied. The methods developed give an excellent approximation for the steady-state probabilities of the contents of a buffer driven by heterogeneous sources.
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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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Strauss, Arne Karsten. "Numerical Analysis of Jump-Diffusion Models for Option Pricing." Thesis, Virginia Tech, 2006. http://hdl.handle.net/10919/33917.
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Jump-diffusion models can under certain assumptions be expressed as partial integro-differential equations (PIDE). Such a PIDE typically involves a convection term and a nonlocal integral like for the here considered models of Merton and Kou. We transform the PIDE to eliminate the convection term, discretize it implicitly using finite differences and the second order backward difference formula (BDF2) on a uniform grid. The arising dense linear system is solved by an iterative method, either a splitting technique or a circulant preconditioned conjugate gradient method. Exploiting the Fast Fourier Transform (FFT) yields the solution in only $O(n\log n)$ operations and just some vectors need to be stored. Second order accuracy is obtained on the whole computational domain for Merton's model whereas for Kou's model first order is obtained on the whole computational domain and second order locally around the strike price. The solution for the PIDE with convection term can oscillate in a neighborhood of the strike price depending on the choice of parameters, whereas the solution obtained from the transformed problem is stabilized.Master of Science
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Veraart, Almut Elisabeth Dorothea. "Volatility estimation and inference in the presence of jumps." Thesis, University of Oxford, 2007. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.670107.
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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 Lévy 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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Zhang, Siyu. "Pricing caps and swaptions when bond prices follow jump-diffusion processes and have log-price volatility." [Bloomington, Ind.] : Indiana University, 2008. http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqdiss&rft_dat=xri:pqdiss:3307569.
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Thesis (Ph.D.)--Indiana University, Dept. of Mathematics, 2008.Title from PDF t.p. (viewed Dec. 9, 2008). Source: Dissertation Abstracts International, Volume: 69-05, Section: B, page: 3039. Adviser: Victor Goodman.
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Mongwe, Wilson Tsakane. "Analysis of equity and interest rate returns in South Africa under the context of jump diffusion processes." Master's thesis, University of Cape Town, 2015. http://hdl.handle.net/11427/16600.
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Includes bibliographical referencesOver the last few decades, there has been vast interest in the modelling of asset returns using jump diffusion processes. This was in part as a result of the realisation that the standard diffusion processes, which do not allow for jumps, were not able to capture the stylized facts that return distributions are leptokurtic and have heavy tails. Although jump diffusion models have been identified as being useful to capture these stylized facts, there has not been consensus as to how these jump diffusion models should be calibrated. This dissertation tackles this calibration issue by considering the basic jump diffusion model of Merton (197G) applied to South African equity and interest rate market data. As there is little access to frequently updated volatility surfaces and option price data in South Africa, the calibration methods that are used in this dissertation are those that require historical returns data only. The methods used are the standard Maximum Likelihood Estimation (MLE) approach, the likelihood profiling method of Honore (1998), the Method of Moments Estimation (MME) technique and the Expectation Maximisation (EM) algorithm. The calibration methods are applied to both simulated and empirical returns data. The simulation and empirical studies show that the standard MLE approach sometimes produces estimators which are not reliable as they are biased and have wide confidence intervals. This is because the likelihood function required for the implementation of the MLE method is not bounded. In the simulation studies, the MME approach produces results which do not make statistical sense, such as negative variances, and is thus not used in the empirical analysis. The best method for calibrating the jump diffusion model to the empirical data is chosen by comparing the width of the bootstrap confidence intervals of the estimators produced by the methods. The empirical analysis indicates that the best method for calibrating equity returns is the EM approach and the best method for calibrating interest rate returns is the likelihood profiling method of Honore (1998).
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Gleeson, Cameron Banking & Finance Australian School of Business UNSW. "Pricing and hedging S&P 500 index options : a comparison of affine jump diffusion models." Awarded by:University of New South Wales. School of Banking and Finance, 2005. http://handle.unsw.edu.au/1959.4/22379.
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This thesis examines the empirical performance of four Affine Jump Diffusion models in pricing and hedging S&P 500 Index options: the Black Scholes (BS) model, Heston???s Stochastic Volatility (SV) model, a Stochastic Volatility Price Jump (SVJ) model and a Stochastic Volatility Price-Volatility Jump (SVJJ) model. The SVJJ model structure allows for simultaneous jumps in price and volatility processes, with correlated jump size distributions. To the best of our knowledge this is the first empirical study to test the hedging performance of the SVJJ model. As part of our research we derive the SVJJ model minimum variance hedge ratio. We find the SVJ model displays the best price prediction. The SV model lacks the structural complexity to eliminate Black Scholes pricing biases, whereas our results indicate the SVJJ model suffers from overfitting. Despite significant evidence from in and out-of-sample pricing that the SV and SVJ models were better specified than the BS model, this did not result in an improvement in dynamic hedging performance. Overall the BS delta hedge and SV minimum variance hedge produced the lowest errors, although their performance across moneyness-maturity categories differed greatly. The SVJ model???s results were surprisingly poor given its superior performance in out-of-sample pricing. We attribute the inadequate performance of the jump models to the lower hedging ratios these models provided, which may be a result of the negative expected jump sizes.
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Neuhoff, Daniel. "Reversible Jump Markov Chain Monte Carlo." Doctoral thesis, Humboldt-Universität zu Berlin, Wirtschaftswissenschaftliche Fakultät, 2016. http://dx.doi.org/10.18452/17461.
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Die vier in der vorliegenden Dissertation enthaltenen Studien beschäftigen sich vorwiegend mit dem dynamischen Verhalten makroökonomischer Zeitreihen. Diese Dynamiken werden sowohl im Kontext eines einfachen DSGE Modells, als auch aus der Sichtweise reiner Zeitreihenmodelle untersucht.The four studies of this thesis are concerned predominantly with the dynamics of macroeconomic time series, both in the context of a simple DSGE model, as well as from a pure time series modeling perspective.
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Mboussa, Anga Gael. "Calibration and Model Risk in the Pricing of Exotic Options Under Pure-Jump Lévy Dynamics." Thesis, Stellenbosch : Stellenbosch University, 2015. http://hdl.handle.net/10019.1/98030.
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Thesis (MSc)--Stellenbosch University, 2015AFRIKAANSE OPSOMMING : Die groeiende belangstelling in kalibrering en modelrisiko is ’n redelik resente ontwikkeling in finansiële wiskunde. Hierdie proefskrif fokusseer op hierdie sake, veral in verband met die prysbepaling van vanielje-en eksotiese opsies, en vergelyk die prestasie van verskeie Lévy modelle. ’n Nuwe metode om modelrisiko te meet word ook voorgestel (hoofstuk 6). Ons kalibreer eers verskeie Lévy modelle aan die log-opbrengs van die S&P500 indeks. Statistiese toetse en grafieke voorstellings toon albei aan dat suiwer sprongmodelle (VG, NIG en CGMY) die verdeling van die opbrengs beter beskryf as die Black-Scholes model. Daarna kalibreer ons hierdie vier modelle aan S&P500 indeks opsie data en ook aan "CGMY-wˆ ereld" data (’n gesimuleerde wÃłreld wat beskryf word deur die CGMY-model) met behulp van die wortel van gemiddelde kwadraat fout. Die CGMY model vaar beter as die VG, NIG en Black-Scholes modelle. Ons waarneem ook ’n effense verskil tussen die nuwe parameters van CGMY model en sy wisselende parameters, ten spyte van die feit dat CGMY model gekalibreer is aan die "CGMYwêreld" data. Versperrings-en terugblik opsies word daarna geprys, deur gebruik te maak van die gekalibreerde parameters vir ons modelle. Hierdie pryse word dan vergelyk met die "ware" pryse (bereken met die ware parameters van die "CGMY-wêreld), en ’n beduidende verskil tussen die modelpryse en die "ware" pryse word waargeneem. Ons eindig met ’n poging om hierdie modelrisiko te kwantiseer
ENGLISH ABSTRACT : The growing interest in calibration and model risk is a fairly recent development in financial mathematics. This thesis focussing on these issues, particularly in relation to the pricing of vanilla and exotic options, and compare the performance of various Lévy models. A new method to measure model risk is also proposed (Chapter 6). We calibrate only several Lévy models to the log-return of S&P500 index data. Statistical tests and graphs representations both show that pure jump models (VG, NIG and CGMY) the distribution of the proceeds better described as the Black-Scholes model. Then we calibrate these four models to the S&P500 index option data and also to "CGMY-world" data (a simulated world described by the CGMY model) using the root mean square error. Which CGMY model outperform VG, NIG and Black-Scholes models. We observe also a slight difference between the new parameters of CGMY model and its varying parameters, despite the fact that CGMY model is calibrated to the "CGMY-world" data. Barriers and lookback options are then priced, making use of the calibrated parameters for our models. These prices are then compared with the "real" prices (calculated with the true parameters of the "CGMY world), and a significant difference between the model prices and the "real" rates are observed. We end with an attempt to quantization this model risk.
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Dillinger, Michael L. "Component processes of simultaneous interpreting." Thesis, McGill University, 1989. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=39215.
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The component processes specific to simultaneous interpreting and common to interpreting and listening were investigated. Experienced conference interpreters and inexperienced bilinguals performed aural-to-oral simultaneous interpreting of a narrative and a procedure from English into French and then gave a free recall of each immediately afterwards. A comparison group of bilinguals performed a simple listening task with the same materials. The texts were on an unfamiliar topic (positron emission tomography) and differed only with respect to frame type.Experience showed a main effect on interpreting measures, (experienced interpreters performed more accurately), and interacted with text-structure variables that indexed proposition generation, but did not affect recall. Task did not have a main effect on recall and interacted weakly with text-structure variables. Text and Text-structure variables had very strong effects both for the interpreting and the recall measures.
The results were viewed as evidence that interpreting involves the same component processes as normal listening comprehension rather than constituting a specialized comprehension skill. Analyses of text-structure variables provided evidence for influence of high-level conceptual processing and other component processes both on line and off line. Since there was no evidence that interpreting interfered with comprehension, the qualitative on-line measures possible in the interpreting task appear to be generalizable to comprehension under more usual circumstances.
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Thiffault, Johanne. "Estimation for homogeneous Poisson processes." Thesis, McGill University, 1985. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=63370.
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Ferns, Norman Francis. "Metrics for Markov decision processes." Thesis, McGill University, 2003. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=80263.
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We present a class of metrics, defined on the state space of a finite Markov decision process (MDP), each of which is sound with respect to stochastic bisimulation, a notion of MDP state equivalence derived from the theory of concurrent processes. Such metrics are based on similar metrics developed in the context of labelled Markov processes, and like those, are suitable for state space aggregation. Furthermore, we restrict our attention to a subset of this class that is appropriate for certain reinforcement learning (RL) tasks, specifically, infinite horizon tasks with an expected total discounted reward optimality criterion. Given such an RL metric, we provide bounds relating it to the optimal value function of the original MDP as well as to the value function of the aggregate MDP. Finally, we present an algorithm for calculating such a metric up to a prescribed degree of accuracy and some empirical results.
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Chaput, Philippe. "Approximating Markov processes by averaging." Thesis, McGill University, 2009. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=66654.
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We recast the theory of labelled Markov processes in a new setting, in a way "dual" to the usual point of view. Instead of considering state transitions as a collection of subprobability distributions on the state space, we view them as transformers of real-valued functions. By generalizing the operation of conditional expectation, we build a category consisting of labelled Markov processes viewed as a collection of operators; the arrows of this category behave as projections on a smaller state space. We define a notion of equivalence for such processes, called bisimulation, which is closely linked to the usual definition for probabilistic processes. We show that we can categorically construct the smallest bisimilar process, and that this smallest object is linked to a well-known modal logic. We also expose an approximation scheme based on this logic, where the state space of the approximants is finite; furthermore, we show that these finite approximants categorically converge to the smallest bisimilar process.Nous reconsidérons les processus de Markov étiquetés sous une nouvelle approche, dans un certain sens "dual'' au point de vue usuel. Au lieu de considérer les transitions d'état en état en tant qu'une collection de distributions de sous-probabilités sur l'espace d'états, nous les regardons en tant que transformations de fonctions réelles. En généralisant l'opération d'espérance conditionelle, nous construisons une catégorie où les objets sont des processus de Markov étiquetés regardés en tant qu'un rassemblement d'opérateurs; les flèches de cette catégorie se comportent comme des projections sur un espace d'états plus petit. Nous définissons une notion d'équivalence pour de tels processus, que l'on appelle bisimulation, qui est intimement liée avec la définition usuelle pour les processus probabilistes. Nous démontrons que nous pouvons construire, d'une manière catégorique, le plus petit processus bisimilaire à un processus donné, et que ce plus petit object est lié à une logique modale bien connue. Nous développons une méthode d'approximation basée sur cette logique, où l'espace d'états des processus approximatifs est fini; de plus, nous démontrons que ces processus approximatifs convergent, d'une manière catégorique, au plus petit processus bisimilaire.
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Jarvandi, Soghra. "Learning processes in food intake." Thesis, McGill University, 2008. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=111915.
Full textAbstract:
Learning processes play a major role in controlling intake of food. Through repeated experiences an animal acquires the ability to predict the postingestive effects of a particular food (i.e., of its nutrients and energy) from its sensory characteristics. What is unclear from the literature, however, is whether an animal can anticipate the duration of subsequent food deprivation from predictive sensory qualities of a food, and hence increase the amount eaten of that cueing food. Therefore, the aim of this work was to investigate the characteristics of this under-researched type of learning, i.e., anticipatory eating, using laboratory rats trained on two lengths of fasting (short: 2-3 h, long: 8-10 h). The main findings were as follows. 1) Anticipatory eating is learnt when a choice is given between protein- and carbohydrate-rich foods as well as on a single balanced test food. 2) The learnt extra intake of food is instrumental to preventing the return of hunger, removal of which negative reinforcement extinguishes the response. 3) The resulting return of hunger induces re-learning of anticipatory eating. 4) During the training sessions, learning of anticipatory eating competes with classical conditioning of sensory preference. Conditioning of preference is likely to be stronger with the shorter than with the longer length of fasting. Therefore, the difference between intakes before the long and the short fast at each trial is the summed result of these two mechanisms of acquired increase in intake. While preference conditioning usually reaches a maximum rapidly, depletion-avoidance increases for as long as has been tested, with interruptions of rapid self-extinction and re-learning, This self-extinction contributes to the homeostatic character of this learning. 5) High-fat maintenance diet attenuates the learning of anticipatory eating. Overall, the findings provided robust evidence that eating in rats can be controlled by instrumental learning reinforced by hunger. Accordingly, the design of an experiment on such instrumental control of eating in human subjects is proposed to conclude this thesis.
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Lifshitz, Michael. "Suggestion modulates deeply ingrained processes." Thesis, McGill University, 2014. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=123096.
Full textAbstract:
Behavioural scientists typically classify cognitive processes as either controlled or automatic. Whereas controlled processes are slow and effortful, automatic processes are fast and involuntary. Cognitive researchers have recently begun investigating how top-down influence in the form of suggestion can allow individuals to modulate the automaticity of deeply ingrained processes. The present thesis surveys a background of converging findings that collectively indicate that certain individuals can derail involuntary processes, such as reading. We extend previous Stroop findings to several other well-established automatic paradigms, including the McGurk effect. We thus demonstrate how, in the case of highly suggestible individuals, suggestion seems to wield control over a process that is likely even more automatic than the Stroop effect. Furthermore, we present findings from two novel experimental paradigms exploring the potential of shifting automaticity in the opposite direction – i.e., transforming, without practice, a controlled task into one that is automatic. In addition, we present findings from an experiment leveraging de-automatization to illuminate a longstanding debate on the nature of hypnotic suggestibility: whether it reflects a stable trait determined by cognitive aptitude or a flexible skill amenable to attitudinal factors such as beliefs and expectations. We surreptitiously controlled light and sound stimuli to convince participants that they were responding strongly to hypnotic suggestions for visual and auditory hallucinations. Extending our previous findings, we indexed hypnotic suggestibility by de-automatizing an involuntary audiovisual phenomenon—the McGurk effect. Our findings intimate that, at least in the present experimental context, expectation hardly correlates with—and is unlikely to be a primary determinant of—high hypnotic suggestibility. Finally, the thesis concludes by addressing related evidence from the neuroscience of contemplative practices and discussing how these findings pave the road to a more scientific understanding of voluntary control and automaticity.Les scientifiques distinguent habituellement deux classes de processus cognitifs : les processus contrôlés et les processus automatiques. Tandis que les processus contrôlés sont lents et requièrent un effort, les processus automatiques sont rapides et involontaires. Les chercheurs en sciences cognitives ont récemment commencé à étudier comment l'influence des suggestions peut de moduler l'automaticité de processus profondément enracinés. La présente thèse examine un ensemble de découvertes qui indiquent collectivement que certaines personnes peuvent modifier des processus involontaires. Nous étendons les découvertes précédentes sur l'effet Stroop à plusieurs autres paradigmes automatiques bien établis, y compris l'effet McGurk. Nous démontrons ainsi comment, dans le cas des individus très suggestibles, la suggestion semble exercer un contrôle sur un processus qui est probablement encore plus automatique que l'effet Stroop. En outre, nous présentons les résultats de deux nouveaux paradigmes expérimentaux qui explorent la possibilité de déplacer l'automaticité dans la direction opposée – c'est-à-dire de transformer, sans entraînement, une tâche contrôlée en une tâche automatique. Par ailleurs, nous présentons les résultats d'une expérience qui mobilise la dé-automatisation pour éclairer un débat de longue date sur la nature de la suggestibilité hypnotique: la question de savoir si elle reflète un trait de caractère stable et déterminé par une aptitude cognitive, ou bien une compétence flexible et exprimable en termes de facteurs comportementaux. En étendant nos résultats précédents, nous avons indexé la suggestibilité hypnotique en dé-automatisant un phénomène audiovisuel involontaire : l'effet McGurk. Nos résultats montrent que, au moins dans ce contexte expérimental, l'attente est très peu corrélée à la suggestibilité hypnotique, et est peu susceptible d'en être un facteur déterminant. Enfin, nous concluons cette thèse en abordant les données apparentées en neurosciences des pratiques contemplatives, et en discutant comment ces résultats ouvrent la voie à une compréhension plus scientifique du contrôle volontaire et de l'automaticité.
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Bastow, Trevor. "Sedimentary Processes Involving Aromatic Hydrocarbons." Curtin University of Technology, School of Applied Chemistry, 1998. http://espace.library.curtin.edu.au:80/R/?func=dbin-jump-full&object_id=9379.
Full textAbstract:
Sedimentary organic matter contains many compounds that have no obvious biogenic precursors, so their formation and occurrence are of geochemical interest. The first part of this thesis (chapters 2-5) discusses the results obtained from studying hydrocarbon racemates. Some of the compounds identified are also suggested as intermediates in the formation of alkylnaphthalenes identified in chapters 6-7. The second part of this thesis (chapters 6-11) covers the identification of a range of alkylnaphthalenes and alkylphenanthrenes in sedimentary organic matter. Possible pathways for the formation of these hydrocarbons are outlined and their application as probes into the processes of petroleum formation are described.In chapter 2 the use of permethylated cyclodextrin capillary gas chromatography columns to separate hydrocarbon racemates are reported. Chapter 3 reports the synthesis of 1,2,2,5-tetramethyltetralin and 1,2,2,5,6-pentamethyltetralin and identifies them as racemates in crude oil. They are proposed as intermediates in the formation of sedimentary alkylnaphthalenes (identified in chapters 6 and 7).The identification of isodihydro-ar-curcumene in sedimentary organic matter is described in chapters 4 and 5. It co-occurs in crude oil with dihydro-ar-curcumene and is suggested to originate from this compound via a sedimentary rearrangement process. Chiral GC-MS techniques have been used to show the presence of both enantiomers of these compounds in crude oils. The elution order of the enantiomers has been established using reference compounds of known configuration. The effects of maturity and biodegradation on dihydro-ar-curcumene and isodihydro-ar-curcumene enantiomers is reported. Optically pure dihydro-ar-curcumene from natural products undergoes rapid racemisation in the subsurface, yielding a racemic mixture before the onset of significant oil formation. ++1,2-Alkyl shifts on the aromatic ring also begin at an early stage to yield isodihydro-ar-curcumene and these processes continue with increasing maturity. Laboratory experiments using proton and clay catalysts (Lewis acid catalyst) show that the alkyl shift reaction is catalysed by both proton and Lewis acids, and racemisation is only catalysed by Lewis acids. A moderately biodegraded crude oil has been shown to be depleted in the R enantiomer of dihydro-ar-curcumene and an extensively degraded oil has dihydro-ar-curcumene depleted relative to isodihydro-ar-curcumene.The identification of a number alkylnaphthalenes and their possible origins in sedimentary organic matter is described in chapters 6 and 7. In chapter 6 a previously unreported tetramethylnaphthalene (TeMN) was identified in petroleum. This compound is structurally similar to bicyclic compounds of microbial origin and these are suggested as a likely source, via a tetralin intermediate identified in chapter 3. In chapter 7 isomeric pentamethylnaphthalenes previously unreported in sedimentary organic matter are reported. These isomeric pentamethylnaphthalenes (PMNs) were identified in a number of crude oils and sediments, ranging in age from Proterozoic to Tertiary. 1,2,3,5,6-PMN is suggested to form predominantly from the aromatisation of drimanoid precursors via 1,2,2,5,6-pentamethyltetralin identified in chapter 3. In laboratory experiments, the other pentamethylnaphthalenes were generated from 1,2,3,5,6-PMN in proportions that reflect the relative stability of the isomers. By analogy, the other PMNs in sediments are suggested to arise via acid catalysed isomerisation or transalkylation processes. A maturity parameter was developed based on laboratory experiments in conjunction with observed distributions of pentamethylnaphthalenes.The formation of alkylnaphthalenes and alkylphenanthrenes through a ++
methylation process is discussed in chapters 8-10. Several crude oils and shales which contain anomalously high concentrations of 1,6-dimethylnaphthalene, 1,2,5-trimethylnaphthalene, 1,2,7-trimethylnaphthalene, 1,2,3,5-tetramethylnaphthalene, 1,2,3,5,6-pentamethylnaphthalene, 2-methyl-6-isopropyl-1(4-methylpentyl)naphthalene, phenanthrene, 1-methylphenanthrene, 1,7-dimethylphenanthrene and retene have been shown to contain relatively high concentrations of their corresponding methylated counterparts. In laboratory experiments carried out under mild conditions, each of the alkylnaphthalenes and alkylphenanthrenes have been shown to be methylated in specific positions when heated with a methyl donor in the presence of a clay catalyst. These observations have been interpreted as evidence for a sedimentary methylation process.The effect of biodegradation on alkylnaphthalenes and alkylphenanthrenes formed from sedimentary methylation is described in chapter 11. Land-plant-derived aromatic hydrocarbons with a range of susceptibilities to reservoir biodegradation have been identified in crude oils. These compounds are the result of reactions of natural products involving aromatisation, rearrangement and methylation in the sediments (chapters 9 and 10). They are therefore suggested as markers for land-plants in severely biodegraded oils in which most of the other biologically derived compounds cannot be recognised. The order of biodegradability of these compounds has been assessed relative to their non-methylated counterparts namely 6-isopropyl-2-methyl-1-(4-methylpentyl)naphthalene and retene. The order of degradation of the four compounds is : retene < 9-methylretene ~ 6-isopropyl-2-methyl-1-(4-methylpentyl)naphthalene > 6-isopropyl-2,4-dimethyl-1-(4-methylpentyl)naphthalene. These results have been used to assess that a crude oil is a mixture of severely biodegraded and ++
less biodegraded crude oil.