Show simple item record

dc.contributor.advisorRatanov, Nikita 
dc.creatorLópez Alfonso, Oscar Javier 
dc.date.accessioned2016-05-04T19:04:08Z
dc.date.available2016-05-04T19:04:08Z
dc.date.created2014-08-26
dc.date.issued2014 
dc.identifier.urihttp://repository.urosario.edu.co/handle/10336/11954
dc.descriptionEsta tesis está dividida en dos partes: en la primera parte se presentan y estudian los procesos telegráficos, los procesos de Poisson con compensador telegráfico y los procesos telegráficos con saltos. El estudio presentado en esta primera parte incluye el cálculo de las distribuciones de cada proceso, las medias y varianzas, así como las funciones generadoras de momentos entre otras propiedades. Utilizando estas propiedades en la segunda parte se estudian los modelos de valoración de opciones basados en procesos telegráficos con saltos. En esta parte se da una descripción de cómo calcular las medidas neutrales al riesgo, se encuentra la condición de no arbitraje en este tipo de modelos y por último se calcula el precio de las opciones Europeas de compra y venta.
dc.description.abstractThis thesis is divided into two parts: the first part is devoted to present the telegraph processes, the Poisson processes with telegraph compensator and the jump-telegraph processes. The study presented in this first part includes the calculation of the distributions of each process, the means and variances, as well as the moment generating functions among other properties. The second part of the work is devoted to the option pricing models based on telegraph processes with jumps. In this part we show how to calculate the risk-neutral measures, find the no-arbitrage condition in this type of models and finally the price of European call and put options is calculated.
dc.description.sponsorshipFondo de Investigación de la Universidad del Rosario proyecto DVG-140
dc.description.sponsorshipFondo de Investigación de la Universidad del Rosario proyecto DVG-097
dc.description.sponsorshipColciencias - Doctorados Nacionales
dc.format.mimetypeapplication/pdf
dc.language.isospa
dc.rights.urihttp://creativecommons.org/licenses/by-nc/2.5/co/
dc.subjectProcesos telegráficos
dc.subjectProcesos de Poisson
dc.subjectProcesos telegráficos con saltos
dc.subjectValoración de opciones
dc.subject.ddcAnálisis 
dc.subject.lembProcesos de Poisson
dc.subject.lembProcesos telegráficos
dc.titleOption pricing in market models driven by telegraph processes with jumps
dc.typedoctoralThesis
dc.publisherUniversidad del Rosario
dc.creator.degreeDoctor en Economía
dc.publisher.programDoctorado en Economía
dc.publisher.departmentFacultad de Economía
dc.subject.keywordTelegraph processes
dc.subject.keywordPoisson processes
dc.subject.keywordJump-telegraph processes
dc.subject.keywordOption pricing
dc.rights.accesRightsinfo:eu-repo/semantics/openAccess
dc.type.spaTesis de doctorado
dc.rights.accesoAbierto (Texto completo)
dc.type.hasVersioninfo:eu-repo/semantics/acceptedVersion
dc.source.bibliographicCitationBeghin L., Nieddu L. and Orsingher E. (2001). Probabilistic analysis of the telegrapher’s process with drift by mean of relativistic transformations. J. Appl. Math. Stoch. Anal. 14, 11-25.
dc.source.bibliographicCitationBjörk T. Arbitrage theory in continuous time. Thrid edition. Oxford University Press, 2009.
dc.source.bibliographicCitationBlack F. and Scholes M. (1973), The pricing of options and corporate liabilities. Journal of Political Economy, 81, 637-659.
dc.source.bibliographicCitationBrémaud P. Point Processes and Queues: Martingale Dynamics. Springer Series in Statistics. 1981.
dc.source.bibliographicCitationCont R. and Tankov P. Financial Modelling with Jump Processes. Chapman and Hall/CRC, 2003.
dc.source.bibliographicCitationCox D.R. Renewal Theory. Wiley, 1962.
dc.source.bibliographicCitationDelbaen F. and Schachermayer W. The Mathematics of Arbitrage. Springer Finance. 2006.
dc.source.bibliographicCitationDi Crescenzo A., Iuliano A., Martinucci B. and Zacks S. (2013). Generalized telegraph process with random jumps. Journal of Applied Probability. 50, 450- 463.
dc.source.bibliographicCitationDi Crescenzo A. and Martinucci B. (2013). On the Generalized Telegraph Process with Deterministic Jumps. Methodology and Computing in Applied Probability. 15, 215-235.
dc.source.bibliographicCitationDu Q. (1995). A Monotonicity Result for a Single-Server Queue Subject to a Markov-Modulated Poisson Process. Journal of Applied Probability. 32, 1103- 1111.
dc.source.bibliographicCitationElliott R. and Osakwe C.-J. (2006). Option pricing for pure jump processes with Markov switching compensators. Finance and Stochastics. 10, 250-275.
dc.source.bibliographicCitationElliott R. and Siu T. (2013). Option Pricing and Filtering with Hidden Markov- Modulated Pure-Jump Processes. Applied Mathematical Finance. 20, 1-25.
dc.source.bibliographicCitationEthier S.N. and Kurtz T.G. Markov Processes: Characterization and Convergence. 2nd ed. Wiley Series in Probability and Mathematical Statistics. 2005.
dc.source.bibliographicCitationFischer W. and Meier-Hellstern K. (1992). The Markov-Modulated Poisson Process (MMPP) Cookbook. Performance Evaluation. 18, 149-171.
dc.source.bibliographicCitationGoldfeld S. M. and Quandt R. E. (1973). A Markov model for switching regressions. Journal of Econometrics. 1, 3-16.
dc.source.bibliographicCitationGoldstein S. (1951). On diffusion by discontinuous movements and on the telegraph equation. Quart. J. Mech. Appl. Math. 4, 129-156.
dc.source.bibliographicCitationGradshteyn I.S. and Ryzhik I.M. Table of integrals, Series and Products. 7th ed. Academic Press. 2007.
dc.source.bibliographicCitationGulisashvili A. Analytically Tractable Stochastic Stock Price Models. Springer Finance. 2012.
dc.source.bibliographicCitationHadeler, K.P. (1999). Reaction transport systems in biological modelling, in: V. Capasso, O. Diekmann (Eds.),Mathematics Inspired by Biology, Lecture Notes in Mathematics, vol. 1714, Springer, Berlin, 95-150.
dc.source.bibliographicCitationHamilton J. D. (1989). A new approach to the economic analysis of nonstationary time series and the business cycle. Econometrica. 57, 357-384.
dc.source.bibliographicCitationHarrison J. M. and Pliska S.R. (1981). Martingales and stochastic integrals in the theory of continuous trading. Stochastic Processes and their Applications 11, 215-260.
dc.source.bibliographicCitationHarrison J. M. and Pliska S.R. (1983). A stochastic calculus model of continuous trading: Complete markets. Stochastic Processes and their Applications 15, 313-316.
dc.source.bibliographicCitationHe S., Wang J. and Yan J. Semimartingale Theory and Stochastic Calculus. CRC Press. 1992.
dc.source.bibliographicCitationHillen, T. Hadeler, K.P. (2005). Hyperbolic systems and transport equations in mathematical biology, in: G. Warnecke (Ed.), Analysis and Numerics for Conservation Laws. Springer. Berlin, 257-279.
dc.source.bibliographicCitationJacobsen M. Point Process Theory and Applications: Markov Point and Piecewise Deterministic Processes. Birkhäuser. 2006.
dc.source.bibliographicCitationJeanblanc M., Yor M. and Chesney M. Mathematical Methods for Financial Markets. Springer Finance. 2009.
dc.source.bibliographicCitationKac, M. (1974). A stochastic model related to the telegrapher’s equation, Rocky Mountain J. Math. 4, 497–509.
dc.source.bibliographicCitationKolesnik D. and Ratanov N. Telegraph processes and Option Pricing. Springer briefs in statistics. 2013.
dc.source.bibliographicCitationKulkarni V. Modeling, Analysis, Desing, and Control of Stochastic Systems. Springer text in statistics. 1999.
dc.source.bibliographicCitationKonikov M. and Madan B. (2002). Option pricing using variance-gamma Markov chains. Review of Derivative Research. 5, 81-115.
dc.source.bibliographicCitationLópez O. and Ratanov N. (2012). Kac’s rescaling for jump-telegraph processes. Statistics and Probability Letters. 82, 1768-1776.
dc.source.bibliographicCitationLópez O. and Ratanov N. (2012). Option pricing driven by telegraph process with random jumps. Journal of Applied Probability. 49, 838-849.
dc.source.bibliographicCitationLópez O. and Ratanov N. (2014). On the asymmetric telegraph processes. Journal of Applied Probability. 51, 569-589.
dc.source.bibliographicCitationMamon R. and Elliott R. (Eds.) Hidden Markov Models in Finance. International Series in Operations Research and Management Science. Springer. 2007.
dc.source.bibliographicCitationMandelbrot B. (1963). The Variation of Certain Speculative Prices. The Journal of Business. 36, 394-419.
dc.source.bibliographicCitationMandelbrot B. and Taylor H. (1967). On the distribution of stock prices differences. Operation Research. 15, 1057-1062.
dc.source.bibliographicCitationMazza C. and Rullire (2004). A link between wave governed random motions and ruin processes. Insurance: Mathematics and Economics. 35, 205-222.
dc.source.bibliographicCitationMerton, R. C. (1973). The theory of rational option pricing. Bell Journal of Economics and Management Science 4, 141-183.
dc.source.bibliographicCitationMiyahara Y. Option Pricing in Incomplete Markets: Modeling Based on Geometric Lévy Processes and Minimal Entropy Martingale Measures. Imperial College Press. 2012.
dc.source.bibliographicCitationNeuts M.F. Structured Stochastic Matrices of M/G/1 Type and Their Applications. Marcel Dekker, Inc. 1989.
dc.source.bibliographicCitationNg C.-H. and Soong B.-H. Queueing Modelling Fundamentals: With Applications in Communication Networks. Second ed. Wiley Publishing. 2008.
dc.source.bibliographicCitationOkuba, A., Levin, S.A. (2001) Diffusion and Ecological Problems: Modern Perspectives, 2nd edition, Interdisciplinary Applied Mathematics, vol. 14, Springer, Berlin.
dc.source.bibliographicCitationOrsingher E. (1990). Probability law, flow function, maximum distribution of wave-governed random motions and their connections with Kirchoff’s laws. Stochastic Process. Appl. 34, 49-66.
dc.source.bibliographicCitationOrsingher E. (1995). Motions with reflecting and absorbing barriers driven by the telegraph equation. Random Oper. Stochastic Equations. 3, 9-21.
dc.source.bibliographicCitationPrivault N. Understanding Markov Chains: Examples and Applications. Springer Undergraduate Mathematics Series. 2013.
dc.source.bibliographicCitationQuandt R. E. (1958). The estimation of parameters of linear regression system obeying two separate regimes. Journal of the American Statistical Association. 55, 873-880.
dc.source.bibliographicCitationRatanov, N. (1999). Telegraph evolutions in inhomogeneous media. Markov Process. Related Fields. 5 53-68.
dc.source.bibliographicCitationRatanov N. (2007). A jump telegraph model for option pricing. Quantitative Finance. 7, 575-583.
dc.source.bibliographicCitationRatanov N. (2007). Jump telegraph processes and financial markets with memory. Journal of Applied Mathematics and Stochastic Analysis. doi:10.1155/2007/72326.
dc.source.bibliographicCitationRatanov N. (2008). Jump telegraph processes and a volatility smile. Mathematical Methods in Economics and Finance. 3, 93-112.
dc.source.bibliographicCitationRatanov N. and Melnikov A. (2008). On financial markets based on telegraph processes. Stochastics: An International Journal of Probability and Stochastics Processes. 80, 247-268.
dc.source.bibliographicCitationRydén T. (1995). Consistent and Asymptotically Normal Parameter Estimates for Markov Modulated Poisson Processes. Scandinavian Journal of Statistics. 22, 295-303.
dc.source.bibliographicCitationScott S. L. and Smyth P. (2003). The Markov Modulated Poisson Process and Markov Poisson Cascade With Applications to Web Traffic Data. Bayesian Statistics (Vol. 7), eds. J. M. Bernardo, M. J. Bayarri, J. O. Berger, A.P. Dawid, D. Heckerman, A. F. M. Smith, and M. West, Oxford University Press, 671-680.
dc.source.bibliographicCitationTaylor G.I. (1922). Diffusion by continuous movements. Proc. London Math. Soc. 20, 196-212.
dc.source.bibliographicCitationTong H. (1978). On a threshold model. In: C. H. Chen (Ed.), Pattern Recognition and Signal Processing, NATO ASI Series E: Applied Sc. 29, 575-586 (The Netherlands: Sijthoff & Noordhoff).
dc.source.bibliographicCitationTong H. Threshold Models in Non-linear Time Series Analysis. Springer-Verlag. 1983.
dc.source.bibliographicCitationWebster A.G. Partial differential equations of mathematical physics. 2nd corr. ed. Dover, New York. 1955.
dc.source.bibliographicCitationWeiss, G.H. (2002). Some applications of persistent random walks and the telegrapher’s equation. Physica A. 311 381-410.
dc.rights.ccAtribución-NoComercial 2.5 Colombia
dc.rights.licenciaEL AUTOR, manifiesta que la obra objeto de la presente autorización es original y la realizó sin violar o usurpar derechos de autor de terceros, por lo tanto la obra es de exclusiva autoría y tiene la titularidad sobre la misma. PARGRAFO: En caso de presentarse cualquier reclamación o acción por parte de un tercero en cuanto a los derechos de autor sobre la obra en cuestión, EL AUTOR, asumirá toda la responsabilidad, y saldrá en defensa de los derechos aquí autorizados; para todos los efectos la universidad actúa como un tercero de buena fe. EL AUTOR, autoriza a LA UNIVERSIDAD DEL ROSARIO, para que en los términos establecidos en la Ley 23 de 1982, Ley 44 de 1993, Decisión andina 351 de 1993, Decreto 460 de 1995 y demás normas generales sobre la materia, utilice y use la obra objeto de la presente autorización. -------------------------------------- POLITICA DE TRATAMIENTO DE DATOS PERSONALES. Declaro que autorizo previa y de forma informada el tratamiento de mis datos personales por parte de LA UNIVERSIDAD DEL ROSARIO para fines académicos y en aplicación de convenios con terceros o servicios conexos con actividades propias de la academia, con estricto cumplimiento de los principios de ley. Para el correcto ejercicio de mi derecho de habeas data cuento con la cuenta de correo habeasdata@urosario.edu.co, donde previa identificación podré solicitar la consulta, corrección y supresión de mis datos.


Files in this item

Thumbnail

This item appears in the following Collection(s)

Show simple item record

http://creativecommons.org/licenses/by-nc/2.5/co/
Except where otherwise noted, this item's license is described as http://creativecommons.org/licenses/by-nc/2.5/co/