Show simple item record

dc.contributor.advisorSerrano, Rafael 
dc.creatorLázaro Salcedo, Javier Jaher Alfonso 
dc.date.accessioned2018-02-20T12:03:54Z
dc.date.available2018-02-20T12:03:54Z
dc.date.created2018-02-15
dc.identifier.urihttp://repository.urosario.edu.co/handle/10336/14418
dc.descriptionThis study find by empirical evidence a fast and accurate way to calculate the price of a European Call using the Heston (1993) model. It calculate and uses a benchmark price calculated with the mentioned Heston 1993 pricing approaches and the trapezoidal rule with a = 1e-20000; b = 300; N = 10000000, to find which combination of Heston pricing process and numerical schems leads to a computationally faster and more accurate price process. Two equivalent pricing methods and seven numerical schemes are calculated in order to find wich combination take less time to be compute and is closes to the benchmark as posible. The study uses Q-measure in the sense of spot data, and the other P-measure in the sense of historical data. That mean the study calculate two parameter sets. one under mesure Q and other under P by Maximum Likelihood and non-linear least square function, respectively, to somehow proof the conclution dose not depents on how the parameter are found. Study stands that the accuraste way to calculate the Heston price in the Colombian FX market data used is consolidating the integrals for the probability P1 and P2 that the original framework propose and solve the integral using Gauss-Legendre or Gauss-Laguerre.
dc.format.mimetypeapplication/pdf
dc.language.isospa
dc.sourcereponame:Repositorio Institucional EdocUR
dc.sourceinstname:Universidad del Rosario
dc.subjectHeston model
dc.subjectUSD-COP
dc.subjectFourier pricing
dc.subjectGaussian cuadrature
dc.subjectNewton cotes
dc.subject.ddc338
dc.subject.lembPrecios
dc.subject.lembModelos econométricos
dc.titleAn accurate heston implementation with Usd-Cop Data
dc.typemasterThesis
dc.publisherUniversidad del Rosario
dc.creator.degreeMagíster en Finanzas Cuantitativas
dc.publisher.programMaestría en Finanzas Cuantitativas
dc.publisher.departmentFacultad de Economía
dc.rights.accesRightsinfo:eu-repo/semantics/openAccess
dc.type.spaTesis de maestría
dc.rights.accesoAbierto (Texto Completo)
dc.type.hasVersioninfo:eu-repo/semantics/acceptedVersion
dc.source.bibliographicCitationC. Alexander, Market risk analysis, pricing, hedging and trading financial instruments, Market Risk Analysis, Wiley, 2008.
dc.source.bibliographicCitationH Albrecher, P Mayer, and W Tistaert Schoutens, The little heston trap, Wilmott Magazine, January issue, 83–92.
dc.source.bibliographicCitationMilton Abramowitz and Irene A Stegun, Handbook of mathematical functions: with formulas, graphs, and mathematical tables, vol. 55, Courier Corporation, 1964.
dc.source.bibliographicCitationAmir F Atiya and Steve Wall, An analytic approximation of the likelihood function for the heston model volatility estimation problem, Quantitative Finance 9 (2009), no. 3, 289–296.
dc.source.bibliographicCitationK. Back, A course in derivative securities: Introduction to theory and computation, Springer Finance, Springer Berlin Heidelberg, 2005
dc.source.bibliographicCitationDavid S Bates, Jumps and stochastic volatility: Exchange rate processes implicit in deutsche mark options, Review of financial studies 9 (1996), no. 1, 69–107.
dc.source.bibliographicCitationR.L. Burden and J.D. Faires, Numerical analysis, Cengage Learning, 2010
dc.source.bibliographicCitationTim Bollerslev, Michael Gibson, and Hao Zhou, Dynamic estimation of volatility risk premia and investor risk aversion from option-implied and realized volatilities, Journal of econometrics 160 (2011), no. 1, 235–245.
dc.source.bibliographicCitationE. Berlinger, F. Ill´es, M. Badics, A. Banai, G. Dar´oczi, B. D¨om¨ot¨or, ´ G. Gabler, D. Havran, P. Juh´asz, I. Margitai, et al., Mastering r for quantitative finance, Community experience distilled, Packt Publishing, 2015.
dc.source.bibliographicCitationT. Bj¨ork, Arbitrage theory in continuous time, Oxford Finance Series, OUP Oxford, 2009.
dc.source.bibliographicCitationGurdip Bakshi and Dilip Madan, Spanning and derivative-security valuation, Journal of financial economics 55 (2000), no. 2, 205–238.
dc.source.bibliographicCitationClaus Christian Beier and Christoph Renner, Foreign exchange options: Delta-and at-the-money conventions, Encyclopedia of Quantitative Finance (2010).
dc.source.bibliographicCitationFr´ed´eric Bossens, Gr´egory Ray´ee, Nikos S Skantzos, and Griselda Deelstra, Vanna-volga methods applied to fx derivatives: from theory to market practice, International journal of theoretical and applied finance 13 (2010), no. 08, 1293–1324.
dc.source.bibliographicCitationA. Castagna, Fx options and smile risk, The Wiley Finance Series, Wiley, 2010.
dc.source.bibliographicCitationPeter Christoffersen, Steven Heston, and Kris Jacobs, The shape and term structure of the index option smirk: Why multifactor stochastic volatility models work so well, Management Science 55 (2009), no. 12, 1914–1932.
dc.source.bibliographicCitationKyriakos Chourdakis, Option pricing using the fractional fft, Journal of Computational Finance 8 (2004), no. 2, 1–18.
dc.source.bibliographicCitationI.J. Clark, Foreign exchange option pricing: A practitioner’s guide, The Wiley Finance Series, Wiley, 2011.
dc.source.bibliographicCitationG. Cohen, The bible of options strategies: The definitive guide for practical trading strategies, Pearson Education, 2015
dc.source.bibliographicCitationR. Cont, Encyclopedia of quantitative finance, 4 volume set, Wiley, 2010.
dc.source.bibliographicCitationMarc Chesney and Louis Scott, Pricing european currency options: A comparison of the modified black-scholes model and a random variance model, Journal of Financial and Quantitative Analysis 24 (1989), 267– 284.
dc.source.bibliographicCitationMyron Scholes Fischer Black, The pricing of options and corporate liabilities, Journal of Political Economy 81 (1973), no. 3, 637–654.
dc.source.bibliographicCitationP. Glasserman, Monte carlo methods in financial engineering, Applications of mathematics : stochastic modelling and applied probability, Springer, 2004.
dc.source.bibliographicCitationJ Gil-Pelaez, Note on the inversion theorem, Biometrika 38 (1951), no. 3-4, 481–482.
dc.source.bibliographicCitationJ. Gatheral and N.N. Taleb, The volatility surface: A practitioner’s guide, Wiley Finance, Wiley, 2011.
dc.source.bibliographicCitationR. Hafner, Stochastic implied volatility: A factor-based model, Lecture Notes in Economics and Mathematical Systems, Springer Berlin Heidelberg, 2004.
dc.source.bibliographicCitationSteven L Heston, A closed-form solution for options with stochastic volatility with applications to bond and currency options, Review of financial studies 6 (1993), no. 2, 327–343.
dc.source.bibliographicCitationPatrick S Hagan, Deep Kumar, Andrew S Lesniewski, and Diana E Woodward, Managing smile risk, The Best of Wilmott (2002), 249.
dc.source.bibliographicCitationA. Hirsa and S.N. Neftci, An introduction to the mathematics of financial derivatives, Elsevier Science, 2013.
dc.source.bibliographicCitationJ. Hull, Options, futures, and other derivatives, Options, Futures, and Other Derivatives, Prentice Hall, 2012.
dc.source.bibliographicCitationJohn Hull and Alan White, The pricing of options on assets with stochastic volatilities, The journal of finance 42 (1987), no. 2, 281–300.
dc.source.bibliographicCitationS.M. Iacus, Option pricing and estimation of financial models with r, Wiley, 2011.
dc.source.bibliographicCitationM. Jeanblanc, M. Yor, and M. Chesney, Mathematical methods for fi- nancial markets, Springer Finance, Springer London, 2009.
dc.source.bibliographicCitationFiodar Kilin, Accelerating the calibration of stochastic volatility models.
dc.source.bibliographicCitationChristian Kahl and Peter J¨ackel, Not-so-complex logarithms in the heston model, Wilmott magazine 19 (2005), no. 9, 94–103.
dc.source.bibliographicCitationAlan L Lewis et al., Option valuation under stochastic volatility, Option Valuation under Stochastic Volatility (2000).
dc.source.bibliographicCitationRoger W Lee et al., Option pricing by transform methods: extensions, unification and error control, Journal of Computational Finance 7 (2004), no. 3, 51–86.
dc.source.bibliographicCitationRoger Lord and Christian Kahl, Optimal fourier inversion in semianalytical option pricing.
dc.source.bibliographicCitationDavid G. Luenberger, Investment science, Oxford University Press, 1998
dc.source.bibliographicCitationDilip B Madan, Peter P Carr, and Eric C Chang, The variance gamma process and option pricing, European finance review 2 (1998), no. 1, 79–105.
dc.source.bibliographicCitationS. Natenberg, Option volatility & pricing: Advanced trading strategies and techniques: Advanced trading strategies and techniques, McGrawHill Education, 1994.
dc.source.bibliographicCitationDimitri Reiswich, The foreign exchange volatility surface, Ph.D. thesis, Frankfurt School of Finance & Management, 2010.
dc.source.bibliographicCitationF.D. Rouah and S.L. Heston, The heston model and its extensions in matlab and c#, Wiley Finance, Wiley, 2013.
dc.source.bibliographicCitationF.D. Rouah and G. Vainberg, Option pricing models and volatility using excel-vba, Wiley Finance, Wiley, 2012.
dc.source.bibliographicCitationLouis O. Scott, Option pricing when the variance changes randomly: Theory, estimation, and an application, Journal of Financial and Quantitative Analysis 22 (1987), 419–438.
dc.source.bibliographicCitationS.E. Shreve, Stochastic calculus for finance ii: Continuous-time models, Springer Finance Textbooks, no. v. 11, Springer, 2004
dc.source.bibliographicCitationElias M Stein and Jeremy C Stein, Stock price distributions with stochastic volatility: an analytic approach, Review of financial Studies 4 (1991), no. 4, 727–752.
dc.source.bibliographicCitationSantiago Stozitzky, General bounds for arithmetic asian option prices: Colombian fx option market application, Master’s thesis, The University of Edinburgh, 2013.
dc.source.bibliographicCitationRainer Sch¨obel and Jianwei Zhu, Stochastic volatility with an ornstein– uhlenbeck process: an extension, European Finance Review 3 (1999), no. 1, 23–46
dc.source.bibliographicCitationN. Webber, Implementing models of financial derivatives: Object oriented applications with vba, The Wiley Finance Series, Wiley, 2011.
dc.source.bibliographicCitationRobert E Whaley, Derivatives: Markets, Valuation, and Risk Management 345 (2006).
dc.source.bibliographicCitationJames B Wiggins, Option values under stochastic volatility: Theory and empirical estimates, Journal of financial economics 19 (1987), no. 2, 351–372.
dc.source.bibliographicCitationP. Wilmott, Paul wilmott on quantitative finance, 3 volume set, Paul Wilmott on Quantitative Finance, Wiley, 2006
dc.source.bibliographicCitationPaul wilmott introduces quantitative finance, The Wiley Finance Series, Wiley, 2013.
dc.source.bibliographicCitationU. Wystup, Fx options and structured products, The Wiley Finance Series, Wiley, 2007.
dc.source.bibliographicCitationJ. Zhu, Applications of fourier transform to smile modeling: Theory and implementation, Springer Finance, Springer Berlin Heidelberg, 2009.
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