IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/78961.html

Estudio empírico sobre el tipo de cambio MXN/USD: Movimiento Browniano Geométrico vs. Proceso Varianza-Gamma
[Empirical analysis of the MXN/USD exchange rate: geometric Brownian motion vs. variance-gamma process]

Author

Listed:
  • Mosiño, Alejandro
  • Salomón-Núñez, Laura A.
  • Moreno-Okuno, Alejandro T.

Abstract

En este artículo examinamos el comportamiento del mercado cambiario, el cual se caracteriza por movimientos extremos muy frecuentes ocasionados por la información generada dentro del mercado financiero y el entorno macroeconómico internacional. Utilizando datos del tipo de cambio MXN/USD, comparamos dos modelos estocásticos: el movimiento browniano geométrico (MBG), el cual está basado en la densidad normal, y el proceso varianza-gamma (PVG), el cual nos permite capturar el sesgo y el exceso de curtosis de los cambios en los precios. Concluimos que, en general, el PVG ajusta mejor a los datos que el MBG. Mostramos, además, que el ajuste mejora conforme aumenta la ventana temporal utilizada para calcular los rendimientos del mercado cambiario.

Suggested Citation

  • Mosiño, Alejandro & Salomón-Núñez, Laura A. & Moreno-Okuno, Alejandro T., 2017. "Estudio empírico sobre el tipo de cambio MXN/USD: Movimiento Browniano Geométrico vs. Proceso Varianza-Gamma [Empirical analysis of the MXN/USD exchange rate: geometric Brownian motion vs. variance-gamma process]," MPRA Paper 78961, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:78961
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/78961/1/MPRA_paper_78961.pdf
    File Function: original version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Dilip B. Madan & Peter P. Carr & Eric C. Chang, 1998. "The Variance Gamma Process and Option Pricing," Review of Finance, European Finance Association, vol. 2(1), pages 79-105.
    2. repec:boz:journl:v:27:y:2013:i:2:p:1-18 is not listed on IDEAS
    3. Conall O'Sullivan & Michael Moloney, 2010. "The Variance Gamma Scaled Self-Decomposable Process in Actuarial Modelling," Working Papers 201030, Geary Institute, University College Dublin.
    4. Ahmet Göncü & Mehmet Oguz Karahan & Tolga Umut Kuzubas, 2013. "Fitting the Variance-Gamma Model: A Goodness-of-Fit Check for Emerging Markets," Bogazici Journal, Review of Social, Economic and Administrative Studies, Bogazici University, Department of Economics, vol. 27(2), pages 1-10.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Alejandro Mosiño & Alejandro Tatsuo Moreno-Okuno, 2018. "On modeling fossil fuel prices: geometric Brownian motion vs. variance-gamma process," Economics Bulletin, AccessEcon, vol. 38(1), pages 509-519.
    2. Lord, Roger & Fang, Fang & Bervoets, Frank & Oosterlee, Kees, 2007. "A fast and accurate FFT-based method for pricing early-exercise options under Lévy processes," MPRA Paper 1952, University Library of Munich, Germany.
    3. Fenglong Guo, 2025. "Pricing Vulnerable Options With Variance Gamma Systematic and Idiosyncratic Factors by Laplace Transform Inversion," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 45(1), pages 47-76, January.
    4. Mei Xing, 2017. "Existence Conditions of Super-Replication Cost in a Multinomial Model," Journal of Mathematics Research, Canadian Center of Science and Education, vol. 9(4), pages 185-195, August.
    5. Buchmann, Boris & Kaehler, Benjamin & Maller, Ross & Szimayer, Alexander, 2017. "Multivariate subordination using generalised Gamma convolutions with applications to Variance Gamma processes and option pricing," Stochastic Processes and their Applications, Elsevier, vol. 127(7), pages 2208-2242.
    6. Yun, Jaeho, 2014. "Out-of-sample density forecasts with affine jump diffusion models," Journal of Banking & Finance, Elsevier, vol. 47(C), pages 74-87.
    7. Simi, Wei W. & Wang, Xiaoli, 2013. "Time-changed Lévy jump processes with GARCH model on reverse convertibles," Review of Financial Economics, Elsevier, vol. 22(4), pages 206-212.
    8. Yeap, Claudia & Kwok, Simon S. & Choy, S. T. Boris, 2016. "A Flexible Generalised Hyperbolic Option Pricing Model and its Special Cases," Working Papers 2016-14, University of Sydney, School of Economics.
    9. Mahmoud Zarepour & Thierry Bedard & Andre Dabrowski, 2008. "Return and Value at Risk using the Dirichlet Process," Applied Mathematical Finance, Taylor & Francis Journals, vol. 15(3), pages 205-218.
    10. Dilip B. Madan & Wim Schoutens & King Wang, 2017. "Measuring And Monitoring The Efficiency Of Markets," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(08), pages 1-32, December.
    11. Nicolas Huth & Frédéric Abergel, 2012. "The times change: multivariate subordination, empirical facts," Post-Print hal-00620841, HAL.
    12. Jose Cruz & Daniel Sevcovic, 2020. "On solutions of a partial integro-differential equation in Bessel potential spaces with applications in option pricing models," Papers 2003.03851, arXiv.org.
    13. Yongxin Yang & Yu Zheng & Timothy M. Hospedales, 2016. "Gated Neural Networks for Option Pricing: Rationality by Design," Papers 1609.07472, arXiv.org, revised Mar 2020.
    14. Samuel Asante Gyamerah & Philip Ngare & Dennis Ikpe, 2018. "Regime-Switching Temperature Dynamics Model for Weather Derivatives," International Journal of Stochastic Analysis, Hindawi, vol. 2018, pages 1-15, July.
    15. Lam, K. & Chang, E. & Lee, M. C., 2002. "An empirical test of the variance gamma option pricing model," Pacific-Basin Finance Journal, Elsevier, vol. 10(3), pages 267-285, June.
    16. Kun Gao & Roger Lee, 2014. "Asymptotics of implied volatility to arbitrary order," Finance and Stochastics, Springer, vol. 18(2), pages 349-392, April.
    17. Fu, Qi & So, Jacky Yuk-Chow & Li, Xiaotong, 2024. "Stable paretian distribution, return generating processes and habit formation—The implication for equity premium puzzle," The North American Journal of Economics and Finance, Elsevier, vol. 70(C).
    18. Zura Kakushadze, 2016. "Volatility Smile as Relativistic Effect," Papers 1610.02456, arXiv.org, revised Feb 2017.
    19. Yacine Aït‐Sahalia, 2002. "Telling from Discrete Data Whether the Underlying Continuous‐Time Model Is a Diffusion," Journal of Finance, American Finance Association, vol. 57(5), pages 2075-2112, October.
    20. Henri Bertholon & Alain Monfort & Fulvio Pegoraro, 2006. "Pricing and Inference with Mixtures of Conditionally Normal Processes," Working Papers 2006-28, Center for Research in Economics and Statistics.

    More about this item

    Keywords

    ;
    ;
    ;

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • F31 - International Economics - - International Finance - - - Foreign Exchange

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:pra:mprapa:78961. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Joachim Winter (email available below). General contact details of provider: https://edirc.repec.org/data/vfmunde.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.