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Posouzení odhadu měnového rizika portfolia pomocí Lévyho modelů
[Examination of Portfolio Currency Risk Estimation by Means of Lévy Models]

Author

Listed:
  • Tomáš Tichý

Abstract

Financial risk modeling, measuring, and managing are an inherent part of management in financial institutions. It is also an important step within the setting of optimal level of capital eligible to cover risk exposures. A significant portion of capital is usually assigned to cover the risk of unexpected changes in FX rates. FX rates (the returns) commonly exhibit significant skewness and relatively huge kurtosis. In this paper, we apply subordinated Lévy models coupled together by ordinary elliptical copula functions in order to estimate the FX rate risk of normalized portfolio. Selected models are applied in order to estimate the risk ex-post, as well as ex-ante. The models are also compared to the more standard assumption of the joint normal distribution. Although the results for both types of modeling are quite different and Lévy measure is ignored, suggested models deliver us improved risk estimation.

Suggested Citation

  • Tomáš Tichý, 2010. "Posouzení odhadu měnového rizika portfolia pomocí Lévyho modelů
    [Examination of Portfolio Currency Risk Estimation by Means of Lévy Models]
    ," Politická ekonomie, University of Economics, Prague, vol. 2010(4), pages 504-521.
  • Handle: RePEc:prg:jnlpol:v:2010:y:2010:i:4:id:744:p:504-521
    as

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    References listed on IDEAS

    as
    1. Dilip B. Madan & Frank Milne, 1991. "Option Pricing With V. G. Martingale Components," Mathematical Finance, Wiley Blackwell, vol. 1(4), pages 39-55.
    2. Nikolay Nenovsky & S. Statev, 2006. "Introduction," Post-Print halshs-00260898, HAL.
    3. Vít Bubák & Filip Žikeš, 2009. "Distribution and Dynamics of Central-European Exchange Rates: Evidence from Intraday Data," Czech Journal of Economics and Finance (Finance a uver), Charles University Prague, Faculty of Social Sciences, vol. 59(4), pages 334-359, Oktober.
    4. Madan, Dilip B & Seneta, Eugene, 1990. "The Variance Gamma (V.G.) Model for Share Market Returns," The Journal of Business, University of Chicago Press, vol. 63(4), pages 511-524, October.
    5. Mejra Festić & Dejan Romih, 2008. "Cyclicality of the banking sector performance and macro environment in the Czech republic, Slovakia and Slovenia," Prague Economic Papers, University of Economics, Prague, pages 99-117.
    6. repec:sae:ecolab:v:16:y:2006:i:2:p:1-2 is not listed on IDEAS
    7. Tomáš Tichý, 2006. "Model Dependency of the Digital Option Replication – Replication under an Incomplete Model (in English)," Czech Journal of Economics and Finance (Finance a uver), Charles University Prague, Faculty of Social Sciences, vol. 56(7-8), pages 361-379, July.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    variance gamma model; normal inverse Gaussian model; Lévy models; ordinary elliptical copula function; financial risk; backtesting;

    JEL classification:

    • C4 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics
    • C5 - Mathematical and Quantitative Methods - - Econometric Modeling
    • G2 - Financial Economics - - Financial Institutions and Services

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