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Examination of Portfolio Currency Risk Estimation by Means of Lévy Models

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  • Tomáš Tichý
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    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.

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    Bibliographic Info

    Article provided by University of Economics, Prague in its journal Politická ekonomie.

    Volume (Year): 2010 (2010)
    Issue (Month): 4 ()
    Pages: 504-521

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    Handle: RePEc:prg:jnlpol:v:2010:y:2010:i:4:id:744:p:504-521

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    Related research

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

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    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. 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.
    3. 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.
    4. 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, vol. 2008(2), pages 99-117.
    5. 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 511-24, October.
    6. repec:sae:ecolab:v:16:y:2006:i:2:p:1-2 is not listed on IDEAS
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