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Implied Volatilities of Caps: a Gaussian approach

Author

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  • Flavio Angelini
  • Stefano Herzel

Abstract

Implied volatilities of interest rate derivatives present some distinctive features, like the inverse relation with the underlying rates and the humped or decreasing shape of their term structure. The objective of this paper is to analyze and explain such features in a Gaussian framework. We will use an approximate relation which separates in a simple and natural way the effects on the implied volatility of the level and of the uncertainty of the interest rates. This is a useful tool for understanding the features of different models and to interpret some characteristics of the market.

Suggested Citation

  • Flavio Angelini & Stefano Herzel, 2005. "Implied Volatilities of Caps: a Gaussian approach," Quaderni del Dipartimento di Economia, Finanza e Statistica 09/2005, Università di Perugia, Dipartimento Economia.
    • Handle: RePEc:pia:wpaper:09/2005
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    File URL: http://www2.ec.unipg.it/quaderni/ah2005_qdip.pdf
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    References listed on IDEAS

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    1. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
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    Cited by:

    1. Damiani, Mirella & Pompei, Fabrizio & Ricci, Andrea, 2011. "Temporary job protection and productivity growth in EU economies," MPRA Paper 29698, University Library of Munich, Germany.
    2. Silvia Micheli, 2010. "Learning Curve and Wind Power," Quaderni del Dipartimento di Economia, Finanza e Statistica 81/2010, Università di Perugia, Dipartimento Economia.
    3. Francesco Venturini, 2011. "Product variety, product quality, and evidence of Schumpeterian endogenous growth: a note," Quaderni del Dipartimento di Economia, Finanza e Statistica 93/2011, Università di Perugia, Dipartimento Economia.
    4. Stefano Herzel & Marco Nicolosi & Cătălin Stărică, 2012. "The cost of sustainability in optimal portfolio decisions," The European Journal of Finance, Taylor & Francis Journals, vol. 18(3-4), pages 333-349, May.
    5. Mirella Damiani, 2010. "Labour regulation, corporate governance and varieties of capitalism," Quaderni del Dipartimento di Economia, Finanza e Statistica 76/2010, Università di Perugia, Dipartimento Economia.
    6. Davide Castellani & Fabio Pieri, 2011. "Foreign Investments and Productivity Evidence from European Regions," Quaderni del Dipartimento di Economia, Finanza e Statistica 83/2011, Università di Perugia, Dipartimento Economia.
    7. Flavio Angelini & Stefano Herzel, 2006. "Notes and Comments: An approximation of caplet implied volatilities in Gaussian models," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 28(2), pages 113-127, February.

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    More about this item

    Keywords

    Implied volatility; forward rates; HJM models; calibration;
    All these keywords.

    JEL classification:

    • E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Interest Rates: Determination, Term Structure, and Effects
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General

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