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An E-ARCH model for the term structure of implied volatility of FX options

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  • Yingzi Zhu
  • Marco Avellaneda
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    Abstract

    We construct a statistical model for the term-structure of implied volatilities of currency options based on daily historical data for 13 currency pairs over a 19-month period. We examine the joint evolution of 1 month, 2 month, 3 month, 6 month and 1 year at-the-money (50 δ) options in all the currency pairs. We show that there exist three uncorrelated state variables (principal components) which account for the parallel movement, slope oscillation, and curvature of the term structure and which explain, on average, the movements of the termstructure of volatility to more than 95% in all cases. We test and construct an exponential ARCH, or E-ARCH, model for each state variable. One of the applications of this model is to produce confidence bands for the term structure of volatility.

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    File URL: http://www.tandfonline.com/doi/abs/10.1080/13504869700000001
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    Bibliographic Info

    Article provided by Taylor & Francis Journals in its journal Applied Mathematical Finance.

    Volume (Year): 4 (1997)
    Issue (Month): 2 ()
    Pages: 81-100

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    Handle: RePEc:taf:apmtfi:v:4:y:1997:i:2:p:81-100

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    Web page: http://www.tandfonline.com/RAMF20

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    Related research

    Keywords: currency options; term structure of volatility; ARCH; E-ARCH;

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    Cited by:
    1. Philipp Maier & Garima Vasishtha, 2008. "Good Policies or Good Fortune: What Drives the Compression in Emerging Market Spreads?," Working Papers 08-25, Bank of Canada.

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