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

Author

Listed:
  • Yingzi Zhu
  • Marco Avellaneda

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.

Suggested Citation

  • Yingzi Zhu & Marco Avellaneda, 1997. "An E-ARCH model for the term structure of implied volatility of FX options," Applied Mathematical Finance, Taylor & Francis Journals, vol. 4(2), pages 81-100.
  • Handle: RePEc:taf:apmtfi:v:4:y:1997:i:2:p:81-100
    DOI: 10.1080/13504869700000001
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    Cited by:

    1. Jacinto Marabel Romo, 2012. "Volatility Regimes For The Vix Index," Revista de Economia Aplicada, Universidad de Zaragoza, Departamento de Estructura Economica y Economia Publica, vol. 20(2), pages 111-134, Autumn.
    2. Philipp Maier & Garima Vasishtha, 2008. "Good Policies or Good Fortune: What Drives the Compression in Emerging Market Spreads?," Staff Working Papers 08-25, Bank of Canada.
    3. repec:eee:jbfina:v:84:y:2017:i:c:p:41-52 is not listed on IDEAS

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