 An E-ARCH model for the term structure of implied volatility of FX optionsYingzi Zhu and Marco Avellaneda Applied Mathematical Finance, 1997, vol. 4, issue 2, 81-100 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. Keywords: currency options; term structure of volatility; ARCH; E-ARCH (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:taf:apmtfi:v:4:y:1997:i:2:p:81-100 Ordering information: This journal article can be ordered from DOI: 10.1080/13504869700000001 Access Statistics for this article Applied Mathematical Finance is currently edited by Professor Ben Hambly and Christoph Reisinger More articles in Applied Mathematical Finance from Taylor & Francis Journals |
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