An E-Arch Model for the Term Structure of Implied Volatility of FX Options

25 Pages Posted: 1 Apr 1997

See all articles by Marco Avellaneda

Marco Avellaneda

New York University (NYU) - Courant Institute of Mathematical Sciences; Finance Concepts LLC

Yingzi Zhu

Tsinghua University - School of Economics & Management

Date Written: January 27, 1997

Abstract

We construct a statistical model for term-structure of implied volatilities of currency options based on daily historical data for 13 currency pairs in a 19-month period. We examine the joint evolution of 1 month, 2 month, 3 month, 6 month and 1 year 50-delta 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 term-structure 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.

JEL Classification: C32, G13

Suggested Citation

Avellaneda, Marco and Zhu, Yingzi, An E-Arch Model for the Term Structure of Implied Volatility of FX Options (January 27, 1997). Available at SSRN: https://ssrn.com/abstract=15150 or http://dx.doi.org/10.2139/ssrn.15150

Marco Avellaneda (Contact Author)

New York University (NYU) - Courant Institute of Mathematical Sciences ( email )

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Yingzi Zhu

Tsinghua University - School of Economics & Management ( email )

Beijing, 100084
China
+86-10-62786041 (Phone)

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