E-ARCH MODEL FOR IMPLIED VOLATILITY TERM STRUCTURE OF FX OPTIONS

Yingzi Zhu and Marco Avellaneda
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Yingzi Zhu: Citibank, N.A., 909 Third Avenue, 29th Floor, Zone 1, New York, NY 10043, USA
Marco Avellaneda: Courant Institute of Mathematical Sciences, 251 Mercer Street, New York, NY 10012, USA

Chapter 11 in Quantitative Analysis in Financial Markets:Collected Papers of the New York University Mathematical Finance Seminar, 1999, pp 271-291 from World Scientific Publishing Co. Pte. Ltd.

Abstract: AbstractWe construct a statistical model for term structure of implied volatility 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 Δ options in all the currency pairs. We show that from these five observable variables, 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.

Date: 1999
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