Foreign Exchange, Fractional Cointegration and the Implied-Realized Volatility Relation

30 Pages Posted: 6 Mar 2007 Last revised: 26 Mar 2008

See all articles by Neil Kellard

Neil Kellard

University of Essex - Essex Business School

Christian Dunis

John Moores University - Business School

Nicholas Sarantis

London Metropolitan University - Department of Economics, Finance and International Business (EFIB)

Abstract

Almost all relevant literature has characterized implied volatility as a biased predictor of realized volatility. This paper provides new time series techniques to assess the validity of this finding within a foreign exchange market context. We begin with the empirical observation that the fractional order of volatility is often found to have confidence intervals that span the stationary/non-stationary boundary. However, no existing fractional cointegration test has been shown to be robust to both regions. Therefore, a new test for fractional cointegration is developed and shown to be robust to the relevant orders of integration. Secondly, employing a dataset that includes the relatively new Euro markets, it is shown that implied and realized volatility are fractionally cointegrated with a slope coefficient of unity. Moreover, the non-standard asymptotic distribution of estimators when using fractionally integrated data is overcome by employing a bootstrap procedure in the frequency domain. Strikingly, tests then show that implied volatility is an unbiased predictor of realized volatility!

Keywords: market efficiency, traded volatility, narrow band least squares, fractional cointegration, bootstrap

JEL Classification: F31, G14, C14, C22

Suggested Citation

Kellard, Neil and Dunis, Christian and Sarantis, Nicholas, Foreign Exchange, Fractional Cointegration and the Implied-Realized Volatility Relation. Available at SSRN: https://ssrn.com/abstract=968195 or http://dx.doi.org/10.2139/ssrn.968195

Neil Kellard (Contact Author)

University of Essex - Essex Business School ( email )

Wivenhoe Park
Colchester CO4 3SQ
United Kingdom
+44-1206-87-4153 (Phone)

Christian Dunis

John Moores University - Business School ( email )

John Foster Building
98 Mount Pleasant
Liverpool, L3 5UZ
United Kingdom

Nicholas Sarantis

London Metropolitan University - Department of Economics, Finance and International Business (EFIB) ( email )

Economics Subject Group, LMBS
London EC2M 6SQ, EC2M 6SQ
United Kingdom

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