Foreign exchange, fractional cointegration and the implied–realized volatility relation

Abstract

JEL classification: F31 G14 C14 C22 Keywords:Market efficiency Options markets Fractional cointegration Narrow band least squares Bootstrap Traded volatility Intra-day data a b s t r a c t Almost all relevant literature has characterized implied volatility as a biased predictor of realized volatility. In this paper we provide new time series techniques to investigate the validity of this finding in several foreign exchange options markets, including the Euro market. First, we develop a new fractional cointegration test that is shown to be robust to both stationary and non-stationary regions. Second, we employ both intra-day and daily data to measure realized volatility in order to assess the relevance of data frequency in resolving the bias. Third, we use data on implied volatility traded on the market. In contrast to previous studies, we show that the frequency of data used for measuring realized volatility within a fractionally cointegrating framework is important for the results of unbiasedness tests. Significantly, for many popular exchange rates, the use of intra-day rather than daily data affects the emergence of a different bias, as the possibility of a fractionally integrated risk premium admits itself! Ó

Long memory and structural breaks in commodity futures markets

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