Long memory and volatility behaviour in Paris option market

Abstract

This paper investigates the relationship between realised-implied volatility, by examining the empirical evidence for the aspect followed by two volatility process. The analysis is undertaken using daily from May 2005 to April 2009 at the EURONEXT. We consider semi parametric frequency domain analysis of fractional cointegration between long memory processes. The estimation of predictive regression narrow band least square (NBLS) is based on the Fourier frequencies number included in the spectral regression. Consistent with exploration the GPH and Local Whittle estimators, the results notice the non stationary long memory in realised-implied volatility and the mean reverting behaviour. An application to NBLS model, we indicate that implied volatility is a consistent estimate of realised volatility. The contribution of this paper is to demonstrate that options prices display long memory and that form of long memory is persistence during the 2008 crisis.