A No Arbitrage Fractional Cointegration Analysis of the Range Based Volatility

Abstract

The no arbitrage relation between futures and spot prices implies an analogous relation between futures and spot volatilities as measured by daily range. Long memory features of the range-based volatility estimators of the two series are analyzed, and their joint dynamics are modeled via a fractional vector error correction model (FVECM), in order to explicitly consider the no arbitrage constraints. We introduce a two-step estimation procedure for the FVECM parameters and we show the properties by a Monte Carlo simulation. The out-of-sample forecasting superiority of FVECM, with respect to competing models, is documented. The results highlight the importance of giving fully account of long-run equilibria in volatilities in order to obtain better forecasts.

Keywords: Range-based volatility estimator, Long memory, Fractional cointegration, Fractional VECM, Stock Index Futures

JEL Classification: C32, C13, G13