Bipower variation with jumps and correlated returns

•We propose a jump robust estimator of volatility for the correlated returns.•We model correlated returns using fractional Brownian motion.•Our method is robust to stochastic volatility and the rare jumps.•Simulations show that our method outperforms the bipower variation method.

This paper extends the classical work of bipower variation by allowing the return process to be autocorrelated. We propose a method of estimating the return volatility when the price process is described by a fractal Brownian motion with jumps.