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.