Carrier-envelope phase stabilization of few cycle optical pulses has recently been realized. This advance in femtosecond technology is important in both extreme nonlinear optics and optical frequency metrology. The development of air-silica microstructure fiber was an enabling technology for performing phase stabilization. The microstructure fiber provides a group-velocity zero within the spect...

We consider a new class of estimators for volatility functionals in the setting of frequently observed Itō diffusions which are disturbed by i.i.d. noise. These statistics extend the approach of pre-averaging as a general method for the estimation of integrated volatility in the presence of microstructure noise and are closely related to the original concept of bipower variation in the no-noise...

We analyze the impact of time series dependence in market microstructure noise on the properties of estimators of the integrated volatility of an asset price based on data sampled at frequencies high enough for that noise to be a dominant consideration. We show that combining two time scales for that purpose will work even when the noise exhibits time series dependence, analyze in that context ...

The main objective of this paper is to propose a feasible, model free estimator of the predictive density of integrated volatility. In this sense, we extend recent papers by Andersen, Bollerslev, Diebold and Labys (2003), and by Andersen, Bollerslev and Meddahi (2004, 2005), who address the issue of pointwise prediction of volatility via ARMA models, based on the use of realized volatility. Our...

Exploring a possible correlation between the efficient price and the noise, as HL do, is an exciting and challenging task. By examining the volatility signature plots of trades and quotes, HL report that RV estimates based on quotes at very high frequency decrease. This is different from many earlier findings on volatility signature plots based on transaction prices. It is important to figure o...

We introduce a new stochastic model for the variations of asset prices at the tick-by-tick level in dimension 1 (for a single asset) and 2 (for a pair of assets). The construction is based on marked point processes and relies on mutually exciting stochastic intensities as introduced by Hawkes. We associate a counting process with the positive and negative jumps of an asset price. By coupling su...

Measuring and forecasting volatility of asset returns is very important for asset trading and risk management. There are various forms of volatility estimates, including implied volatility, realized volatility and volatility assumed under stochastic volatility models and GARCH models. Research has shown that these different methods are closely related but have different perspectives, strengths ...