Estimating Quadratic Variation When Quoted Prices Change By A Constant Increment

Abstract

For financial assets whose best quotes almost always change by jumping by the market's price tick size (one cent, five cents, etc.), this paper proposes an estimator of Quadratic Variation which controls for microstructure effects. It measures the prevalence of 'alternations', where quotes jump back to their just-previous price. It defines a simple property called 'uncorrelated alternation', which under conditions implies that the estimator is consistent in an asymptotic limit theory, where jumps become very frequent and small. Feasible limit theory is developed, and in simulations works well.