Functional modelling of volatility in the Swedish limit order book

The publicly available electronic limit order book at the Stockholm Stock Exchange consists of five levels of prices and quantities of a given stock with a bid and ask side. All changes in the book during one day can be recorded with a time quote. Studying the variation of the quoted price returns as a function of quantity is discussed. In particular, discovering and modelling dynamic behaviours in the volatility of prices and liquidity measures are considered. Applying a functional approach, estimation of the volatility dynamics of the spreads, created as differences between the ask and bid prices, is presented through a case study. For that purpose two-step estimation of functional linear models is used, extending this method to a time series context.