We model the dynamics of ask and bid curves in a limit order book market using a dynamic semiparametric factor model. The shape of the curves is captured by a factor structure which is estimated nonparametrically. Corresponding factor loadings are modelled jointly with best bid and best ask quotes using a vector error correction specification. Applying the framework to four stocks traded at the Australian Stock Exchange (ASX) in 2002, we show that the suggested model captures the spatial and temporal dependencies of the limit order book. We find spillover effects between both sides of the market and provide evidence for short-term quote predictability. Relating the shape of the curves to variables reflecting the current state of the market, we show that the recent liquidity demand has the strongest impact. In an extensive forecasting analysis we show that the model is successful in forecasting the liquidity supply over various time horizons during a trading day. Moreover, it is shown that the model's forecasting power can be used to improve optimal order execution strategies.
We propose a generalized risk measure for expectile-based expected shortfall estimation. The generalization is designed with a mixture of Gaussian and Laplace densities. Our plug-in estimator is derived from an analytic relationship between expectiles and expected shortfall. We investigate the sensitivity and robustness of the expected shortfall to the underlying mixture parameter specification and the risk level. Empirical results from US, German and UK stock markets and for selected NASDAQ blue chip companies indicate that expected shortfall can be successfully estimated using the proposed method on a monthly, weekly, daily, and intra-daily basis using a one-year or one-day time horizon across different risk levels.
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