On Risk Prediction
Abstract: This thesis comprises four papers concerning risk prediction.Paper [I] suggests a nonlinear and multivariate time series modelframework that enables the study of simultaneity in returns and involatilities, as well as asymmetric effects arising from shocks. Usingdaily data 2000-2006 for the Baltic state stock exchanges and that ofMoscow we find recursive structures with Riga directly depending inreturns on Tallinn and Vilnius, and Tallinn on Vilnius. For volatilitiesboth Riga and Vilnius depend on Tallinn. In addition, we find evidenceof asymmetric effects of shocks arising in Moscow and in the Baltic stateson both returns and volatilities.Paper [II] argues that the estimation error in Value at Risk predictorsgives rise to underestimation of portfolio risk. A simple correction isproposed and in an empirical illustration it is found to be economicallyrelevant.Paper [III] studies some approximation approaches to computing theValue at Risk and the Expected Shortfall for multiple period asset re-turns. Based on the result of a simulation experiment we conclude thatamong the approaches studied the one based on assuming a skewed t dis-tribution for the multiple period returns and that based on simulationswere the best. We also found that the uncertainty due to the estimationerror can be quite accurately estimated employing the delta method. Inan empirical illustration we computed five day Value at Risk's for theS&P 500 index. The approaches performed about equally well.Paper [IV] argues that the practise used in the valuation of the port-folio is important for the calculation of the Value at Risk. In particular,when liquidating a large portfolio the seller may not face horizontal de-mandcurves. We propose a partially new approach for incorporatingthis fact in the Value at Risk and in an empirical illustration we compareit to a competing approach. We find substantial differences.
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