@MISC\{IMM2012-06234,
    author       = "P. Nystrup",
    title        = "Scenario generation for financial market indices",
    year         = "2012",
    publisher    = "Technical University of Denmark, {DTU} Informatics, {E-}mail: reception@imm.dtu.dk",
    address      = "Asmussens Alle, Building 305, {DK-}2800 Kgs. Lyngby, Denmark",
    note         = "Supervisors Lasse Engbo Christiansen,lec@imm.dtu.dk, {DTU} Informatics, and Kourosh Marjani Rasmussen, {DTU} Management",
    url          = "http://www.imm.dtu.dk/English.aspx",
    abstract     = "The purpose of the project is to analyse the given index data with the aim of generating scenarios that can form the basis of decisions regarding strategic asset allocation. The data available is observations of the daily closing value of eleven financial market indices; six stock market indices, four bond market indices, and one money market index. The distribution of the log returns is a mixture of a normal distribution and a few extreme observations from a different distribution. Traditional measures reject any resemblance with the normal distribution due to the presence of extreme values. Yet, more robust measures are able to find certain similarities. The index data has a growing mean trend, a time dependent variance, auto and cross-correlation. A log return transformation is suitable for making the mean stationary, sampling on weekly basis instead of daily eliminates most of the autocorrelation, a regime model, where upturns and downturns are modelled independently, handles the changing cross-correlation, and finally {ARCH-}models are employed to model the changing variance. The approach taken is to model the principal components of the log return series. The advantage of modelling the independent principal components is the possibility of reducing the dimensionality based on the strong cross-correlation exhibited, as well as easy applicability for scenario generation. The simulated scenarios were compared to bootstrapped scenarios, and were found to be better at reproducing the crises observed in the dataset. The ability to reproduce realistic crises appeared to be connected with the ability to reproduce volatility clustering correctly. The bootstrapped scenarios were also more optimistic with median returns closer to the average returns from the dataset, where the scenarios simulated from the regime model were more influenced by the recession at the end of the data period/the beginning of the scenarios."
}