Ph.d.-forsvar: Thor Pajhede Nielsen: "Tales From the Unit Interval: Backtesting, Forecasting and Modeling"
This thesis comprises three self-contained chapters, related to either credit or market risk.
Chapter one discusses new likelihood ratio tests for evaluating Value-at-Risk (VaR) forecasts. We provide closed form expressions for the tests as well as asymptotic theory. Not only do the generalized tests have power against k'th order dependence by definition, but also included simulations indicate improved power performance over existing tests. The chapter is forthcoming in the Journal of Forecasting.
Chapter two discusses how to best forecast VaR of a portfolio. In particular one faces a number of choices in how to construct a model; Univariate or multivariate models, Interday or intraday based data and distributional alternatives. We consider A portfolio of 44 major US stocks from the S&P 500 index and compare using both recently developed backtests and the model confidence set approach. We also consider the square-root-of-time scaling rule for a 10 day period as suggested in the Basel accords.
Chapter three discuss an observation driven, conditionally beta distributed model. The model includes both explanatory variables and autoregressive dependence in the mean and precision parameters using the mean-precision parameterization of the beta distribution suggested by Ferrari et al. (2004). Our model is a generalization of the β ARMA model proposed in Rocha et al. (2009). We also highlight some errors in their derivations of the score and information which has implications for the asymptotic theory. Included simulations suggest that standard asymptotics for estimators and test statistics apply. In an empirical application to Moody's monthly US 12-month issuer default rates in the period 1972-2015 , we revisit the results of Agosto et al. (2016) in examining the conditional independence hypothesis of Lando et al. (2010).