Date of Award
Doctor of Philosophy (PhD)
Risk Management and Insurance
The first chapter examines statistical inference in the context of a generalized version of the widely used Vasicek credit default model, whereby the purely static model is extended to allow for autocorrelated default rates and macroeconomic risk factors. The proposed inference method proceeds by numerically inverting a likelihood ratio test and then it exploits projection techniques to produce simultaneous confidence intervals for general non-linear functions of the model parameters, including multi-step ahead expected losses. An extensive simulation study reveals that the new method outperforms Delta method and even the usual residual and parametric bootstrap procedures. The results of an empirical application to U.S. bank loan losses show that moving from the static to the dynamic default rate distribution significantly lowers the implied economic capital requirements.
The second chapter studies long-term risk management which has gained great importance following several tremendous financial crises. It focuses on the 10-day and 30-day ahead forecast of the most popular tail risk measure, value-at-risk(VaR). Two categories of approaches are utilized: 1, direct VaR forecast by square-root-of-time rule (SRTR) and pseudo return generation by GARCH model, using Monte Carlo Simulation (GARCH-MC). 2, indirect VaR forecast through a volatility forecast by autoregressive models of realized volatility and mixed-frequency sampling (MIDAS) method. By an extensive comparison of out-of-sample forecasts and back-testing statistics, it is shown that SRTR combined with Cornish-Fisher approximation outperforms the alternatives and provides adequate forecasting accuracy. The possible reason is that serial correlation is not significant in the returns and the effects of other stylized facts in returns offset each other. The indirect forecast approach does not perform as well as the direct approach.
The last chapter proposes an innovative approach of forecasting swap spreads. It is shown that swap spreads and the risk factors tend to be random walk processes, and the residual obtained from regressing swap spread on a set of contemporaneous risk factors is a mean-reverting process. Information contained in the residual is explored by using it as the predictor of future swap spread. In terms of forecasting methodology, this chapter introduces an efficient and simple method through modeling residual as an Ornstein-Uhlenbeck (OU) process. The forecasting is implemented over a continuous set of horizons from 1 day to 200 days. Two measures of forecasting errors are utilized: mean squared error (MSE) and mean absolute error(MAE). By comparing errors of both in-sample and out-of-sample forecasting, evidence is found that the residual obtained from a contemporaneous regression of swap spreads on the risk factors contains significant predicative information. Moreover, modeling residual as an OU process achieves superior forecasting performance than the alternatives.
Yu, Jinyu, "Essays on Financial Risk Modeling and Forecasting." Dissertation, Georgia State University, 2014.