Volatility and Dependence in Fixed Income Forward Rates with Application to Market Risk of Derivative Portfolios
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This thesis explores the modeling of volatility and dependence in forward rates in the fixed income market for the purpose of risk estimation in derivative portfolios. A brief background on popular quantile-based risk measures is given. A short introduction is given to GARCH-type volatility models, as well as copula and vine models for dependence between random variables. Some details on parameter estimation and sampling related to these models are also provided. A backtesting procedure is performed using various combinations of volatility and dependence models. The results of this procedure indicate that the Student's t copula is preferable among the dependence structures considered. Also, none of the choices of conditional distribution for the volatility models provide good results at all the percentiles considered, but the normal distribution appears to be a good choice far into the tails.