Aspects of estimation uncertainty in risk management

Abstract

This dissertation studies the impact of estimation uncertainty in short-rate interest rate models and its effect upon risk measures based on such models. The estimation uncertainty is described in a Bayesian framework. First, the Bayesian methodology is introduced and computational methods used to apply it are thoroughly discussed. Then, the impact of estimation uncertainty in the Chan-Karolyi-Longstaff-Sanders model is studied by estimating it both with maximum likelihood and Bayesian methods on nine currencies. This study also tests the predictive ability of this model both with and without estimation uncertainty. Additionally, this dissertation studies the impact of such estimation uncertainties upon risk measures for a term-fix insurance contract with cliquet-style guarantees and implicit options. The impact of estimation uncertainty is studied for two risk management techniques: static reserving and dynamic hedging. Additionally, this dissertation extends two existing pricing methods in order to price the aforementioned contract efficiently: The first is the extension of a trinomial tree to a bivariate trinomial tree, the second is the extension of the QUAD-algorithm to the Black-Scholes-Vasicek model.