The impact of model risk on capital reserves: a quantitative analysis

Philip Bertram and Philipp Sibbertsen and Gerhard Stahl

Journal of Risk

Abstract: ABSTRACT This paper analyzes and quantifies the idea of model risk in the environment of internal model building. We define various types of model risk including estimation risk, model risk in distribution and model risk in functional form. By quantifying these concepts we analyze the impact of the modeling process of an econometric model on the resulting company model. Utilizing real insurance data we specify, estimate and simulate various linear and nonlinear time series models for the inflation rate and examine its impact on pension liabilities from the aspect of model risk. By considering different risk measures we show that model risk can differ profoundly due to the specification process of the econometric model resulting in substantial variations of capital reserves. We further compare our definition of model risk with the standard Basel approach, which interprets model risk as a constant multiplication factor with regard to market risk. We show that these different definitions of model risk can lead to remarkable monetary differences concerning induced capital reserves.

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