A convexity adjusted duration gap model to measure interest rate risk application to a hypothetical small bank

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University of New Brunswick


The price/yield relationship of a debt instrument, without any embedded option, is convex and it is theoretically well established that duration of the debt instrument provides only the first order (linear) effect, on the price in response to unexpected changes in the yield. Therefore, the duration model overestimates the decline in the price when there is a large increase in the yield and underestimates the increase in the price when there is a large decrease in the yield. The convexity measure of the debt instrument reduces the error of overestimation and underestimation by providing the second order (curvilinear) effect on the price of large changes in the yield. Despite this recognition of the role of the convexity measure, the convexity adjustment to the duration gap model has been neglected in the extend literature to quantify interest rate risk of banks (see, for example, Beets (2004), Entrol et al. (2009), the Basel Committee on Banking Supervision. (2004), among others). This study proposes a convexity adjusted duration gap model to quantify interest rate risk of a bank. In addition, recognizing that the yield curve is normally upward sloping, not flat as is normally assumed, the study uses different interest rates and yields for different assets and different liabilities of the bank. Finally, it permits different adoption of changes in interest rates to different classes of assets and liabilities. The study also presents an application of the model so developed to a hypothetical bank to quantify its interest rate risk and strategies to reduce interest rate risk in the context of a convexity adjusted duration model.