Modeling of Risk Measure Bonds Using the Beta Model

Abstract

Duration and convexity are important measures in fixed-income portfolio management. In this paper, we analyze this measure of the bonds by applying the beta model. The general usefulness of the beta probability distribution enhances its applicability in a wide range of reliability analyses, especially in the theory and practice of reliability management. We estimate the beta density function of the duration/convexity. This estimate is based on two important and simple models of short rates, namely, Vasicek and CIR (Cox, Ingersoll, and Ross CIR). The models are described and then their sensitivity of the models with respect to changes in the parameters is studied. We generate the stochastic interest rate on the duration and convexity model. The main results show that the beta probability distribution can be applied to model each phase of the risk function. This distribution approved its effectiveness, simplicity and flexibility. In this paper, we are interested in providing a decision-making tool for the manager in order to minimize the portfolio risk. It is helpful to have a model that is reasonably simple and suitable to different maturity of bonds. Also, it is widely used by investors for choosing bond portfolio immunization through the investment strategy. The finding also shows that the probability of risk measured by the reliability function is to highlight the relationship between duration/convexity and different risk levels. With these new results, this paper offers several implications for investors and risk management purposes.