Title: A portfolio optimisation model for credit risky bonds with Markov model credit rating dynamics
Authors: Arti Singh; Selvamuthu Dharmaraja
Addresses: Department of Mathematics, IIT Delhi, Hauz Khas, New Delhi 110016, India ' Department of Mathematics, IIT Delhi, Hauz Khas, New Delhi 110016, India
Abstract: In this paper, a credit risk optimisation model for the portfolio of credit risky bonds with linfin;-norm risk measure is proposed. The proposed model is formulated as a linear programming problem which makes it computationally efficient for the portfolio of large size. The rates of returns of the bonds are the input parameters of the proposed model and of the other portfolio optimisation models which are considered for the comparison with the former. The complete approach of generating rate of returns of the bonds, given their initial credit ratings and transition probability matrices, is presented. The time homogeneous discrete time Markov chain model is assumed for the credit rating dynamics of bonds. With extensive numerical illustrations, the proposed approach of obtaining rate of returns of the bonds is demonstrated. Furthermore, comparison of the proposed credit risk optimisation model with other inline existing portfolio optimisation models is performed.
Keywords: credit risk; credit rating; discrete time Markov chain; DTMC; portfolio optimisation; l∞-norm; efficient frontier; mean absolute deviation; MAD.
International Journal of Financial Markets and Derivatives, 2017 Vol.6 No.2, pp.102 - 119
Accepted: 17 Jul 2017
Published online: 13 Nov 2017 *