Pricing credit card loans with default risks: A discrete-time approach

The main purpose of this paper is to modify the Jarrow and van Deventer model by using Das and Sundaram (Manag Sci 46:46-62, 2000) model to extend the Heath-Jarrow-Morton (J Finan Quant Anal 25:419-440, 1990) term-structure model to facilitate the consideration of default risks for pricing credit card loans. Furthermore, we derive closed-form solutions within a continuous-time framework. In addition, we also provide a numerical method for the evaluation of credit card loans within a discrete-time framework. Using the market segmentation argument to describe the characteristics of the credit card industry, our simulation results show that the shapes of the forward rate and forward spread (default risk premium) term structures play extremely important roles in determining the value of credit card loans.