Dr Ferhana Ahmad is an Assistant Professor at Suleman Dawood School of Business in the area of Mathematical and Computational Finance. She has a DPhil and MSc in Mathematical and Computational Finance from University of Oxford, England. She was an Associate Member of Oxford-Man Institute of Quantitative Finance at University of Oxford. She was also the student representative on the Mathematical, Physical and Life Sciences Division’s Divisional Graduate Joint Consultative Forum and a graduate student representative on Consultative Committee for Graduates, Mathematical Institute at University of Oxford. Her areas of interest are in modeling mortgage and mortgage-backed securities, energy and credit derivatives, numerical simulations and stochastic calculus.
In this paper, a model for a single mortgage in an intensity-based framework is developed while considering both prepayment and default risks. The random time to default is modeled as the first time the intensity of default reaches a random level, whereas the random time to prepayment is modeled as the first time the intensity of prepayment reaches a random level. Since the mortgage contract ends when either of the two events occurs, the intensity process for the minimum of default and prepayment times is found. Using credit risk modeling framework to model the present value of the individual mortgage with continuous payments, an implicit equation for mortgage rate is established. A numerical technique to solve the equation after defining the intensities is presented along with detailed sensitivity analysis of model parameters.