The Valuation at Origination of Mortgages with Full Prepayment and Default Risks

We investigate the valuation problem of a mortgage contract with full prepayment and default risks using the reduced-form model with regime switching. The hazard rates of full prepayment and default are specified as linear functions of the risk-free interest rate and house prices, respectively, which are characterized by Ornstein-Uhlenbeck processes with regime switching. To derive the explicit valuation formula, we derive the distribution of the number of transitions for two-state Markov processes in finite time and the conditional joint probability density function of transition times using the uniformization technique. Finally, we analyze the effect of parameters on the valuation of the mortgage.