Assessing mortgage servicing rights using a reduced-form model: Considering the effects of interest rate risks, prepayment and default risks, and random state variables

Assessing an MSR's value is difficult in practice because it involves various revenues and costs that are influenced by both the stochastic property of interest rates and the likelihood of prepayment and default. This paper derives a pricing formula using a reduced-form model in order to appraise the MSR's breakeven servicing fee. Numerical examples are given to demonstrate the applications of this reduced-form pricing formula in deriving the breakeven servicing fee and analyzing profits of an MSR. We also provide numerical sensitivity analysis results for operational and state variables to show how the breakeven servicing fee changes with respect to various operational conditions and economic circumstances. Results reveal that changes in the breakeven servicing fee depend mainly on direct servicing costs, the initial interest rate, and the volatility of the interest rate. Our model can assist financial institutions and regulators in evaluating fair servicing fees and in turn improve the management of the various risks of an MSR in response to changing economic conditions and operating costs.