Valuation of fixed and variable rate mortgages: binomial tree versus analytical approximations (Q1938899)

The author considers the simplified binomial tree approximation to diffusion processes proposed by \textit{M. Costabile} et al., [Decis. Econ. Finance 32, No. 2, 161--181 (2009; Zbl 1176.91152)] and analyzes its applicability to the mortgage valuation problem for the Vasicek and Cox-Ingersoll-Ross interest rate models. The pricing models for the amortized fixed and and variable rate mortgage contracts are introduced. The construction by Costabile and Massabo of computationally simple binomial trees is recalled and it is shown how to apply it to the evaluation of prices and Greeks for non-callable and callable mortgages as well as the associated prepayment option. Fixed rate mortgage under the Vasicek/CIR model are considered. Some exact and limiting analytical formulas and approximations for Vasicek model are displayed. Numerical comparisons and examples are provided.