ROBUST NUMERICAL SCHEME FOR A FIXED-RATE MORTGAGE VALUATION MODEL UNDER CIR INTEREST RATES
ZHONGDI CEN *
Institute of Mathematics, Zhejiang Wanli University, Ningbo 315100, Zhejiang, P. R. China.
*Author to whom correspondence should be addressed.
In this paper we present a robust numerical scheme for the linear complementarity problem arising from the valuation of fixed rate mortgages. Under the assumption that the underlying interest rate follows the CIR model, the differential operator of the continuous linear complementarity problem is convection-dominated. We discretize the spatial derivatives by a hybrid finite difference method on a piecewise uniform mesh, and meanwhile, use the implicit Euler method to discretize the time derivative. It is shown that the numerical scheme is unconditionally stable. We prove that the scheme is almost second order convergent with respect to the interest rate. Finally, the numerical examples demonstrate the stability and accuracy of the scheme.
Keywords: Fixed-rate mortgage, prepayment, linear complementarity problem, hybrid difference scheme, CIR