• 论文 •

### 固定利率抵押贷款模型的基于自适应网格的有限差分法

1. 浙江万里学院数学研究所,宁波 315100
• 收稿日期:2010-10-11 出版日期:2014-01-25 发布日期:2014-04-11

CEN Zhongdi , XU Aimin , LE Anbo. A FINITE DIFFERENCE SCHEME BASED ON A LAYER-ADAPTIVE MESH FOR THE FIXED RATE MORTGAGES MODEL[J]. Journal of Systems Science and Mathematical Sciences, 2014, 34(1): 10-19.

### A FINITE DIFFERENCE SCHEME BASED ON A LAYER-ADAPTIVE MESH FOR THE FIXED RATE MORTGAGES MODEL

CEN Zhongdi , XU Aimin , LE Anbo

1. Institute of Mathematics, Zhejiang Wanli University,Ningbo  315100
• Received:2010-10-11 Online:2014-01-25 Published:2014-04-11

In this paper we adopt the adaptive mesh approach to solve the model for pricing the fixed-rate mortgage, which is a convection-dominated problem when the volatility or the asset price is small. It is well known that when using the standard inite difference method to solve those convection-dominated problems, numerical difficulty can be caused. Our numerical  method combines  a central difference spatial discretization on a piecewise uniform mesh with an implicit time stepping technique. The matrix associated with discrete operator is an $M$-matrix, which ensures that the scheme is stable for arbitrary volatility and
arbitrary interest rate without any extra conditions. We apply the maximum principle to the discrete linear complementarity problem in two mesh sets and derive the error estimates. It is proved that the scheme is second order convergent with respect to the spatial variable. Numerical results indicate that the numerical solutions by our method are non-oscillatory and the scheme is second order convergent with respect to the spatial variable.

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