Finite Difference Approach to Steady State Problems Arising from Mortgage and Option Pricing

Xie, Dejun1; Zheng, Jin2; Zhang, Nan3; Chen, Kun1; Wang, Huaiqing1

10.1007/978-3-642-54900-7_61

2014

18761119

MULTIMEDIA AND UBIQUITOUS ENGINEERING

308

429-435

Zhangjiajie, China

233 SPRING STREET, NEW YORK, NY 10013, UNITED STATES

SPRINGER

Motivated by mortgage valuation, the paper proposes a finite difference approach to solve a class of free boundary problems which may be useful for option pricing in general. Given certain financially meaningful conditions, a mortgage borrower wishes to find the level of market interest rate at which it is optimal to make prepayment. The problem is an analog of finding the optimal level of stock price for early exercise in American put. Mathematically they both can be formulated as free boundary problems. In this paper an algorithm based on the finite difference scheme is designed to find the numerical solution to the steady state of such problems. The approach is calibrated with the perpetual American put option whose solution is explicitly known. The efficiency of the algorithm is tested by numerical simulations.

Finite Difference Numerical Methods Mortgage Valuation Option Pricing

第一 ; 通讯

英语

CPCI-S ; EI

Computer Science

Computer Science, Information Systems ; Computer Science, Theory & Methods

WOS:000342986500061

20151100635906

Boundary value problems ; Costs ; Economics ; Electronic trading ; Finite difference method ; Numerical methods

Computer Applications:723.5 ; Cost and Value Engineering; Industrial Economics:911 ; Numerical Methods:921.6 ; Social Sciences:971

Web of Science

1.South Univ Sci & Technol China, Dept Financial Math & Financial Engn, Shenzhen, Peoples R China
2.Univ Liverpool, Dept Math Sci, Liverpool, Merseyside, England
3.Xian Jiaotong Liverpool Univ, Dept Comp Sci & Software Engn, Xian, Peoples R China

Xie, Dejun,Zheng, Jin,Zhang, Nan,et al. Finite Difference Approach to Steady State Problems Arising from Mortgage and Option Pricing[C]. 233 SPRING STREET, NEW YORK, NY 10013, UNITED STATES:SPRINGER,2014:429-435.