Finite difference approach to steady state problems arising from mortgage and option pricing

Dejun Xie; Jin Zheng; Nan Zhang; Kun Chen; Huaiqing Wang

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

Finite difference approach to steady state problems arising from mortgage and option pricing

Dejun Xie
, Jin Zheng
, Nan Zhang
, Kun Chen
, Huaiqing Wang

Southern University of Science and Technology
University of Liverpool

Research output: Chapter in Book or Report/Conference proceeding › Conference Proceeding › peer-review

Abstract

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.

Original language	English
Title of host publication	Multimedia and Ubiquitous Engineering
Editors	Shu-Ching Chen, James J. Park, Neil Y. Yen, Joon-Min Gil
Publisher	Springer Verlag
Pages	429-435
Number of pages	7
ISBN (Electronic)	9783642548994
DOIs	https://doi.org/10.1007/978-3-642-54900-7_61
Publication status	Published - 2014
Event	FTRA 8th International Conference on Multimedia and Ubiquitous Engineering, MUE 2014 - Zhangjiajie, China Duration: 28 May 2014 → 31 May 2014

Publication series

Name	Lecture Notes in Electrical Engineering
Volume	308
ISSN (Print)	1876-1100
ISSN (Electronic)	1876-1119

Conference

Conference	FTRA 8th International Conference on Multimedia and Ubiquitous Engineering, MUE 2014
Country/Territory	China
City	Zhangjiajie
Period	28/05/14 → 31/05/14

Keywords

Finite Difference
Mortgage Valuation
Numerical Methods
Option Pricing

Access to Document

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

Cite this

Xie, D., Zheng, J., Zhang, N., Chen, K., & Wang, H. (2014). Finite difference approach to steady state problems arising from mortgage and option pricing. In S.-C. Chen, J. J. Park, N. Y. Yen, & J.-M. Gil (Eds.), Multimedia and Ubiquitous Engineering (pp. 429-435). (Lecture Notes in Electrical Engineering; Vol. 308). Springer Verlag. https://doi.org/10.1007/978-3-642-54900-7_61

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title = "Finite difference approach to steady state problems arising from mortgage and option pricing",

abstract = "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.",

keywords = "Finite Difference, Mortgage Valuation, Numerical Methods, Option Pricing",

author = "Dejun Xie and Jin Zheng and Nan Zhang and Kun Chen and Huaiqing Wang",

note = "Publisher Copyright: {\textcopyright} Springer-Verlag Berlin Heidelberg 2014.; FTRA 8th International Conference on Multimedia and Ubiquitous Engineering, MUE 2014 ; Conference date: 28-05-2014 Through 31-05-2014",

year = "2014",

doi = "10.1007/978-3-642-54900-7\_61",

language = "English",

series = "Lecture Notes in Electrical Engineering",

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editor = "Shu-Ching Chen and Park, \{James J.\} and Yen, \{Neil Y.\} and Joon-Min Gil",

booktitle = "Multimedia and Ubiquitous Engineering",

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Xie, D, Zheng, J, Zhang, N, Chen, K & Wang, H 2014, Finite difference approach to steady state problems arising from mortgage and option pricing. in S-C Chen, JJ Park, NY Yen & J-M Gil (eds), Multimedia and Ubiquitous Engineering. Lecture Notes in Electrical Engineering, vol. 308, Springer Verlag, pp. 429-435, FTRA 8th International Conference on Multimedia and Ubiquitous Engineering, MUE 2014, Zhangjiajie, China, 28/05/14. https://doi.org/10.1007/978-3-642-54900-7_61

Finite difference approach to steady state problems arising from mortgage and option pricing. / Xie, Dejun; Zheng, Jin; Zhang, Nan et al.
Multimedia and Ubiquitous Engineering. ed. / Shu-Ching Chen; James J. Park; Neil Y. Yen; Joon-Min Gil. Springer Verlag, 2014. p. 429-435 (Lecture Notes in Electrical Engineering; Vol. 308).

Research output: Chapter in Book or Report/Conference proceeding › Conference Proceeding › peer-review

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AU - Xie, Dejun

AU - Zheng, Jin

AU - Zhang, Nan

AU - Chen, Kun

AU - Wang, Huaiqing

N1 - Publisher Copyright: © Springer-Verlag Berlin Heidelberg 2014.

PY - 2014

Y1 - 2014

N2 - 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.

AB - 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.

KW - Finite Difference

KW - Mortgage Valuation

KW - Numerical Methods

KW - Option Pricing

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Y2 - 28 May 2014 through 31 May 2014

ER -

Finite difference approach to steady state problems arising from mortgage and option pricing

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