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

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Multimedia and Ubiquitous Engineering

Part of the book series: Lecture Notes in Electrical Engineering ((LNEE,volume 308))

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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.

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References

  1. Baxter, M., Rennie, A.: Financial Calculus, An introductin to derivative pricing. Cambridge University Press (2005)

    Google Scholar 

  2. Cox, J., Ingersoll, J., Ross, S.: A theory of the term structure of interest rates. Econometrica 53, 385–407 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  3. Vasicek, O.A.: An equilibrium characterization of the term structure. J. Fin. Econ. 5, 177–188 (1977)

    Article  Google Scholar 

  4. Friedman, A.: Variational Principles and Free Boundary Problems. John Wiley & Sons, Inc., New York (1982)

    MATH  Google Scholar 

  5. Wilmott, P., Howison, S., Dewynne, J.: The Mathemaitcs of Financial Derivatives. Cambridge University Press (2002)

    Google Scholar 

  6. Xie, D.: An Steady State Problem Arising from Mortgage Valuations, arxiv.org/abs/0909.5389 (2009)

    Google Scholar 

  7. Ascher, U.M., Petzold, L.R.: Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations. Society for Industrial and Applied Mathematics (1998)

    Google Scholar 

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Authors and Affiliations

  1. Department of Financial Mathematics and Financial Engineering, South University of Science and Technology of China, Shenzhen, China

    Dejun Xie, Kun Chen & Huaiqing Wang

  2. Department of Mathematical Sciences, University of Liverpool, Liverpool, UK

    Jin Zheng

  3. Department of Computer Science and Software Engineering, Xi’an Jiaotong-Liverpool University, Suzhou, China

    Nan Zhang

Authors
  1. Dejun Xie
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  2. Jin Zheng
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  3. Nan Zhang
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  4. Kun Chen
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  5. Huaiqing Wang
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Corresponding author

Correspondence to Dejun Xie .

Editor information

Editors and Affiliations

  1. Department of Computer Science and Engineering, Seoul University of Science & and Technology (SeoulTech), Seoul, Korea, Republic of (South Korea)

    James J. (Jong Hyuk) Park

  2. School of Computing and Information Sciences, Florida International University, Miami, Florida, Florida, USA

    Shu-Ching Chen

  3. School of IT Engineering, Catholic University of Daegu, Kyungsan-shi, Korea, Republic of (South Korea)

    Joon-Min Gil

  4. School of Computer Science and Engineeri, The University of Aizu, Aizu-Wakamatsu City, Fukushima, Japan

    Neil Y. Yen

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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: Park, J., Chen, SC., Gil, JM., Yen, N. (eds) Multimedia and Ubiquitous Engineering. Lecture Notes in Electrical Engineering, vol 308. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-54900-7_61

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  • DOI: https://doi.org/10.1007/978-3-642-54900-7_61

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-54899-4

  • Online ISBN: 978-3-642-54900-7

  • eBook Packages: EngineeringEngineering (R0)

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