IDEAS home Printed from https://ideas.repec.org/a/taf/eurjfi/v13y2007i6p545-564.html

A Technique for Reducing Discretization Bias from Monte Carlo Simulations: Option Pricing under Stochastic Interest Rates

Author

Listed:
  • Snorre Lindset
  • Arne-Christian Lund

Abstract

Control variates are often used to reduce variability in Monte Carlo estimates and their effectiveness is traditionally measured by the so-called speed-up factor. The main objective of this paper is to demonstrate that a control variate can also be applied to reduce the bias stemming from the discretization of the state variable dynamics. This is particularly valuable when stochastic interest rate models are discretized, since bias reduction through more grid points is computationally expensive.

Suggested Citation

  • Snorre Lindset & Arne-Christian Lund, 2007. "A Technique for Reducing Discretization Bias from Monte Carlo Simulations: Option Pricing under Stochastic Interest Rates," The European Journal of Finance, Taylor & Francis Journals, vol. 13(6), pages 545-564.
    • Handle: RePEc:taf:eurjfi:v:13:y:2007:i:6:p:545-564
    DOI: 10.1080/13518470701198791
    as

    Download full text from publisher

    File URL: http://www.tandfonline.com/doi/abs/10.1080/13518470701198791
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/13518470701198791?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    2. Vasicek, Oldrich Alfonso, 1977. "Abstract: An Equilibrium Characterization of the Term Structure," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(4), pages 627-627, November.
    3. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    4. Miltersen, Kristian R. & Persson, Svein-Arne, 1999. "Pricing rate of return guarantees in a Heath-Jarrow-Morton framework," Insurance: Mathematics and Economics, Elsevier, vol. 25(3), pages 307-325, December.
    5. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    6. Geske, Robert, 1979. "The valuation of compound options," Journal of Financial Economics, Elsevier, vol. 7(1), pages 63-81, March.
    7. David Heath & Robert Jarrow & Andrew Morton, 2008. "Bond Pricing And The Term Structure Of Interest Rates: A New Methodology For Contingent Claims Valuation," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 13, pages 277-305, World Scientific Publishing Co. Pte. Ltd..
    8. Kaushik I. Amin & Robert A. Jarrow, 1992. "Pricing Options On Risky Assets In A Stochastic Interest Rate Economy1," Mathematical Finance, Wiley Blackwell, vol. 2(4), pages 217-237, October.
    9. Geske, Robert & Johnson, H. E., 1984. "The Valuation of Corporate Liabilities as Compound Options: A Correction," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 19(2), pages 231-232, June.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Bjork, Tomas, 2009. "Arbitrage Theory in Continuous Time," OUP Catalogue, Oxford University Press, edition 3, number 9780199574742.
    2. Samuel Chege Maina, 2011. "Credit Risk Modelling in Markovian HJM Term Structure Class of Models with Stochastic Volatility," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 1-2011, January-A.
    3. Suresh M. Sundaresan, 2000. "Continuous‐Time Methods in Finance: A Review and an Assessment," Journal of Finance, American Finance Association, vol. 55(4), pages 1569-1622, August.
    4. Duffie, Darrell, 2003. "Intertemporal asset pricing theory," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, edition 1, volume 1, chapter 11, pages 639-742, Elsevier.
    5. Samuel Chege Maina, 2011. "Credit Risk Modelling in Markovian HJM Term Structure Class of Models with Stochastic Volatility," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 5, July-Dece.
    6. Mondher Bellalah, 2009. "Derivatives, Risk Management & Value," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 7175, March.
    7. Carl Chiarella & Xue-Zhong He & Christina Sklibosios Nikitopoulos, 2015. "Derivative Security Pricing," Dynamic Modeling and Econometrics in Economics and Finance, Springer, edition 127, number 978-3-662-45906-5, March.
    8. Fergusson, Kevin, 2020. "Less-Expensive Valuation And Reserving Of Long-Dated Variable Annuities When Interest Rates And Mortality Rates Are Stochastic," ASTIN Bulletin, Cambridge University Press, vol. 50(2), pages 381-417, May.
    9. Lim, Terence & Lo, Andrew W. & Merton, Robert C. & Scholes, Myron S., 2006. "The Derivatives Sourcebook," Foundations and Trends(R) in Finance, now publishers, vol. 1(5–6), pages 365-572, April.
    10. repec:uts:finphd:40 is not listed on IDEAS
    11. Eichler, Stefan & Karmann, Alexander & Maltritz, Dominik, 2011. "The term structure of banking crisis risk in the United States: A market data based compound option approach," Journal of Banking & Finance, Elsevier, vol. 35(4), pages 876-885, April.
    12. Giandomenico, Rossano, 2008. "Asset Liability Management for Banks," MPRA Paper 18848, University Library of Munich, Germany.
    13. Boero, G. & Torricelli, C., 1996. "A comparative evaluation of alternative models of the term structure of interest rates," European Journal of Operational Research, Elsevier, vol. 93(1), pages 205-223, August.
    14. Li, Qian & Wang, Li, 2024. "Option pricing under jump diffusion model," Statistics & Probability Letters, Elsevier, vol. 211(C).
    15. repec:wyi:journl:002108 is not listed on IDEAS
    16. Chiang, Shu Ling & Tsai, Ming Shann, 2020. "The valuation of deposit insurance allowing for the interest rate spread and early-bankruptcy risk," The Quarterly Review of Economics and Finance, Elsevier, vol. 76(C), pages 345-356.
    17. Dammak, Wael & Hamad, Salah Ben & de Peretti, Christian & Eleuch, Hichem, 2023. "Pricing of European currency options considering the dynamic information costs," Global Finance Journal, Elsevier, vol. 58(C).
    18. Shane Miller, 2007. "Pricing of Contingent Claims Under the Real-World Measure," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 2-2007, January-A.
    19. repec:dau:papers:123456789/5374 is not listed on IDEAS
    20. Zhang, Kun & Liu, Jing & Wang, Erkang & Wang, Jin, 2017. "Quantifying risks with exact analytical solutions of derivative pricing distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 471(C), pages 757-766.
    21. Dimson, Elroy & Mussavian, Massoud, 1999. "Three centuries of asset pricing," Journal of Banking & Finance, Elsevier, vol. 23(12), pages 1745-1769, December.
    22. repec:wyi:journl:002109 is not listed on IDEAS
    23. Ravi Kashyap, 2016. "Options as Silver Bullets: Valuation of Term Loans, Inventory Management, Emissions Trading and Insurance Risk Mitigation using Option Theory," Papers 1609.01274, arXiv.org, revised Mar 2022.
    24. repec:abd:kauiea:v:30:y:2017:i:2:p:135-157 is not listed on IDEAS
    25. Kevin John Fergusson, 2018. "Less-Expensive Pricing and Hedging of Extreme-Maturity Interest Rate Derivatives and Equity Index Options Under the Real-World Measure," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 3-2018, January-A.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:taf:eurjfi:v:13:y:2007:i:6:p:545-564. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/REJF20 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.