IDEAS home Printed from https://ideas.repec.org/p/ant/wpaper/2003027.html
   My bibliography  Save this paper

Path integrals as a tool for pricing interest rate contingent claims: The case of reflecting and absorbing boundaries

Author

Listed:
  • DECAMPS, Marc
  • DE SCHEPPER, Ann
  • GOOVAERTS, Marc

Abstract

Common interest rate models are faced with the problem of volatilities vanishing for spot rates in the vicinity of zero. A possible answer to this difficulty can be given by the introduction of a reflecting boundary at zero, at the same time guaranteeing the spot rate to be non-negative, which is needed in order to avoid the possibility of arbitrage. In the present paper, we obtain closed form expressions for transition probalities and for prices of general interest-rate contingent claims by means of path integrals, when the spot rate process is modelled by means of a general diffusion with a reflecting or absorbing boundary. We also show how to derive accurate closed form approximations in case the path integrals are not analytically computable.

Suggested Citation

  • DECAMPS, Marc & DE SCHEPPER, Ann & GOOVAERTS, Marc, "undated". "Path integrals as a tool for pricing interest rate contingent claims: The case of reflecting and absorbing boundaries," Working Papers 2003027, University of Antwerp, Faculty of Business and Economics.
  • Handle: RePEc:ant:wpaper:2003027
    as

    Download full text from publisher

    File URL: https://repository.uantwerpen.be/docman/irua/aca324/4a6664ee.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. J. Michael Harrison & Michael I. Taksar, 1983. "Instantaneous Control of Brownian Motion," Mathematics of Operations Research, INFORMS, vol. 8(3), pages 439-453, August.
    2. Ait-Sahalia, Yacine, 1996. "Testing Continuous-Time Models of the Spot Interest Rate," The Review of Financial Studies, Society for Financial Studies, vol. 9(2), pages 385-426.
    3. GOOVAERTS, Marc & DE SCHEPPER, Ann & DECAMPS, Marc, 2002. "Transition probabilities for diffusion equations by means of path integrals," Working Papers 2002026, University of Antwerp, Faculty of Business and Economics.
    4. Merton, Robert C, 1973. "An Intertemporal Capital Asset Pricing Model," Econometrica, Econometric Society, vol. 41(5), pages 867-887, September.
    5. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    6. Montagna, Guido & Nicrosini, Oreste & Moreni, Nicola, 2002. "A path integral way to option pricing," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 310(3), pages 450-466.
    7. G. Montagna & O. Nicrosini & N. Moreni, 2002. "A Path Integral Way to Option Pricing," Papers cond-mat/0202143, arXiv.org.
    8. Marco Rosa-Clot & Stefano Taddei, 2002. "A Path Integral Approach To Derivative Security Pricing Ii: Numerical Methods," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 5(02), pages 123-146.
    9. Chiarella, Carl & El-Hassan, Nadima & Kucera, Adam, 1999. "Evaluation of American option prices in a path integral framework using Fourier-Hermite series expansions," Journal of Economic Dynamics and Control, Elsevier, vol. 23(9-10), pages 1387-1424, September.
    10. Dhaene, J. & Denuit, M. & Goovaerts, M. J. & Kaas, R. & Vyncke, D., 2002. "The concept of comonotonicity in actuarial science and finance: applications," Insurance: Mathematics and Economics, Elsevier, vol. 31(2), pages 133-161, October.
    11. 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.
    12. Stanton, Richard, 1997. "A Nonparametric Model of Term Structure Dynamics and the Market Price of Interest Rate Risk," Journal of Finance, American Finance Association, vol. 52(5), pages 1973-2002, December.
    13. Brennan, Michael J. & Schwartz, Eduardo S., 1979. "A continuous time approach to the pricing of bonds," Journal of Banking & Finance, Elsevier, vol. 3(2), pages 133-155, July.
    14. Black, Fischer, 1995. "Interest Rates as Options," Journal of Finance, American Finance Association, vol. 50(5), pages 1371-1376, December.
    15. Carl Chiarella, Nadima El-Hassan, & Adam Kucera, "undated". "Option Pricing in a Path Integral Framework Using Fourier-Hermite Series Expansions," Computing in Economics and Finance 1997 132, Society for Computational Economics.
    16. Michael J. Brennan and Eduardo S. Schwartz., 1979. "A Continuous-Time Approach to the Pricing of Bonds," Research Program in Finance Working Papers 85, University of California at Berkeley.
    17. Montagna, Guido & Morelli, Marco & Nicrosini, Oreste & Amato, Paolo & Farina, Marco, 2003. "Pricing derivatives by path integral and neural networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 324(1), pages 189-195.
    18. Kleinert, Hagen, 2002. "Option pricing from path integral for non-Gaussian fluctuations. Natural martingale and application to truncated Lèvy distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 312(1), pages 217-242.
    19. Dhaene, J. & Denuit, M. & Goovaerts, M. J. & Kaas, R. & Vyncke, D., 2002. "The concept of comonotonicity in actuarial science and finance: theory," Insurance: Mathematics and Economics, Elsevier, vol. 31(1), pages 3-33, August.
    20. Carl Chiarella & Nadima El-Hassan, 1997. "Evaluation of Derivative Security Prices in the Heath-Jarrow-Morton Framework as Path Integrals Using Fast Fourier Transform Techniques," Working Paper Series 72, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
    21. Kohei Marumo & Takashi Nakayama & Shinichi Nishioka & Toshihiro Yoshida, 2003. "Extracting Market Expectations on the Duration of the Zero Interest Rate Policy from Japan's Bond Prices," Bank of Japan Working Paper Series Financial Markets Departm, Bank of Japan.
    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. Zura Kakushadze, 2014. "Path Integral and Asset Pricing," Papers 1410.1611, arXiv.org, revised Aug 2016.
    2. Decamps, Marc & De Schepper, Ann & Goovaerts, Marc, 2004. "Applications of δ-function perturbation to the pricing of derivative securities," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 342(3), pages 677-692.
    3. Zura Kakushadze, 2015. "Path integral and asset pricing," Quantitative Finance, Taylor & Francis Journals, vol. 15(11), pages 1759-1771, November.
    4. 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.
    5. repec:wyi:journl:002108 is not listed on IDEAS
    6. repec:wyi:journl:002109 is not listed on IDEAS
    7. Radu Tunaru, 2015. "Model Risk in Financial Markets:From Financial Engineering to Risk Management," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 9524, August.
    8. Zongwu Cai & Yongmiao Hong, 2013. "Some Recent Developments in Nonparametric Finance," Working Papers 2013-10-14, Wang Yanan Institute for Studies in Economics (WISE), Xiamen University.
    9. Jun Yu & Peter C. B. Phillips, 2001. "A Gaussian approach for continuous time models of the short-term interest rate," Econometrics Journal, Royal Economic Society, vol. 4(2), pages 1-3.
    10. Cai, Zongwu & Hong, Yongmiao, 2003. "Nonparametric Methods in Continuous-Time Finance: A Selective Review," SFB 373 Discussion Papers 2003,15, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    11. Mahdavi, Mahnaz, 2008. "A comparison of international short-term rates under no arbitrage condition," Global Finance Journal, Elsevier, vol. 18(3), pages 303-318.
    12. Das, Sanjiv Ranjan, 1998. "A direct discrete-time approach to Poisson-Gaussian bond option pricing in the Heath-Jarrow-Morton model," Journal of Economic Dynamics and Control, Elsevier, vol. 23(3), pages 333-369, November.
    13. Mark Trede & Bernd Wilfling, 2007. "Estimating exchange rate dynamics with diffusion processes: an application to Greek EMU data," Empirical Economics, Springer, vol. 33(1), pages 23-39, July.
    14. Bu, Ruijun & Cheng, Jie & Hadri, Kaddour, 2016. "Reducible diffusions with time-varying transformations with application to short-term interest rates," Economic Modelling, Elsevier, vol. 52(PA), pages 266-277.
    15. Yao, Yong, 1999. "Term structure modeling and asymptotic long rate," Insurance: Mathematics and Economics, Elsevier, vol. 25(3), pages 327-336, December.
    16. Kozicki, Sharon & Tinsley, P. A., 2001. "Shifting endpoints in the term structure of interest rates," Journal of Monetary Economics, Elsevier, vol. 47(3), pages 613-652, June.
    17. Constantin Mellios, 2007. "Interest rate options valuation under incomplete information," Annals of Operations Research, Springer, vol. 151(1), pages 99-117, April.
    18. Dillen, Hans, 1997. "A model of the term structure of interest rates in an open economy with regime shifts1," Journal of International Money and Finance, Elsevier, vol. 16(5), pages 795-819, September.
    19. Decamps, Marc & De Schepper, Ann & Goovaerts, Marc, 2006. "A path integral approach to asset-liability management," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 363(2), pages 404-416.
    20. Muteba Mwamba, John & Thabo, Lethaba & Uwilingiye, Josine, 2014. "Modelling the short-term interest rate with stochastic differential equation in continuous time: linear and nonlinear models," MPRA Paper 64386, University Library of Munich, Germany.
    21. Broze, Laurence & Scaillet, Olivier & Zakoian, Jean-Michel, 1995. "Testing for continuous-time models of the short-term interest rate," Journal of Empirical Finance, Elsevier, vol. 2(3), pages 199-223, September.
    22. repec:dau:papers:123456789/5374 is not listed on IDEAS
    23. Dette, Holger & Podolskij, Mark, 2008. "Testing the parametric form of the volatility in continuous time diffusion models--a stochastic process approach," Journal of Econometrics, Elsevier, vol. 143(1), pages 56-73, March.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:ant:wpaper:2003027. 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: Joeri Nys (email available below). General contact details of provider: https://edirc.repec.org/data/ftufsbe.html .

    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.