IDEAS home Printed from https://ideas.repec.org/p/nbr/nberte/0212.html
   My bibliography  Save this paper

An Efficient Generalized Discrete-Time Approach to Poisson-Gaussian Bond Option Pricing in the Heath-Jarrow-Morton Model

Author

Listed:
  • Sanjiv Ranjan Das

Abstract

Term structure models employing Poisson-Gaussian processes may be used to accommodate the observed skewness and kurtosis of interest rates. This paper extends the discrete-time, pure-Gaussian version of the Heath-Jarrow-Morton model to the pricing" of American-type bond options when the underlying term structure of interest rates follows a Poisson-Gaussian process. The Poisson-Gaussian process is specified using a hexanomial tree (six nodes emanating from each node), and the tree is shown to be recombining. The scheme is parsimonious and convergent. This model extends the class of HJM models by (i) introducing a more generalized volatility specification than has been used so far, and (ii) inducting jumps, yet retaining lattice recombination, thus making the model useful for practical applications.

Suggested Citation

  • Sanjiv Ranjan Das, 1997. "An Efficient Generalized Discrete-Time Approach to Poisson-Gaussian Bond Option Pricing in the Heath-Jarrow-Morton Model," NBER Technical Working Papers 0212, National Bureau of Economic Research, Inc.
    • Handle: RePEc:nbr:nberte:0212
    Note: AP
    as

    Download full text from publisher

    File URL: http://www.nber.org/papers/t0212.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Chan, K C, et al, 1992. "An Empirical Comparison of Alternative Models of the Short-Term Interest Rate," Journal of Finance, American Finance Association, vol. 47(3), pages 1209-1227, July.
    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. Robert Jarrow & Dilip Madan, 1995. "Option Pricing Using The Term Structure Of Interest Rates To Hedge Systematic Discontinuities In Asset Returns1," Mathematical Finance, Wiley Blackwell, vol. 5(4), pages 311-336, October.
    4. Merton, Robert C, 1976. "The Impact on Option Pricing of Specification Error in the Underlying Stock Price Returns," Journal of Finance, American Finance Association, vol. 31(2), pages 333-350, May.
    5. Harrison, J. Michael & Kreps, David M., 1979. "Martingales and arbitrage in multiperiod securities markets," Journal of Economic Theory, Elsevier, vol. 20(3), pages 381-408, June.
    6. Harrison, J. Michael & Pliska, Stanley R., 1981. "Martingales and stochastic integrals in the theory of continuous trading," Stochastic Processes and their Applications, Elsevier, vol. 11(3), pages 215-260, August.
    7. Peter Ritchken & L. Sankarasubramanian, 1995. "Volatility Structures Of Forward Rates And The Dynamics Of The Term Structure1," Mathematical Finance, Wiley Blackwell, vol. 5(1), pages 55-72, January.
    8. 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.
    9. Heath, David & Jarrow, Robert & Morton, Andrew, 1990. "Bond Pricing and the Term Structure of Interest Rates: A Discrete Time Approximation," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 25(4), pages 419-440, December.
    10. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    11. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
    12. Amin, Kaushik I, 1993. "Jump Diffusion Option Valuation in Discrete Time," Journal of Finance, American Finance Association, vol. 48(5), pages 1833-1863, December.
    13. Hiroshi Shirakawa, 1991. "Interest Rate Option Pricing With Poisson‐Gaussian Forward Rate Curve Processes," Mathematical Finance, Wiley Blackwell, vol. 1(4), pages 77-94, October.
    14. Rubinstein, Mark, 1994. "Implied Binomial Trees," Journal of Finance, American Finance Association, vol. 49(3), pages 771-818, July.
    15. Robert A. Jarrow & Arkadev Chatterjea, 2019. "The Heath–Jarrow–Morton Libor Model," World Scientific Book Chapters, in: An Introduction to Derivative Securities, Financial Markets, and Risk Management, chapter 25, pages 618-654, World Scientific Publishing Co. Pte. Ltd..
    16. Mark Rubinstein., 1994. "Implied Binomial Trees," Research Program in Finance Working Papers RPF-232, University of California at Berkeley.
    17. Black, Fischer, 1976. "The pricing of commodity contracts," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 167-179.
    18. Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, vol. 7(3), pages 229-263, September.
    19. 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.
    20. 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.
    21. Ho, Thomas S Y & Lee, Sang-bin, 1986. "Term Structure Movements and Pricing Interest Rate Contingent Claims," Journal of Finance, American Finance Association, vol. 41(5), pages 1011-1029, December.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Sanghoon Lee, 2004. "Approximation of A Jump-Diffusion Process," Econometric Society 2004 Far Eastern Meetings 412, Econometric Society.

    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. 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.
    2. 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, July-Dece.
    3. Bjork, Tomas, 2009. "Arbitrage Theory in Continuous Time," OUP Catalogue, Oxford University Press, edition 3, number 9780199574742, Decembrie.
    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. Mark Broadie & Jerome B. Detemple, 2004. "ANNIVERSARY ARTICLE: Option Pricing: Valuation Models and Applications," Management Science, INFORMS, vol. 50(9), pages 1145-1177, September.
    6. 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.
    7. repec:wyi:journl:002108 is not listed on IDEAS
    8. repec:dau:papers:123456789/5374 is not listed on IDEAS
    9. Mondher Bellalah, 2009. "Derivatives, Risk Management & Value," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 7175, January.
    10. 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.
    11. 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.
    12. 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.
    13. repec:uts:finphd:40 is not listed on IDEAS
    14. Gibson, Rajna & Lhabitant, Francois-Serge & Talay, Denis, 2010. "Modeling the Term Structure of Interest Rates: A Review of the Literature," Foundations and Trends(R) in Finance, now publishers, vol. 5(1–2), pages 1-156, December.
    15. 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.
    16. Constantin Mellios, 2001. "Valuation of Interest Rate Options in a Two-Factor Model of the Term Structure of Interest Rate," Working Papers 2001-1, Laboratoire Orléanais de Gestion - université d'Orléans.
    17. Robert A. Jarrow, 2009. "The Term Structure of Interest Rates," Annual Review of Financial Economics, Annual Reviews, vol. 1(1), pages 69-96, November.
    18. Casassus, Jaime & Collin-Dufresne, Pierre & Goldstein, Bob, 2005. "Unspanned stochastic volatility and fixed income derivatives pricing," Journal of Banking & Finance, Elsevier, vol. 29(11), pages 2723-2749, November.
    19. 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.
    20. Constantinides, George M. & Jackwerth, Jens Carsten & Perrakis, Stylianos, 2005. "Option pricing: Real and risk-neutral distributions," CoFE Discussion Papers 05/06, University of Konstanz, Center of Finance and Econometrics (CoFE).
    21. C. Mancini, 2002. "The European options hedge perfectly in a Poisson-Gaussian stock market model," Applied Mathematical Finance, Taylor & Francis Journals, vol. 9(2), pages 87-102.
    22. Isabelle Bajeux-Besnainou & Roland Portait, 1998. "Pricing stock and bond derivatives with a multi-factor Gaussian model," Applied Mathematical Finance, Taylor & Francis Journals, vol. 5(3-4), pages 207-225.
    23. Josheski Dushko & Apostolov Mico, 2021. "Equilibrium Short-Rate Models Vs No-Arbitrage Models: Literature Review and Computational Examples," Econometrics. Advances in Applied Data Analysis, Sciendo, vol. 25(3), pages 42-71, September.

    More about this item

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

    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:nbr:nberte:0212. 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: the person in charge (email available below). General contact details of provider: https://edirc.repec.org/data/nberrus.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.