IDEAS home Printed from https://ideas.repec.org/a/wsi/ijtafx/v21y2018i04ns0219024918500231.html
   My bibliography  Save this article

A Lattice-Based Model For Evaluating Bonds And Interest-Sensitive Claims Under Stochastic Volatility

Author

Listed:
  • EMILIO RUSSO

    (Department of Economics, Statistics and Finance, University of Calabria, Ponte Bucci, cubo 1C 87036 Rende (CS), Italy)

  • ALESSANDRO STAINO

    (Department of Economics, Statistics and Finance, University of Calabria, Ponte Bucci, cubo 1C 87036 Rende (CS), Italy)

Abstract

We propose a flexible lattice model for pricing bonds and interest-sensitive claims under stochastic volatility, which is able to accommodate different dynamics specifications, and permits correlation between the interest rate and volatility diffusion. The model is based on the forward shooting grid method where the volatility process, as the primary state variable, is discretized by means of a recombining binomial tree. Then, the interest rate, as the auxiliary state variable, is discretized by attaching a subset of representative realizations to each node of the volatility lattice to cover the range of possible interest rates at each time slice. Finally, we develop a bivariate lattice presenting four branches for each node, where the joint probabilities for the possible jumps embed the correlation. Since the model works on representative interest rate values, a linear interpolation technique is used when solving backward through the lattice to compute the bond present value or the interest-sensitive claim price.

Suggested Citation

  • Emilio Russo & Alessandro Staino, 2018. "A Lattice-Based Model For Evaluating Bonds And Interest-Sensitive Claims Under Stochastic Volatility," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(04), pages 1-18, June.
    • Handle: RePEc:wsi:ijtafx:v:21:y:2018:i:04:n:s0219024918500231
    DOI: 10.1142/S0219024918500231
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S0219024918500231
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S0219024918500231?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 search 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. Kirkby, J. Lars & Nguyen, Duy & Cui, Zhenyu, 2017. "A unified approach to Bermudan and barrier options under stochastic volatility models with jumps," Journal of Economic Dynamics and Control, Elsevier, vol. 80(C), pages 75-100.
    3. Lo, C.C. & Nguyen, D. & Skindilias, K., 2017. "A Unified Tree approach for options pricing under stochastic volatility models," Finance Research Letters, Elsevier, vol. 20(C), pages 260-268.
    4. Lim Kian Guan & Guo Xiaoqiang, 2000. "Pricing American options with stochastic volatility: Evidence from S&P 500 futures options," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 20(7), pages 625-659, August.
    5. 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.
    6. P. Forsyth & K. Vetzal & R. Zvan, 2002. "Convergence of numerical methods for valuing path-dependent options using interpolation," Review of Derivatives Research, Springer, vol. 5(3), pages 273-314, October.
    7. 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..
    8. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    9. Andersen, Torben G. & Lund, Jesper, 1997. "Estimating continuous-time stochastic volatility models of the short-term interest rate," Journal of Econometrics, Elsevier, vol. 77(2), pages 343-377, April.
    10. Anders B. Trolle & Eduardo S. Schwartz, 2009. "A General Stochastic Volatility Model for the Pricing of Interest Rate Derivatives," The Review of Financial Studies, Society for Financial Studies, vol. 22(5), pages 2007-2057, May.
    11. Jérôme Barraquand & Thierry Pudet, 1996. "Pricing Of American Path‐Dependent Contingent Claims," Mathematical Finance, Wiley Blackwell, vol. 6(1), pages 17-51, January.
    12. Schaefer, Stephen M. & Schwartz, Eduardo S., 1984. "A Two-Factor Model of the Term Structure: An Approximate Analytical Solution," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 19(4), pages 413-424, December.
    13. 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.
    14. Clifford A. Ball & Walter N. Torous, 1999. "The Stochastic Volatility of Short‐Term Interest Rates: Some International Evidence," Journal of Finance, American Finance Association, vol. 54(6), pages 2339-2359, December.
    15. Longstaff, Francis A & Schwartz, Eduardo S, 1992. "Interest Rate Volatility and the Term Structure: A Two-Factor General Equilibrium Model," Journal of Finance, American Finance Association, vol. 47(4), pages 1259-1282, September.
    16. Linus Kaisajuntti & Joanne Kennedy, 2014. "Stochastic volatility for interest rate derivatives," Quantitative Finance, Taylor & Francis Journals, vol. 14(3), pages 457-480, March.
    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. 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.
    2. repec:wyi:journl:002109 is not listed on IDEAS
    3. 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.
    4. Lourdes Gómez-Valle & Julia Martínez-Rodríguez, 2010. "Improving the term structure of interest rates: two-factor models," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 15(3), pages 275-287.
    5. Christiansen, Charlotte, 2005. "Multivariate term structure models with level and heteroskedasticity effects," Journal of Banking & Finance, Elsevier, vol. 29(5), pages 1037-1057, May.
    6. 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.
    7. Giuseppe Arbia & Michele Di Marcantonio, 2015. "Forecasting Interest Rates Using Geostatistical Techniques," Econometrics, MDPI, vol. 3(4), pages 1-28, November.
    8. repec:wyi:journl:002108 is not listed on IDEAS
    9. Jacob Boudoukh & Matthew Richardson & Richard Stanton & Robert Whitelaw, 1999. "A Multifactor, Nonlinear, Continuous-Time Model of Interest Rate Volatility," New York University, Leonard N. Stern School Finance Department Working Paper Seires 99-042, New York University, Leonard N. Stern School of Business-.
    10. 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.
    11. Berardi, Andrea, 1995. "Estimating the Cox, ingersoll and Ross model of the term structure: a multivariate approach," Ricerche Economiche, Elsevier, vol. 49(1), pages 51-74, March.
    12. Jin-Chuan Duan & Kris Jacobs, 2001. "Short and Long Memory in Equilibrium Interest Rate Dynamics," CIRANO Working Papers 2001s-22, CIRANO.
    13. 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.
    14. Duan, Jin-Chuan & Jacobs, Kris, 2008. "Is long memory necessary? An empirical investigation of nonnegative interest rate processes," Journal of Empirical Finance, Elsevier, vol. 15(3), pages 567-581, June.
    15. 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.
    16. Andrew Jeffrey & Linton, Oliver Linton & Thong Nguyen & Peter C.B. Phillips, 2001. "Nonparametric Estimation of a Multifactor Heath-Jarrow-Morton Model: An Integrated Approach," Cowles Foundation Discussion Papers 1311, Cowles Foundation for Research in Economics, Yale University.
    17. Vetzal, Kenneth R., 1997. "Stochastic volatility, movements in short term interest rates, and bond option values," Journal of Banking & Finance, Elsevier, vol. 21(2), pages 169-196, February.
    18. 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.
    19. 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.
    20. Jacob Boudoukh & Matthew Richardson & Richard Stanton & Robert F. Whitelaw, 1999. "A Multifactor, Nonlinear, Continuous-Time Model of Interest Rate Volatility," NBER Working Papers 7213, National Bureau of Economic Research, Inc.
    21. 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.
    22. Franco Parisi, 1998. "Tasas de Interés Nominal de Corto Plazo en Chile: Una Comparación Empírica de sus Modelos," Latin American Journal of Economics-formerly Cuadernos de Economía, Instituto de Economía. Pontificia Universidad Católica de Chile., vol. 35(105), pages 161-182.

    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:wsi:ijtafx:v:21:y:2018:i:04:n:s0219024918500231. 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: Tai Tone Lim (email available below). General contact details of provider: http://www.worldscinet.com/ijtaf/ijtaf.shtml .

    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.