IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v249y2016i1p359-377.html
   My bibliography  Save this article

An explicitly solvable Heston model with stochastic interest rate

Author

Listed:
  • Recchioni, M.C.
  • Sun, Y.

Abstract

This paper deals with a variation of the Heston hybrid model with stochastic interest rate illustrated in Grzelak and Oosterlee (2011). This variation leads to a multi-factor Heston model where one factor is the stochastic interest rate. Specifically, the dynamics of the asset price is described through two stochastic factors: one related to the stochastic volatility and the other to the stochastic interest rate. The proposed model has the advantage of being analytically tractable while preserving the good features of the Heston hybrid model in Grzelak and Oosterlee (2011) and of the multi-factor Heston model in Christoffersen et al. (2009). The analytical treatment is based on an appropriate parametrization of the probability density function which allows us to compute explicitly relevant integrals which define option pricing and moment formulas. The moments and mixed moments of the asset price and log-price variables are given by elementary formulas which do not involve integrals. A procedure to estimate the model parameters is proposed and validated using three different data-sets: the prices of call and put options on the U.S. S&P 500 index, the values of the Credit Agricole index linked policy, Azione Più Capitale Garantito Em.64., and the U.S. three-month, two and ten year government bond yields. The empirical analysis shows that the stochastic interest rate plays a crucial role as a volatility factor and provides a multi-factor model that outperforms the Heston model in pricing options. This model can also provide insights into the relationship between short and long term bond yields.

Suggested Citation

  • Recchioni, M.C. & Sun, Y., 2016. "An explicitly solvable Heston model with stochastic interest rate," European Journal of Operational Research, Elsevier, vol. 249(1), pages 359-377.
  • Handle: RePEc:eee:ejores:v:249:y:2016:i:1:p:359-377
    DOI: 10.1016/j.ejor.2015.09.035
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221715008772
    Download Restriction: Full text for ScienceDirect subscribers only

    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. Peter Christoffersen & Steven Heston & Kris Jacobs, 2009. "The Shape and Term Structure of the Index Option Smirk: Why Multifactor Stochastic Volatility Models Work So Well," Management Science, INFORMS, vol. 55(12), pages 1914-1932, December.
    2. Christensen, Jens H.E. & Diebold, Francis X. & Rudebusch, Glenn D., 2011. "The affine arbitrage-free class of Nelson-Siegel term structure models," Journal of Econometrics, Elsevier, vol. 164(1), pages 4-20, September.
    3. Griselda Deelstra & Grégory Rayée, 2013. "Local Volatility Pricing Models for Long-Dated FX Derivatives," Applied Mathematical Finance, Taylor & Francis Journals, vol. 20(4), pages 380-402, September.
    4. Stein, Elias M & Stein, Jeremy C, 1991. "Stock Price Distributions with Stochastic Volatility: An Analytic Approach," Review of Financial Studies, Society for Financial Studies, vol. 4(4), pages 727-752.
    5. 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: Theory Of Valuation, chapter 5, pages 129-164 World Scientific Publishing Co. Pte. Ltd..
    6. Torben G. Andersen & Luca Benzoni, 2010. "Do Bonds Span Volatility Risk in the U.S. Treasury Market? A Specification Test for Affine Term Structure Models," Journal of Finance, American Finance Association, vol. 65(2), pages 603-653, April.
    7. Moreno, Manuel & Platania, Federico, 2015. "A cyclical square-root model for the term structure of interest rates," European Journal of Operational Research, Elsevier, vol. 241(1), pages 109-121.
    8. Darrell Duffie & Jun Pan & Kenneth Singleton, 2000. "Transform Analysis and Asset Pricing for Affine Jump-Diffusions," Econometrica, Econometric Society, vol. 68(6), pages 1343-1376, November.
    9. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    10. Choi, Youngsoo & Wirjanto, Tony S., 2007. "An analytic approximation formula for pricing zero-coupon bonds," Finance Research Letters, Elsevier, vol. 4(2), pages 116-126, June.
    11. Islyaev, Suren & Date, Paresh, 2015. "Electricity futures price models: Calibration and forecasting," European Journal of Operational Research, Elsevier, vol. 247(1), pages 144-154.
    12. Leif Andersen & Vladimir Piterbarg, 2007. "Moment explosions in stochastic volatility models," Finance and Stochastics, Springer, vol. 11(1), pages 29-50, January.
    13. Carl Chiarella & Oh Kwon, 2003. "Finite Dimensional Affine Realisations of HJM Models in Terms of Forward Rates and Yields," Review of Derivatives Research, Springer, vol. 6(2), pages 129-155, May.
    14. Pun, Chi Seng & Chung, Shing Fung & Wong, Hoi Ying, 2015. "Variance swap with mean reversion, multifactor stochastic volatility and jumps," European Journal of Operational Research, Elsevier, vol. 245(2), pages 571-580.
    15. E. Benhamou & E. Gobet & M. Miri, 2012. "Analytical formulas for a local volatility model with stochastic rates," Quantitative Finance, Taylor & Francis Journals, vol. 12(2), pages 185-198, September.
    16. Anders B. Trolle & Eduardo S. Schwartz, 2009. "A General Stochastic Volatility Model for the Pricing of Interest Rate Derivatives," Review of Financial Studies, Society for Financial Studies, vol. 22(5), pages 2007-2057, May.
    17. Ball, Clifford A. & Roma, Antonio, 1994. "Stochastic Volatility Option Pricing," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 29(04), pages 589-607, December.
    18. Date, Paresh & Islyaev, Suren, 2015. "A fast calibrating volatility model for option pricing," European Journal of Operational Research, Elsevier, vol. 243(2), pages 599-606.
    19. Milevsky, Moshe A. & David Promislow, S., 2001. "Mortality derivatives and the option to annuitise," Insurance: Mathematics and Economics, Elsevier, vol. 29(3), pages 299-318, December.
    20. Lorella Fatone & Francesca Mariani & Maria Cristina Recchioni & Francesco Zirilli, 2009. "An explicitly solvable multi‐scale stochastic volatility model: Option pricing and calibration problems," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 29(9), pages 862-893, September.
    21. Wong, Hoi Ying & Lo, Yu Wai, 2009. "Option pricing with mean reversion and stochastic volatility," European Journal of Operational Research, Elsevier, vol. 197(1), pages 179-187, August.
    22. Lech A. Grzelak & Cornelis W. Oosterlee & Sacha Van Weeren, 2012. "Extension of stochastic volatility equity models with the Hull--White interest rate process," Quantitative Finance, Taylor & Francis Journals, vol. 12(1), pages 89-105, July.
    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. repec:wsi:ijfexx:v:04:y:2017:i:01:n:s242478631750013x is not listed on IDEAS
    2. repec:eee:ejores:v:262:y:2017:i:3:p:1116-1135 is not listed on IDEAS
    3. Maria Cristina Recchioni & Yu Sun & Gabriele Tedeschi, 2016. "Can negative interest rates really affect option pricing? Empirical evidence from an explicitly solvable stochastic volatility model," Working Papers 2016/23, Economics Department, Universitat Jaume I, Castellón (Spain).
    4. repec:eee:ejores:v:262:y:2017:i:1:p:381-400 is not listed on IDEAS

    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:eee:ejores:v:249:y:2016:i:1:p:359-377. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu). General contact details of provider: http://www.elsevier.com/locate/eor .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.