IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v207y2010i3p1358-1367.html
   My bibliography  Save this article

Pricing caps with HJM models: The benefits of humped volatility

Author

Listed:
  • Falini, Jury

Abstract

In this paper we compare different multifactor HJM models with humped volatility structures, to each other and to models with strictly decreasing volatility. All the models are estimated on Euribor and swap rates panel data maximizing the quasi-likelihood function obtained from the Kalman filter. We develop the analysis in two steps: first we study the in-sample properties of the estimated models, then we test the pricing performance on caps. We find the humped volatility specification to greatly improve the model estimation and to provide sufficiently accurate cap prices, although the models has been calibrated on interest rates data and not on cap prices. Moreover, we find the two-factor humped volatility model to outperform the three-factor models in pricing caps.

Suggested Citation

  • Falini, Jury, 2010. "Pricing caps with HJM models: The benefits of humped volatility," European Journal of Operational Research, Elsevier, vol. 207(3), pages 1358-1367, December.
    • Handle: RePEc:eee:ejores:v:207:y:2010:i:3:p:1358-1367
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377-2217(10)00425-X
    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. Narasimhan Jegadeesh & George Pennacchi, 1996. "The behavior of interest rates implied by the term structure of Eurodollar future," Proceedings, Federal Reserve Bank of Cleveland, issue Aug, pages 426-451.
    2. Farshid Jamshidian, 1997. "LIBOR and swap market models and measures (*)," Finance and Stochastics, Springer, vol. 1(4), pages 293-330.
    3. Alois L. J. Geyer & Stefan Pichler, 1999. "A State‐Space Approach To Estimate And Test Multifactor Cox‐Ingersoll‐Ross Models Of The Term Structure," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 22(1), pages 107-130, March.
    4. Babbs, Simon H. & Nowman, K. Ben, 1999. "Kalman Filtering of Generalized Vasicek Term Structure Models," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 34(1), pages 115-130, March.
    5. Driessen, Joost & Klaassen, Pieter & Melenberg, Bertrand, 2003. "The Performance of Multi-Factor Term Structure Models for Pricing and Hedging Caps and Swaptions," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 38(3), pages 635-672, September.
    6. 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..
    7. Carl Chiarella & Oh Kang Kwon, 2001. "Forward rate dependent Markovian transformations of the Heath-Jarrow-Morton term structure model," Finance and Stochastics, Springer, vol. 5(2), pages 237-257.
    8. Inui, Koji & Kijima, Masaaki, 1998. "A Markovian Framework in Multi-Factor Heath-Jarrow-Morton Models," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 33(3), pages 423-440, September.
    9. 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..
    10. Carl Chiarella & Oh-Kang Kwon, 1999. "Classes of Interest Rate Models Under the HJM Framework," Research Paper Series 13, Quantitative Finance Research Centre, University of Technology, Sydney.
    11. Moraleda, Juan M. & Vorst, Ton C. F., 1997. "Pricing American interest rate claims with humped volatility models," Journal of Banking & Finance, Elsevier, vol. 21(8), pages 1131-1157, August.
    12. Andrew Carverhill, 1994. "When Is The Short Rate Markovian?," Mathematical Finance, Wiley Blackwell, vol. 4(4), pages 305-312, October.
    13. Flavio Angelini & Stefano Herzel, 2005. "Consistent calibration of HJM models to cap implied volatilities," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 25(11), pages 1093-1120, November.
    14. Alan Brace & Dariusz G¸atarek & Marek Musiela, 1997. "The Market Model of Interest Rate Dynamics," Mathematical Finance, Wiley Blackwell, vol. 7(2), pages 127-155, April.
    15. 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.
    16. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    17. 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.
    18. 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.
    19. Mercurio, F. & Moraleda, J. M., 2000. "An analytically tractable interest rate model with humped volatility," European Journal of Operational Research, Elsevier, vol. 120(1), pages 205-214, January.
    20. de Jong, Frank, 2000. "Time Series and Cross-Section Information in Affine Term-Structure Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 18(3), pages 300-314, July.
    21. Jeffrey, Andrew, 1995. "Single Factor Heath-Jarrow-Morton Term Structure Models Based on Markov Spot Interest Rate Dynamics," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 30(4), pages 619-642, December.
    22. Chiarella, Carl & Hung, Hing & T, Thuy-Duong, 2009. "The volatility structure of the fixed income market under the HJM framework: A nonlinear filtering approach," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2075-2088, April.
    23. Duan, Jin-Chuan & Simonato, Jean-Guy, 1999. "Estimating and Testing Exponential-Affine Term Structure Models by Kalman Filter," Review of Quantitative Finance and Accounting, Springer, vol. 13(2), pages 111-135, September.
    24. Hull, John & White, Alan, 1990. "Pricing Interest-Rate-Derivative Securities," The Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 573-592.
    25. Amin, Kaushik I. & Morton, Andrew J., 1994. "Implied volatility functions in arbitrage-free term structure models," Journal of Financial Economics, Elsevier, vol. 35(2), pages 141-180, April.
    26. de Jong, Frank & Santa-Clara, Pedro, 1999. "The Dynamics of the Forward Interest Rate Curve: A Formulation with State Variables," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 34(1), pages 131-157, March.
    27. Alan Brace & Marek Musiela, 1994. "A Multifactor Gauss Markov Implementation Of Heath, Jarrow, And Morton," Mathematical Finance, Wiley Blackwell, vol. 4(3), pages 259-283, July.
    28. 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.
    29. Andrew Mark Jeffrey, 1995. "Single Factor Heath-Jarrow-Morton Term Structure Models Based on Markov Spot Interest Rate Dynamics," Yale School of Management Working Papers ysm46, Yale School of Management.
    30. Gupta, Anurag & Subrahmanyam, Marti G., 2005. "Pricing and hedging interest rate options: Evidence from cap-floor markets," Journal of Banking & Finance, Elsevier, vol. 29(3), pages 701-733, March.
    31. Black, Fischer, 1976. "The pricing of commodity contracts," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 167-179.
    32. Carl Chiarella & Oh-Kang Kwon, 2001. "State Variables and the Affine Nature of Markovian HJM Term Structure Models," Research Paper Series 52, Quantitative Finance Research Centre, University of Technology, Sydney.
    33. Chen, Ren-Raw & Scott, Louis, 2003. "Multi-factor Cox-Ingersoll-Ross Models of the Term Structure: Estimates and Tests from a Kalman Filter Model," The Journal of Real Estate Finance and Economics, Springer, vol. 27(2), pages 143-172, September.
    34. Geyer, Alois L J & Pichler, Stefan, 1999. "A State-Space Approach to Estimate and Test Multifactor Cox-Ingersoll-Ross Models of the Term Structure," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 22(1), pages 107-130, Spring.
    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. Ben-zhang Yang & Jia Yue & Nan-jing Huang, 2017. "Variance swaps under L\'{e}vy process with stochastic volatility and stochastic interest rate in incomplete markets," Papers 1712.10105, arXiv.org, revised Mar 2018.
    2. Laurini, Márcio Poletti & Ohashi, Alberto, 2015. "A noisy principal component analysis for forward rate curves," European Journal of Operational Research, Elsevier, vol. 246(1), pages 140-153.
    3. 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.
    4. Fanelli, Viviana, 2017. "Implications of implicit credit spread volatilities on interest rate modelling," European Journal of Operational Research, Elsevier, vol. 263(2), pages 707-718.
    5. Mitra, Sovan & Date, Paresh & Mamon, Rogemar & Wang, I-Chieh, 2013. "Pricing and risk management of interest rate swaps," European Journal of Operational Research, Elsevier, vol. 228(1), pages 102-111.
    6. Ben-Zhang Yang & Jia Yue & Nan-Jing Huang, 2019. "Equilibrium Price Of Variance Swaps Under Stochastic Volatility With Lévy Jumps And Stochastic Interest Rate," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(04), pages 1-33, June.

    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. Jury Falini, 2009. "Pricing caps with HJM models: the benefits of humped volatility," Department of Economics University of Siena 563, Department of Economics, University of Siena.
    2. Christina Nikitopoulos-Sklibosios, 2005. "A Class of Markovian Models for the Term Structure of Interest Rates Under Jump-Diffusions," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 1-2005.
    3. Chiarella, Carl & Hung, Hing & T, Thuy-Duong, 2009. "The volatility structure of the fixed income market under the HJM framework: A nonlinear filtering approach," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2075-2088, April.
    4. 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.
    5. Ramaprasad Bhar, 2010. "Stochastic Filtering with Applications in Finance," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 7736.
    6. Bjork, Tomas, 2009. "Arbitrage Theory in Continuous Time," OUP Catalogue, Oxford University Press, edition 3, number 9780199574742.
    7. Frank De Jong & Joost Driessen & Antoon Pelsser, 2001. "Libor Market Models versus Swap Market Models for Pricing Interest Rate Derivatives: An Empirical Analysis," Review of Finance, European Finance Association, vol. 5(3), pages 201-237.
    8. Christina Nikitopoulos-Sklibosios, 2005. "A Class of Markovian Models for the Term Structure of Interest Rates Under Jump-Diffusions," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 6, July-Dece.
    9. Bueno-Guerrero, Alberto & Moreno, Manuel & Navas, Javier F., 2016. "The stochastic string model as a unifying theory of the term structure of interest rates," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 461(C), pages 217-237.
    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. 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.
    12. 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.
    13. Dai, Qiang & Singleton, Kenneth J., 2003. "Fixed-income pricing," 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 20, pages 1207-1246, Elsevier.
    14. Cortazar, Gonzalo & Schwartz, Eduardo S. & Naranjo, Lorezo, 2003. "Term Structure Estimation in Low-Frequency Transaction Markets: A Kalman Filter Approach with Incomplete Panel-Data," University of California at Los Angeles, Anderson Graduate School of Management qt56h775cz, Anderson Graduate School of Management, UCLA.
    15. Wolfgang Lemke & Deutsche Bundesbank, 2006. "Term Structure Modeling and Estimation in a State Space Framework," Lecture Notes in Economics and Mathematical Systems, Springer, number 978-3-540-28344-7, October.
    16. Robert A. Jarrow, 2009. "The Term Structure of Interest Rates," Annual Review of Financial Economics, Annual Reviews, vol. 1(1), pages 69-96, November.
    17. Gonzalo Cortazar & Eduardo S. Schwartz & Lorenzo F. Naranjo, 2007. "Term-structure estimation in markets with infrequent trading," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 12(4), pages 353-369.
    18. Yongwoong Lee & Kisung Yang, 2020. "Finite Difference Method for the Hull–White Partial Differential Equations," Mathematics, MDPI, vol. 8(10), pages 1-11, October.
    19. I‐Doun Kuo & Kai‐Li Wang, 2009. "Implied deterministic volatility functions: An empirical test for Euribor options," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 29(4), pages 319-347, April.
    20. Michael A H Dempster & Elena A Medova & Michael Villaverde, 2010. "Long-term interest rates and consol bond valuation," Journal of Asset Management, Palgrave Macmillan, vol. 11(2), pages 113-135, June.

    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:207:y:2010:i:3:p:1358-1367. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    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.