IDEAS home Printed from https://ideas.repec.org/p/arx/papers/math-0702435.html
   My bibliography  Save this paper

Convexity theory for the term structure equation

Author

Listed:
  • Erik Ekstrom
  • Johan Tysk

Abstract

We study convexity and monotonicity properties for prices of bonds and bond options when the short rate is modeled by a diffusion process. We provide conditions under which convexity of the price in the short rate is guaranteed. Under these conditions the price is decreasing in the drift and increasing in the volatility of the short rate. We also study convexity properties of the logarithm of the price.

Suggested Citation

  • Erik Ekstrom & Johan Tysk, 2007. "Convexity theory for the term structure equation," Papers math/0702435, arXiv.org.
  • Handle: RePEc:arx:papers:math/0702435
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/math/0702435
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Bergman, Yaacov Z & Grundy, Bruce D & Wiener, Zvi, 1996. "General Properties of Option Prices," Journal of Finance, American Finance Association, vol. 51(5), pages 1573-1610, December.
    2. Alvarez, Luis H. R., 2001. "On the form and risk-sensitivity of zero coupon bonds for a class of interest rate models," Insurance: Mathematics and Economics, Elsevier, vol. 28(1), pages 83-90, February.
    3. Erik Ekstrom & Johan Tysk, 2006. "Convexity preserving jump-diffusion models for option pricing," Papers math/0601526, arXiv.org.
    4. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    5. N. Bellamy & M. Jeanblanc, 2000. "Incompleteness of markets driven by a mixed diffusion," Finance and Stochastics, Springer, vol. 4(2), pages 209-222.
    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. Alvarez, Luis H. R. & Koskela, Erkki, 2005. "Wicksellian theory of forest rotation under interest rate variability," Journal of Economic Dynamics and Control, Elsevier, vol. 29(3), pages 529-545, March.
    2. Antonio Mele, 2003. "Fundamental Properties of Bond Prices in Models of the Short-Term Rate," The Review of Financial Studies, Society for Financial Studies, vol. 16(3), pages 679-716, July.
    3. Garcia, R. & Renault, E., 1998. "Risk Aversion, Intertemporal Substitution, and Option Pricing," Cahiers de recherche 9801, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    4. Hyong-Chol O & Ji-Sok Kim, 2013. "General Properties of Solutions to Inhomogeneous Black-Scholes Equations with Discontinuous Maturity Payoffs and Application," Papers 1309.6505, arXiv.org, revised Sep 2013.
    5. 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).
    6. Kanniainen, Juho & Piché, Robert, 2013. "Stock price dynamics and option valuations under volatility feedback effect," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(4), pages 722-740.
    7. Eric Rasmusen, 2004. "When Does Extra Risk Strictly Increase the Value of Options?," Finance 0409004, University Library of Munich, Germany.
    8. Norden, Lars, 2001. "Hedging of American equity options: do call and put prices always move in the direction as predicted by the movement in the underlying stock price?," Journal of Multinational Financial Management, Elsevier, vol. 11(4-5), pages 321-340, December.
    9. Jan Bergenthum & Ludger Rüschendorf, 2006. "Comparison of Option Prices in Semimartingale Models," Finance and Stochastics, Springer, vol. 10(2), pages 222-249, April.
    10. Hyong-Chol O & Tae-Song Choe, 2022. "General properties of the Solutions to Moving Boundary Problems for Black-Sholes Equations," Papers 2203.05726, arXiv.org.
    11. Erik Ekstrom & Johan Tysk, 2006. "Convexity preserving jump-diffusion models for option pricing," Papers math/0601526, arXiv.org.
    12. Eric Rasmusen, 2007. "When Does Extra Risk Strictly Increase an Option's Value?," The Review of Financial Studies, Society for Financial Studies, vol. 20(5), pages 1647-1667, 2007 14.
    13. Kerry W. Fendick, 2013. "Pricing and Hedging Derivative Securities with Unknown Local Volatilities," Papers 1309.6164, arXiv.org, revised Oct 2013.
    14. Chuang Yuang Lin & Dar Hsin Chen & Chin Yu Tsai, 2011. "The limitation of monotonicity property of option prices: an empirical evidence," Applied Economics, Taylor & Francis Journals, vol. 43(23), pages 3103-3113.
    15. Alfredo Ibáñez, 2005. "Option-Pricing in Incomplete Markets: The Hedging Portfolio plus a Risk Premium-Based Recursive Approach," Computing in Economics and Finance 2005 216, Society for Computational Economics.
    16. Mykland, Per Aslak, 2019. "Combining statistical intervals and market prices: The worst case state price distribution," Journal of Econometrics, Elsevier, vol. 212(1), pages 272-285.
    17. Erik Ekstrom & Johan Tysk, 2005. "Properties of option prices in models with jumps," Papers math/0509232, arXiv.org, revised Nov 2005.
    18. Jérôme Detemple & Carlton Osakwe, 2000. "The Valuation of Volatility Options," Review of Finance, European Finance Association, vol. 4(1), pages 21-50.
    19. Stephane Crepey, 2004. "Delta-hedging vega risk?," Quantitative Finance, Taylor & Francis Journals, vol. 4(5), pages 559-579.
    20. José Fajardo & Ernesto Mordecki, 2006. "Skewness Premium with Lévy Processes," IBMEC RJ Economics Discussion Papers 2006-04, Economics Research Group, IBMEC Business School - Rio de Janeiro.

    More about this item

    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:arx:papers:math/0702435. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.