[go: up one dir, main page]
IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1502.06074.html
   My bibliography  Save this paper

Coping with Negative Short-Rates

Author

Listed:
  • Zura Kakushadze
Abstract
We discuss a simple extension of the Ho and Lee model with generic time-dependent drift in which: 1) we compute bond prices analytically; 2) the yield curve is sensible and the asymptotic yield is positive; and 3) our analytical solution provides a clean and simple way of separating volatility from the drift in the short-rate process. Our extension amounts to introducing one or two reflecting barriers for the underlying Brownian motion (as opposed to the short-rate), which allows to have more realistic time-dependent drift (as opposed to constant drift). In our model the spectrum -- or, roughly, the set of short-rate values contributing to bond and other claim prices -- is discrete and positive. We discuss how to calibrate our model using empirical yield data by fitting three parameters and then read off the time-dependent drift.

Suggested Citation

  • Zura Kakushadze, 2015. "Coping with Negative Short-Rates," Papers 1502.06074, arXiv.org, revised Aug 2015.
    • Handle: RePEc:arx:papers:1502.06074
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1502.06074
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Bakshi, Gurdip S & Chen, Zhiwu, 1996. "Inflation, Asset Prices, and the Term Structure of Interest Rates in Monetary Economies," The Review of Financial Studies, Society for Financial Studies, vol. 9(1), pages 241-275.
    2. 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..
    3. Conley, Timothy G, et al, 1997. "Short-Term Interest Rates as Subordinated Diffusions," The Review of Financial Studies, Society for Financial Studies, vol. 10(3), pages 525-577.
    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. Yoichi Ueno & Naohiko Baba & Yuji Sakurai, 2006. "The Use of the Black Model of Interest Rates as Options for Monitoring the JGB Market Expectations," Bank of Japan Working Paper Series 06-E-15, Bank of Japan.
    6. Constantinides, George M, 1992. "A Theory of the Nominal Term Structure of Interest Rates," The Review of Financial Studies, Society for Financial Studies, vol. 5(4), pages 531-552.
    7. 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.
    8. Qiang Dai & Kenneth J. Singleton, 2000. "Specification Analysis of Affine Term Structure Models," Journal of Finance, American Finance Association, vol. 55(5), pages 1943-1978, October.
    9. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    10. repec:bla:jfinan:v:53:y:1998:i:3:p:1165-1190 is not listed on IDEAS
    11. Longstaff, Francis A., 1989. "A nonlinear general equilibrium model of the term structure of interest rates," Journal of Financial Economics, Elsevier, vol. 23(2), pages 195-224, August.
    12. 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.
    13. Rendleman, Richard J. & Bartter, Brit J., 1980. "The Pricing of Options on Debt Securities," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 15(1), pages 11-24, March.
    14. 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..
    15. Darrell Duffie & Rui Kan, 1996. "A Yield‐Factor Model Of Interest Rates," Mathematical Finance, Wiley Blackwell, vol. 6(4), pages 379-406, October.
    16. Peter P. Carr & Robert A. Jarrow, 2008. "The Stop-Loss Start-Gain Paradox and Option Valuation: A new Decomposition into Intrinsic and Time Value," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 4, pages 61-84, World Scientific Publishing Co. Pte. Ltd..
    17. Black, Fischer, 1995. "Interest Rates as Options," Journal of Finance, American Finance Association, vol. 50(5), pages 1371-1376, December.
    18. repec:bla:jfinan:v:44:y:1989:i:1:p:205-09 is not listed on IDEAS
    19. Peter Carr & Vadim Linetsky, 2000. "The Valuation of Executive Stock Options in an Intensity-Based Framework," Review of Finance, European Finance Association, vol. 4(3), pages 211-230.
    20. Viatcheslav Gorovoi & Vadim Linetsky, 2004. "Black's Model of Interest Rates as Options, Eigenfunction Expansions and Japanese Interest Rates," Mathematical Finance, Wiley Blackwell, vol. 14(1), pages 49-78, January.
    21. Paul R. Krugman, 1991. "Target Zones and Exchange Rate Dynamics," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 106(3), pages 669-682.
    22. 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.
    23. Lucas, Robert E, Jr, 1978. "Asset Prices in an Exchange Economy," Econometrica, Econometric Society, vol. 46(6), pages 1429-1445, November.
    24. Markus Leippold & Zvi Wiener, 2005. "Efficient Calibration of Trinomial Trees for One-Factor Short Rate Models," Review of Derivatives Research, Springer, vol. 7(3), pages 213-239, October.
    25. 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.
    26. Nengli Lim & Nicolas Privault, 2016. "Analytic bond pricing for short rate dynamics evolving on matrix Lie groups," Quantitative Finance, Taylor & Francis Journals, vol. 16(1), pages 119-129, January.
    27. Fabricio Tourrucoo & Patrick S. Hagan & Gilberto F. Schleiniger, 2007. "Approximate Formulas for Zero-coupon Bonds," Applied Mathematical Finance, Taylor & Francis Journals, vol. 14(3), pages 207-226.
    28. 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.
    29. 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.
    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. Peter P. Carr & Zura Kakushadze, 2017. "FX options in target zones," Quantitative Finance, Taylor & Francis Journals, vol. 17(10), pages 1477-1486, October.

    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. 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.
    3. repec:wyi:journl:002108 is not listed on IDEAS
    4. Duffie, Darrell, 2003. "Intertemporal asset pricing theory," 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 11, pages 639-742, Elsevier.
    5. repec:wyi:journl:002109 is not listed on IDEAS
    6. 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.
    7. 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.
    8. repec:uts:finphd:40 is not listed on IDEAS
    9. Oldrich Alfons Vasicek & Francisco Venegas-Martínez, 2021. "Models of the Term Structure of Interest Rates: Review, Trends, and Perspectives," Remef - Revista Mexicana de Economía y Finanzas Nueva Época REMEF (The Mexican Journal of Economics and Finance), Instituto Mexicano de Ejecutivos de Finanzas, IMEF, vol. 16(2), pages 1-28, Abril - J.
    10. 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.
    11. repec:dau:papers:123456789/5374 is not listed on IDEAS
    12. 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, January-A.
    13. Oldrich Alfons Vasicek & Francisco Venegas-Martínez, 2021. "Modelos de la estructura de plazos de las tasas de interés: Revisión, tendencias y perspectivas," Remef - Revista Mexicana de Economía y Finanzas Nueva Época REMEF (The Mexican Journal of Economics and Finance), Instituto Mexicano de Ejecutivos de Finanzas, IMEF, vol. 16(2), pages 1-28, Abril - J.
    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. Tunaru, Diana, 2017. "Gaussian estimation and forecasting of the U.K. yield curve with multi-factor continuous-time models," International Review of Financial Analysis, Elsevier, vol. 52(C), pages 119-129.
    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. Oldrich Alfons Vasicek & Francisco Venegas-Martínez, 2021. "Modelos de la estructura de plazos de las tasas de interés: Revisión, tendencias y perspectivas," Remef - Revista Mexicana de Economía y Finanzas Nueva Época REMEF (The Mexican Journal of Economics and Finance), Instituto Mexicano de Ejecutivos de Finanzas, IMEF, vol. 16(2), pages 1-28, Abril - J.
    18. Yedidya Rabinovitz, 2017. "A new S.D.E. and instantaneous mean reversion rate formula (presented via a numerical empirical model comparison)," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 4(02n03), pages 1-22, June.
    19. 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.
    20. Bjork, Tomas, 2009. "Arbitrage Theory in Continuous Time," OUP Catalogue, Oxford University Press, edition 3, number 9780199574742.
    21. Yao, Yong, 1999. "Term structure modeling and asymptotic long rate," Insurance: Mathematics and Economics, Elsevier, vol. 25(3), pages 327-336, December.
    22. Fan, Longzhen & Johansson, Anders C., 2010. "China's official rates and bond yields," Journal of Banking & Finance, Elsevier, vol. 34(5), pages 996-1007, May.
    23. Giuseppe Arbia & Michele Di Marcantonio, 2015. "Forecasting Interest Rates Using Geostatistical Techniques," Econometrics, MDPI, vol. 3(4), pages 1-28, November.
    24. 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.

    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:1502.06074. 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.