IDEAS home Printed from https://ideas.repec.org/a/spt/fininv/v13y2024i4f13_4_2.html
   My bibliography  Save this article

Stochastic Inflation and the Term Structure of Interest Rates: a Simple Diffusion Model

Author

Listed:
  • Cristiano Baldassari
  • Massimiliano Meschini
  • Paola Nascenzi

Abstract

The present paper addresses the problem of valuing contingent claims on the term structure in asingle good economy under uncertain inflation. In the context of arbitrage-free valuation, a simple diffusion model for pricing inflation-indexed securities is proposed. A martingale characterization of nominal and real prices is given and a stochastic generalization of the Fisher equation is provided. An example of two-factor model which can be used to value inflation-linked securities in practical applications, is also discussed. JEL classification numbers: G00, G10, G30. Keywords: Term structure of interest rates, Fisher equation, HJM-methodology, Inflation-linked securities.

Suggested Citation

  • Cristiano Baldassari & Massimiliano Meschini & Paola Nascenzi, 2024. "Stochastic Inflation and the Term Structure of Interest Rates: a Simple Diffusion Model," Journal of Finance and Investment Analysis, SCIENPRESS Ltd, vol. 13(4), pages 1-2.
  • Handle: RePEc:spt:fininv:v:13:y:2024:i:4:f:13_4_2
    as

    Download full text from publisher

    File URL: http://www.scienpress.com/Upload/JFIA%2fVol%2013_4_2.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Schwartz, Eduardo S, 1982. "The Pricing of Commodity-Linked Bonds," Journal of Finance, American Finance Association, vol. 37(2), pages 525-539, May.
    2. J. Michael Harrison & Stanley R. Pliska, 1981. "Martingales and Stochastic Integrals in the Theory of Continous Trading," Discussion Papers 454, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    3. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1981. "A Re-examination of Traditional Hypotheses about the Term Structure of Interest Rates," Journal of Finance, American Finance Association, vol. 36(4), pages 769-799, September.
    4. Heath, David & Jarrow, Robert & Morton, Andrew, 1990. "Bond Pricing and the Term Structure of Interest Rates: A Discrete Time Approximation," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 25(4), pages 419-440, December.
    5. 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..
    6. Thomas Laubach & John C. Williams, 2003. "Measuring the Natural Rate of Interest," The Review of Economics and Statistics, MIT Press, vol. 85(4), pages 1063-1070, November.
    7. Bjorn Flesaker, 1993. "Arbitrage free pricing of interest rate futures and forward contracts," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 13(1), pages 77-91, February.
    8. Martin D. D. Evans, 2003. "Real risk, inflation risk, and the term structure," Economic Journal, Royal Economic Society, vol. 113(487), pages 345-389, April.
    9. Juan Angel Garcia & Adrian van Rixtel, 2007. "Inflation-linked bonds from a central bank perspective," Occasional Papers 0705, Banco de España.
    10. Richard, Scott F., 1978. "An arbitrage model of the term structure of interest rates," Journal of Financial Economics, Elsevier, vol. 6(1), pages 33-57, March.
    11. Singor, Stefan N. & Grzelak, Lech A. & van Bragt, David D.B. & Oosterlee, Cornelis W., 2013. "Pricing inflation products with stochastic volatility and stochastic interest rates," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 286-299.
    12. Pennacchi, George G, 1991. "Identifying the Dynamics of Real Interest Rates and Inflation: Evidence Using Survey Data," The Review of Financial Studies, Society for Financial Studies, vol. 4(1), pages 53-86.
    13. Antulio N. Bomfim, 2001. "Measuring equilibrium real interest rates: what can we learn from yields on indexed bonds?," Finance and Economics Discussion Series 2001-53, Board of Governors of the Federal Reserve System (U.S.).
    14. Mkaouar, Farid & Prigent, Jean-Luc & Abid, Ilyes, 2017. "Long-term investment with stochastic interest and inflation rates: The need for inflation-indexed bonds," Economic Modelling, Elsevier, vol. 67(C), pages 228-247.
    15. Robert Jarrow & Yildiray Yildirim, 2008. "Pricing Treasury Inflation Protected Securities and Related Derivatives using an HJM Model," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 16, pages 349-370, World Scientific Publishing Co. Pte. Ltd..
    16. Van Rixtel, Adrian & Garcí­a, Juan Angel, 2007. "Inflation-linked bonds from a Central Bank perspective," Occasional Paper Series 62, European Central Bank.
    17. Juan Angel Garcia & Adrian van Rixtel, 2007. "Inflation-linked bonds from a central bank perspective," Occasional Papers 0705, Banco de España;Occasional Papers Homepage.
    18. Stambaugh, Robert F., 1988. "The information in forward rates : Implications for models of the term structure," Journal of Financial Economics, Elsevier, vol. 21(1), pages 41-70, May.
    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. Lim, Terence & Lo, Andrew W. & Merton, Robert C. & Scholes, Myron S., 2006. "The Derivatives Sourcebook," Foundations and Trends(R) in Finance, now publishers, vol. 1(5–6), pages 365-572, April.
    2. Chen, Ren-Raw & Liu, Bo & Cheng, Xiaolin, 2010. "Pricing the term structure of inflation risk premia: Theory and evidence from TIPS," Journal of Empirical Finance, Elsevier, vol. 17(4), pages 702-721, September.
    3. Robert A. Jarrow, 2009. "The Term Structure of Interest Rates," Annual Review of Financial Economics, Annual Reviews, vol. 1(1), pages 69-96, November.
    4. Emmanuelle Clément & Christian Gourieroux & Alain Monfort, 1995. "Linear Factor Models and the Term Structure of Interest Rates," Annals of Economics and Statistics, GENES, issue 40, pages 37-65.
    5. Ed Westerhout & Ona Ciocyte, 2017. "The role of inflation-linked bonds," CPB Discussion Paper 344, CPB Netherlands Bureau for Economic Policy Analysis.
    6. Mayerlen, Frank & Sola, Pierre & Be Duc, Louis, 2008. "The monetary presentation of the euro area balance of payments," Occasional Paper Series 96, European Central Bank.
    7. Russo, Daniela & Caviglia, Giacomo & Papathanassiou, Chryssa & Rosati, Simonetta, 2007. "Prudential and oversight requirements for securities settlement," Occasional Paper Series 76, European Central Bank.
    8. 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.
    9. Equiza-Goñi, Juan & Faraglia, Elisa & Oikonomou, Rigas, 2023. "Union debt management," Journal of International Money and Finance, Elsevier, vol. 130(C).
    10. repec:uts:finphd:40 is not listed on IDEAS
    11. Irina Bunda, 2007. "The Changing Role of the Exchange Rate in a Globalised Economy," Post-Print halshs-00372820, HAL.
    12. Mehl, Arnaud & Bussière, Matthieu, 2008. "China's and India's roles in global trade and finance: twin titans for the new millennium?," Occasional Paper Series 80, European Central Bank.
    13. Kajuth, Florian & Watzka, Sebastian, 2011. "Inflation expectations from index-linked bonds: Correcting for liquidity and inflation risk premia," The Quarterly Review of Economics and Finance, Elsevier, vol. 51(3), pages 225-235, June.
    14. Garcí­a, Juan Angel & Werner, Thomas, 2010. "Inflation risks and inflation risk premia," Working Paper Series 1162, European Central Bank.
    15. Abraham Lioui & Patrice Poncet, 2000. "The Minimum Variance Hedge Ratio Under Stochastic Interest Rates," Management Science, INFORMS, vol. 46(5), pages 658-668, May.
    16. González, Fernando & Coppens, François & Winkler, Gerhard, 2007. "The performance of credit rating systems in the assessment of collateral used in Eurosystem monetary policy operations," Occasional Paper Series 65, European Central Bank.
    17. Christian M. Hafner & Helmut Herwartz, 2009. "Testing for linear vector autoregressive dynamics under multivariate generalized autoregressive heteroskedasticity," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 63(3), pages 294-323, August.
    18. David Bolder, 2001. "Affine Term-Structure Models: Theory and Implementation," Staff Working Papers 01-15, Bank of Canada.
    19. Blattner, Tobias Sebastian & Catenaro, Marco & Ehrmann, Michael & Strauch, Rolf & Turunen, Jarkko, 2008. "The predictability of monetary policy," Occasional Paper Series 83, European Central Bank.
    20. Moutot, Philippe & Jung, Alexander & Mongelli, Francesco Paolo, 2008. "The working of the eurosystem: monetary policy preparations and decision-making - selected issues," Occasional Paper Series 79, European Central Bank.
    21. Thimann, Christian & Skala, Martin & Wölfinger, Regine, 2007. "The search for Columbus' egg: finding a new formula to determine quotas at the IMF," Occasional Paper Series 70, European Central Bank.

    More about this item

    Keywords

    term structure of interest rates; fisher equation; hjm-methodology; inflation-linked securities.;
    All these keywords.

    JEL classification:

    • G00 - Financial Economics - - General - - - General
    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • G30 - Financial Economics - - Corporate Finance and Governance - - - General

    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:spt:fininv:v:13:y:2024:i:4:f:13_4_2. 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: Eleftherios Spyromitros-Xioufis (email available below). General contact details of provider: http://www.scienpress.com/ .

    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.