IDEAS home Printed from https://ideas.repec.org/p/mse/wpsorb/b04050.html
   My bibliography  Save this paper

A market model for inflation

Author

Listed:
  • Nabyl Belgrade

    (CERMSEM et CDC IXIS-CM,R&D)

  • Eric Benhamou

    (CDC IXIS-CM,R&D)

  • Etienne Koehler

    (CERMSEM et CDC IXIS Risk)

Abstract

The various macro econometrics models for inflation are helpless when it comes to the pricing of inflation derivatives. The only article targeting inflation option pricing, the Jarrow Yildirim model (2000), relies on non observable data. This makes the estimation of the model parameters a non trivial problem. In addition, their framework does not examine any relationship between the most liquid inflation derivatives instruments: the year to year and zero coupon swap. To fill this gap, we see how to derive a model on inflation, based on traded and liquid market instrument. Applying the same strategy as the one for a market model on interest rates, we derive no-arbitrage relationship between zero coupon and year to year swaps. We explain how to compute the convexity adjustment and what relationship the volatility surface should satisfy. Within this framework, it becomes much easier to estimate model parameters and to price inflation derivatives in a consistent way

Suggested Citation

  • Nabyl Belgrade & Eric Benhamou & Etienne Koehler, 2004. "A market model for inflation," Cahiers de la Maison des Sciences Economiques b04050, Université Panthéon-Sorbonne (Paris 1).
    • Handle: RePEc:mse:wpsorb:b04050
    as

    Download full text from publisher

    File URL: ftp://mse.univ-paris1.fr/pub/mse/cahiers2004/B04050.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Eric Benhamou, 2000. "Pricing Convexity Adjustment with Wiener Chaos," FMG Discussion Papers dp351, Financial Markets Group.
    2. 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.
    3. Benhamou, Eric, 2000. "Pricing convexity adjustment with Wiener chaos," LSE Research Online Documents on Economics 119104, London School of Economics and Political Science, LSE Library.
    4. 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..
    5. Pierre-Daniel G. Sarte, 1998. "Fisher's equation and the inflation risk premium in a simple endowment economy," Economic Quarterly, Federal Reserve Bank of Richmond, issue Fall, pages 53-72.
    6. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    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. Henrik Dam & Andrea Macrina & David Skovmand & David Sloth, 2018. "Rational Models for Inflation-Linked Derivatives," Papers 1801.08804, arXiv.org, revised Jul 2020.
    2. Mordecai Avriel & Jens Hilscher & Alon Raviv, 2013. "Inflation Derivatives Under Inflation Target Regimes," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 33(10), pages 911-938, October.
    3. Fabio Mercurio, 2005. "Pricing inflation-indexed derivatives," Quantitative Finance, Taylor & Francis Journals, vol. 5(3), pages 289-302.
    4. Lixin Wu, 2013. "Inflation-rate Derivatives: From Market Model to Foreign Currency Analogy," Papers 1302.0574, arXiv.org.
    5. Stefan Waldenberger, 2015. "The affine inflation market models," Papers 1503.04979, arXiv.org.
    6. Flavia Antonacci & Cristina Costantini & Marco Papi, 2021. "Short-Term Interest Rate Estimation by Filtering in a Model Linking Inflation, the Central Bank and Short-Term Interest Rates," Mathematics, MDPI, vol. 9(10), pages 1-20, May.
    7. Gabriele Sarais & Damiano Brigo, 2014. "Inflation securities valuation with macroeconomic-based no-arbitrage dynamics," Papers 1403.7799, arXiv.org, revised Jul 2014.
    8. Henrard, Marc, 2006. "TIPS Options in the Jarrow-Yildirim model," MPRA Paper 1423, University Library of Munich, Germany.
    9. Zura Kakushadze & Juan Andrés Serur, 2018. "151 Trading Strategies," Springer Books, Springer, number 978-3-030-02792-6, December.
    10. Stefan Waldenberger, 2015. "Time-inhomogeneous affine processes and affine market models," Papers 1512.03292, arXiv.org.
    11. Emmanuel Gobet & Julien Hok, 2014. "Expansion Formulas For Bivariate Payoffs With Application To Best-Of Options On Equity And Inflation," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 17(02), pages 1-32.
    12. Nabyl Belgrade, 2004. "Market inflation seasonality management," Cahiers de la Maison des Sciences Economiques b04051, Université Panthéon-Sorbonne (Paris 1).
    13. Yue Zhou, 2020. "Rational Kernel on Pricing Models of Inflation Derivatives," Papers 2001.05124, arXiv.org, revised Jan 2020.

    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. Jiří Witzany, 2009. "Valuation of Convexity Related Interest Rate Derivatives," Prague Economic Papers, Prague University of Economics and Business, vol. 2009(4), pages 309-326.
    2. Chuang, Ming-Che & Wen, Chin-Hsiang & Lin, Shih-Kuei, 2020. "Valuation and empirical analysis of currency options," International Review of Economics & Finance, Elsevier, vol. 66(C), pages 71-91.
    3. Henrik Dam & Andrea Macrina & David Skovmand & David Sloth, 2018. "Rational Models for Inflation-Linked Derivatives," Papers 1801.08804, arXiv.org, revised Jul 2020.
    4. Robert A. Jarrow, 2009. "The Term Structure of Interest Rates," Annual Review of Financial Economics, Annual Reviews, vol. 1(1), pages 69-96, November.
    5. Bjork, Tomas, 2009. "Arbitrage Theory in Continuous Time," OUP Catalogue, Oxford University Press, edition 3, number 9780199574742.
    6. Choi, Jaehyung, 2012. "Spontaneous symmetry breaking of arbitrage," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(11), pages 3206-3218.
    7. 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.
    8. Jorgensen, Peter Lochte, 2007. "Traffic light options," Journal of Banking & Finance, Elsevier, vol. 31(12), pages 3698-3719, December.
    9. Jobst, Norbert J. & Zenios, Stavros A., 2005. "On the simulation of portfolios of interest rate and credit risk sensitive securities," European Journal of Operational Research, Elsevier, vol. 161(2), pages 298-324, March.
    10. repec:uts:finphd:40 is not listed on IDEAS
    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 1-2011.
    12. Henrard, Marc, 2006. "TIPS Options in the Jarrow-Yildirim model," MPRA Paper 1423, University Library of Munich, Germany.
    13. Benjamin Cheng & Christina Nikitopoulos-Sklibosios & Erik Schlogl, 2015. "Pricing of Long-dated Commodity Derivatives with Stochastic Volatility and Stochastic Interest Rates," Research Paper Series 366, Quantitative Finance Research Centre, University of Technology, Sydney.
    14. 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.
    15. 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.
    16. Roman Horsky & Tilman Sayer, 2015. "Joining The Heston And A Three-Factor Short Rate Model: A Closed-Form Approach," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 18(08), pages 1-17, December.
    17. Koo, Bonsoo & Linton, Oliver, 2012. "Estimation of semiparametric locally stationary diffusion models," Journal of Econometrics, Elsevier, vol. 170(1), pages 210-233.
    18. repec:wyi:journl:002108 is not listed on IDEAS
    19. Cai, Lili & Swanson, Norman R., 2011. "In- and out-of-sample specification analysis of spot rate models: Further evidence for the period 1982-2008," Journal of Empirical Finance, Elsevier, vol. 18(4), pages 743-764, September.
    20. Alexander Lipton, 2024. "Hydrodynamics of Markets:Hidden Links Between Physics and Finance," Papers 2403.09761, arXiv.org.
    21. Marcello Pericoli, 2014. "Real Term Structure and Inflation Compensation in the Euro Area," International Journal of Central Banking, International Journal of Central Banking, vol. 10(1), pages 1-42, March.
    22. Liu, Yan & Wu, Jing Cynthia, 2021. "Reconstructing the yield curve," Journal of Financial Economics, Elsevier, vol. 142(3), pages 1395-1425.

    More about this item

    Keywords

    Inflation index; forward; zero-coupon; year-on-year; volatility cube; convexity adjustment;
    All these keywords.

    JEL classification:

    • C59 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Other

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:mse:wpsorb:b04050. 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: Lucie Label (email available below). General contact details of provider: https://edirc.repec.org/data/msep1fr.html .

    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.