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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

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    File URL: ftp://mse.univ-paris1.fr/pub/mse/cahiers2004/B04050.pdf
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    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

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    Cited by:

    1. 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.
    2. Fabio Mercurio, 2005. "Pricing inflation-indexed derivatives," Quantitative Finance, Taylor & Francis Journals, vol. 5(3), pages 289-302.
    3. Lixin Wu, 2013. "Inflation-rate Derivatives: From Market Model to Foreign Currency Analogy," Papers 1302.0574, arXiv.org.
    4. 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.
    5. Zura Kakushadze & Juan Andrés Serur, 2018. "151 Trading Strategies," Springer Books, Springer, number 978-3-030-02792-6, March.
    6. Stefan Waldenberger, 2015. "Time-inhomogeneous affine processes and affine market models," Papers 1512.03292, arXiv.org.
    7. Nabyl Belgrade, 2004. "Market inflation seasonality management," Cahiers de la Maison des Sciences Economiques b04051, Université Panthéon-Sorbonne (Paris 1).
    8. Henrik Dam & Andrea Macrina & David Skovmand & David Sloth, 2018. "Rational Models for Inflation-Linked Derivatives," Papers 1801.08804, arXiv.org, revised Jul 2020.
    9. Stefan Waldenberger, 2015. "The affine inflation market models," Papers 1503.04979, arXiv.org.
    10. Gabriele Sarais & Damiano Brigo, 2014. "Inflation securities valuation with macroeconomic-based no-arbitrage dynamics," Papers 1403.7799, arXiv.org, revised Jul 2014.
    11. Henrard, Marc, 2006. "TIPS Options in the Jarrow-Yildirim model," MPRA Paper 1423, University Library of Munich, Germany.
    12. 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.
    13. Yue Zhou, 2020. "Rational Kernel on Pricing Models of Inflation Derivatives," Papers 2001.05124, arXiv.org, revised Jan 2020.

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    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

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