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A market model for inflation

Author

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  • Nabyl Belgrade

    (CERMSEM - CEntre de Recherche en Mathématiques, Statistique et Économie Mathématique - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, CDC IXIS-CM)

  • Eric Benhamou

    (CDC IXIS-CM)

  • Etienne Koehler

    (CDC IXIS Risk Department)

Abstract

The various macro econometrics model for inflation are helpless when it comes to the pricing of inflation derivatives. The only article targeting inflation option pricing, the Jarrow Yildirim model [7], relies on non observable data. This makes the estimation of the model parameters a non trivial problem. In addition, their framework do 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," Post-Print halshs-03331510, HAL.
    • Handle: RePEc:hal:journl:halshs-03331510
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-03331510
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    References listed on IDEAS

    as
    1. Alan Brace & Dariusz G¸atarek & Marek Musiela, 1997. "The Market Model of Interest Rate Dynamics," Mathematical Finance, Wiley Blackwell, vol. 7(2), pages 127-155, April.
    2. 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.
    3. Benninga, Simon & Protopapadakis, Aris, 1983. "Real and Nominal Interest Rates under Uncertainty: The Fisher Theorem and the Term Structure," Journal of Political Economy, University of Chicago Press, vol. 91(5), pages 856-867, October.
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    Cited by:

    1. 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.
    2. Zura Kakushadze & Juan Andrés Serur, 2018. "151 Trading Strategies," Springer Books, Springer, number 978-3-030-02792-6, January.
    3. Stefan Waldenberger, 2015. "Time-inhomogeneous affine processes and affine market models," Papers 1512.03292, arXiv.org.
    4. Nabyl Belgrade, 2004. "Market inflation seasonality management," Cahiers de la Maison des Sciences Economiques b04051, Université Panthéon-Sorbonne (Paris 1).
    5. Henrik Dam & Andrea Macrina & David Skovmand & David Sloth, 2018. "Rational Models for Inflation-Linked Derivatives," Papers 1801.08804, arXiv.org, revised Jul 2020.
    6. Stefan Waldenberger, 2015. "The affine inflation market models," Papers 1503.04979, arXiv.org.
    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. 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.

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