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A market model for inflation

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  • Nabyl Belgrade

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

  • Eric Benhamou

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

  • Etienne Koehler

    ()
    (CERMSEM et CDC IXIS Risk)

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    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.

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

    Paper provided by Université Panthéon-Sorbonne (Paris 1) in its series Cahiers de la Maison des Sciences Economiques with number b04050.

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    Length: 15 pages
    Date of creation: Jan 2004
    Date of revision:
    Handle: RePEc:mse:wpsorb:b04050

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    Related research

    Keywords: Inflation index; forward; zero-coupon; year-on-year; volatility cube; convexity adjustment.;

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    References

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    1. Jarrow, Robert & Yildirim, Yildiray, 2003. "Pricing Treasury Inflation Protected Securities and Related Derivatives using an HJM Model," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 38(02), pages 337-358, June.
    2. Eric Benhamou, 2000. "Pricing Convexity Adjustment with Wiener Chaos," FMG Discussion Papers dp351, Financial Markets Group.
    3. Hull, John & White, Alan, 1990. "Pricing Interest-Rate-Derivative Securities," Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 573-92.
    4. 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.
    5. 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 637-54, May-June.
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    Cited by:
    1. Henrard, Marc, 2006. "TIPS Options in the Jarrow-Yildirim model," MPRA Paper 1423, University Library of Munich, Germany.
    2. Nabyl Belgrade, 2004. "Market inflation seasonality management," Cahiers de la Maison des Sciences Economiques b04051, Université Panthéon-Sorbonne (Paris 1).

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