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Inflation-indexed swaps and swaptions

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  • Hinnerich, Mia
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    Abstract

    This article considers the pricing and hedging of inflation-indexed swaps, and the pricing of inflation-indexed swaptions, and options on inflation-indexed bonds. To price the inflation-indexed swaps, we suggest an extended HJM model. The model allows both the forward rates and the consumer price index to be driven, not only by a standard multidimensional Wiener process but also by a general marked point process. Our model is an extension of the HJM approach proposed by Jarrow and Yildirim [Jarrow, R., Yildirim, Y., 2003. Pricing treasury inflation protected securities and related derivatives using an HJM model. Journal of Financial and Quantitative Analysis 38, 409-430] and later also used by Mercurio [Mercurio, F., 2005. Pricing inflation-indexed derivatives. Quantitative Finance 5 (3), 289-302] to price inflation-indexed swaps. Furthermore we price options on so called TIPS-bonds assuming the model is purely Wiener driven. We then introduce an inflation swap market model to price inflation-indexed swaptions. All prices derived have explicit closed-form solutions. Furthermore, we formally prove the validity of the so called foreign-currency analogy.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Banking & Finance.

    Volume (Year): 32 (2008)
    Issue (Month): 11 (November)
    Pages: 2293-2306

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    Handle: RePEc:eee:jbfina:v:32:y:2008:i:11:p:2293-2306

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    Web page: http://www.elsevier.com/locate/jbf

    Related research

    Keywords: Inflation Index-linked Derivatives Swaps Swaptions Analogy;

    References

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    Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
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    1. Björk, Tomas & di Masi, Giovanni & Kabanov, Yuri & Runggaldier, Wolfgang, 1996. "Towards a General Theory of Bond Markets," Working Paper Series in Economics and Finance 143, Stockholm School of Economics.
    2. Black, Fischer, 1976. "The pricing of commodity contracts," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 167-179.
    3. 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.
    4. Darrell Duffie & Jun Pan & Kenneth Singleton, 2000. "Transform Analysis and Asset Pricing for Affine Jump-Diffusions," Econometrica, Econometric Society, vol. 68(6), pages 1343-1376, November.
    5. Monika Piazzesi, 2005. "Bond Yields and the Federal Reserve," Journal of Political Economy, University of Chicago Press, vol. 113(2), pages 311-344, April.
    6. Tomas Björk & Yuri Kabanov & Wolfgang Runggaldier, 1997. "Bond Market Structure in the Presence of Marked Point Processes," Mathematical Finance, Wiley Blackwell, vol. 7(2), pages 211-239.
    7. 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.
    8. George Chacko, 2002. "Pricing Interest Rate Derivatives: A General Approach," Review of Financial Studies, Society for Financial Studies, vol. 15(1), pages 195-241, March.
    9. Farshid Jamshidian, 1997. "LIBOR and swap market models and measures (*)," Finance and Stochastics, Springer, vol. 1(4), pages 293-330.
    10. Das, Sanjiv R., 2002. "The surprise element: jumps in interest rates," Journal of Econometrics, Elsevier, vol. 106(1), pages 27-65, January.
    11. Fabio Mercurio, 2005. "Pricing inflation-indexed derivatives," Quantitative Finance, Taylor & Francis Journals, vol. 5(3), pages 289-302.
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    Cited by:
    1. Ho, Hsiao-Wei & Huang, Henry H. & Yildirim, Yildiray, 2014. "Affine model of inflation-indexed derivatives and inflation risk premium," European Journal of Operational Research, Elsevier, vol. 235(1), pages 159-169.
    2. Andrea Macrina & Priyanka A. Parbhoo, 2010. "Securities Pricing with Information-Sensitive Discounting," KIER Working Papers 695, Kyoto University, Institute of Economic Research.
    3. Andrea Macrina & Priyanka A. Parbhoo, 2010. "Security Pricing with Information-Sensitive Discounting," Papers 1001.3570, arXiv.org, revised Jun 2010.
    4. Moerman, Gerard A. & van Dijk, Mathijs A., 2010. "Inflation risk and international asset returns," Journal of Banking & Finance, Elsevier, vol. 34(4), pages 840-855, April.
    5. Robert Jarrow & Philip Protter, 2011. "Foreign currency bubbles," Review of Derivatives Research, Springer, vol. 14(1), pages 67-83, April.
    6. Tiong, Serena, 2013. "Pricing inflation-linked variable annuities under stochastic interest rates," Insurance: Mathematics and Economics, Elsevier, vol. 52(1), pages 77-86.

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