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Inflation-indexed swaps and swaptions

  • Hinnerich, Mia
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    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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    File URL: http://www.sciencedirect.com/science/article/B6VCY-4RJRVMK-1/2/e79725577e84581cfc0413fc79c7e388
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    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
    Contact details of provider: Web page: http://www.elsevier.com/locate/jbf

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    1. 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.
    2. Björk, Tomas & di Masi, Giovanni & Kabanov, Yuri & Runggaldier, Wolfgang, 1996. "Towards a General Theory of Bond Markets," SSE/EFI Working Paper Series in Economics and Finance 143, Stockholm School of Economics.
    3. 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.
    4. 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.
    5. Black, Fischer, 1976. "The pricing of commodity contracts," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 167-179.
    6. 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.
    7. Das, Sanjiv R., 2002. "The surprise element: jumps in interest rates," Journal of Econometrics, Elsevier, vol. 106(1), pages 27-65, January.
    8. Farshid Jamshidian, 1997. "LIBOR and swap market models and measures (*)," Finance and Stochastics, Springer, vol. 1(4), pages 293-330.
    9. 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.
    10. Monika Piazzesi, 2005. "Bond Yields and the Federal Reserve," Journal of Political Economy, University of Chicago Press, vol. 113(2), pages 311-344, April.
    11. Fabio Mercurio, 2005. "Pricing inflation-indexed derivatives," Quantitative Finance, Taylor & Francis Journals, vol. 5(3), pages 289-302.
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