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Inflation-indexed swaps and swaptions

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  • Hinnerich, Mia

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.

Suggested Citation

  • Hinnerich, Mia, 2008. "Inflation-indexed swaps and swaptions," Journal of Banking & Finance, Elsevier, vol. 32(11), pages 2293-2306, November.
    • Handle: RePEc:eee:jbfina:v:32:y:2008:i:11:p:2293-2306
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    References listed on IDEAS

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    1. Das, Sanjiv R., 2002. "The surprise element: jumps in interest rates," Journal of Econometrics, Elsevier, vol. 106(1), pages 27-65, January.
    2. Farshid Jamshidian, 1997. "LIBOR and swap market models and measures (*)," Finance and Stochastics, Springer, vol. 1(4), pages 293-330.
    3. Monika Piazzesi, 2005. "Bond Yields and the Federal Reserve," Journal of Political Economy, University of Chicago Press, vol. 113(2), pages 311-344, April.
    4. Ahn, Chang Mo & Thompson, Howard E, 1988. " Jump-Diffusion Processes and the Term Structure of Interest Rates," Journal of Finance, American Finance Association, vol. 43(1), pages 155-174, March.
    5. 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..
    6. Michael Johannes, 2004. "The Statistical and Economic Role of Jumps in Continuous-Time Interest Rate Models," Journal of Finance, American Finance Association, vol. 59(1), pages 227-260, February.
    7. Fabio Mercurio, 2005. "Pricing inflation-indexed derivatives," Quantitative Finance, Taylor & Francis Journals, vol. 5(3), pages 289-302.
    8. Giovanni Di Masi & Tomas Björk & Wolfgang Runggaldier & Yuri Kabanov, 1997. "Towards a general theory of bond markets (*)," Finance and Stochastics, Springer, vol. 1(2), pages 141-174.
    9. 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, April.
    10. 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.
    11. Miltersen, Kristian R & Sandmann, Klaus & Sondermann, Dieter, 1997. "Closed Form Solutions for Term Structure Derivatives with Log-Normal Interest Rates," Journal of Finance, American Finance Association, vol. 52(1), pages 409-430, March.
    12. 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.
    13. Black, Fischer, 1976. "The pricing of commodity contracts," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 167-179.
    14. 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.
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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. Jens H.E. Christensen & Jose A. Lopez & Glenn D. Rudebusch, 2012. "Extracting Deflation Probability Forecasts from Treasury Yields," International Journal of Central Banking, International Journal of Central Banking, vol. 8(4), pages 21-60, December.
    3. Robert Jarrow & Philip Protter, 2011. "Foreign currency bubbles," Review of Derivatives Research, Springer, vol. 14(1), pages 67-83, April.
    4. Matthias Fleckenstein & Francis A. Longstaff & Hanno Lustig, 2010. "Why Does the Treasury Issue Tips? The Tips-Treasury Bond Puzzle," NBER Working Papers 16358, National Bureau of Economic Research, Inc.
    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. Andrea Macrina & Priyanka A. Parbhoo, 2010. "Security Pricing with Information-Sensitive Discounting," Papers 1001.3570, arXiv.org, revised Jun 2010.
    7. Andrea Macrina & Priyanka A. Parbhoo, 2010. "Securities Pricing with Information-Sensitive Discounting," KIER Working Papers 695, Kyoto University, Institute of Economic Research.
    8. 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.
    9. Tiong, Serena, 2013. "Pricing inflation-linked variable annuities under stochastic interest rates," Insurance: Mathematics and Economics, Elsevier, vol. 52(1), pages 77-86.
    10. 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.

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