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Inflation, ECB and short-term interest rates: A new model, with calibration to market data

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  • F. Antonacci
  • C. Costantini
  • F. D'Ippoliti
  • M. Papi

Abstract

We propose a new model for the joint evolution of the European inflation rate, the European Central Bank official interest rate and the short-term interest rate, in a stochastic, continuous time setting. We derive the valuation equation for a contingent claim and show that it has a unique solution. The contingent claim payoff may depend on all three economic factors of the model and the discount factor is allowed to include inflation. Taking as a benchmark the model of Ho, H.W., Huang, H.H. and Yildirim, Y., Affine model of inflation-indexed derivatives and inflation risk premium, (European Journal of Operational Researc, 2014), we show that our model performs better on market data from 2008 to 2015. Our model is not an affine model. Although in some special cases the solution of the valuation equation might admit a closed form, in general it has to be solved numerically. This can be done efficiently by the algorithm that we provide. Our model uses many fewer parameters than the benchmark model, which partly compensates the higher complexity of the numerical procedure and also suggests that our model describes the behaviour of the economic factors more closely.

Suggested Citation

  • F. Antonacci & C. Costantini & F. D'Ippoliti & M. Papi, 2020. "Inflation, ECB and short-term interest rates: A new model, with calibration to market data," Papers 2010.05462, arXiv.org.
    • Handle: RePEc:arx:papers:2010.05462
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    References listed on IDEAS

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    1. Singor, Stefan N. & Grzelak, Lech A. & van Bragt, David D.B. & Oosterlee, Cornelis W., 2013. "Pricing inflation products with stochastic volatility and stochastic interest rates," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 286-299.
    2. D’Amico, Stefania & Kim, Don H. & Wei, Min, 2018. "Tips from TIPS: The Informational Content of Treasury Inflation-Protected Security Prices," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 53(1), pages 395-436, February.
    3. Joseph Haubrich & George Pennacchi & Peter Ritchken, 2012. "Inflation Expectations, Real Rates, and Risk Premia: Evidence from Inflation Swaps," The Review of Financial Studies, Society for Financial Studies, vol. 25(5), pages 1588-1629.
    4. ,, 2004. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 20(2), pages 427-429, April.
    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. ,, 2004. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 20(1), pages 223-229, February.
    7. 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.
    8. Cristina Costantini & Marco Papi & Fernanda D’Ippoliti, 2012. "Singular risk-neutral valuation equations," Finance and Stochastics, Springer, vol. 16(2), pages 249-274, April.
    9. Stefan Waldenberger, 2017. "The affine inflation market models," Applied Mathematical Finance, Taylor & Francis Journals, vol. 24(4), pages 281-301, July.
    10. Fabio Mercurio, 2005. "Pricing inflation-indexed derivatives," Quantitative Finance, Taylor & Francis Journals, vol. 5(3), pages 289-302.
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    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.

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