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Inflation Models with Correlation and Skew

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  • Orcan Ogetbil
  • Bernhard Hientzsch

Abstract

We formulate a forward inflation index model with multi-factor volatility structure featuring a parametric form that allows calibration to correlations between indices of different tenors observed in the market. Assuming the nominal interest rate follows a single factor Gaussian short rate model, we present analytical prices for zero-coupon and year-on-year swaps, caps, and floors. The same method applies to any interest rate model for which one can compute the zero-coupon bond prices and measure shifts. We extend the multi-factor model with leverage functions to capture the entire market volatility skew with a single process. The time-consuming calibration step of this model can be avoided in the simplified model that we further propose. We demonstrate the leveraged and the simplified models with market data.

Suggested Citation

  • Orcan Ogetbil & Bernhard Hientzsch, 2024. "Inflation Models with Correlation and Skew," Papers 2405.05101, arXiv.org.
    • Handle: RePEc:arx:papers:2405.05101
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    References listed on IDEAS

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    1. Leif Andersen, 2010. "Markov models for commodity futures: theory and practice," Quantitative Finance, Taylor & Francis Journals, vol. 10(8), pages 831-854.
    2. 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..
    3. Flavia Antonacci & Cristina Costantini & Fernanda D'Ippoliti & Marco Papi, 2019. "Risk Neutral Valuation of Inflation-Linked Interest Rate Derivatives," Papers 1911.00386, arXiv.org.
    4. Fabio Mercurio, 2005. "Pricing inflation-indexed derivatives," Quantitative Finance, Taylor & Francis Journals, vol. 5(3), pages 289-302.
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