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On the pricing of inflation-indexed caps

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Abstract

We consider the problem of pricing inflation-linked caplets in a Black–Scholes-type framework as well as in the presence of stochastic volatility. By using results on the pricing of forward starting options in Heston’s Model on stochastic volatility, we derive closed-form solutions for inflation caps which aim to receive smile-consistent option prices. Additionally we price options on the inflation development over a longer time horizon. In this paper we develop a new and more suitable formula for pricing inflation-linked options under the assumption of stochastic volatility. The formula in the presence of stochastic volatility allows to cover the smile effects observed in our Black–Scholes type environment, in which the exposure of year-on-year inflation caps to inflation volatility changes is ignored. The chosen diffusion processes reflect the macro-economic concept of Fisher making a connection between interest rates on the market and the expected inflation rate.

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Notes

  1. Germany has issued its first inflation-linked bond with maturity in 2016 in March 2006 and a second one with maturity 2013 in October 2007.

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Acknowledgments

Furthermore, we would like to thank Fabio Mercurio, Banca IMI Milano, for offering to use the market data as in Mercurio and Moreni [14].

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Authors and Affiliations

  1. Hochschule der Sparkassen-Finanzgruppe, University of Applied Sciences, Bonn, Germany

    Susanne Kruse

  2. Department of Financial Mathematics, Fraunhofer Institute for Industrial and Financial Mathematics, Kaiserslautern, Germany

    Susanne Kruse

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  1. Susanne Kruse
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Correspondence to Susanne Kruse.

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Kruse, S. On the pricing of inflation-indexed caps. Eur. Actuar. J. 1 (Suppl 2), 379–393 (2011). https://doi.org/10.1007/s13385-011-0022-4

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  • DOI: https://doi.org/10.1007/s13385-011-0022-4

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