Inflation breakeven in the Jarrow and Yildirim model and resulting pricing formulas |
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Authors: | Alessandro Cipollini Paul Canty |
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Affiliation: | 1. Deutsche Bank AG (London) , Winchester House, 4 Great Winchester Street, London EC2 N2B , UK;2. Department of Mathematics and Applications , University of Milan – Bicocca , Via Cozzi 34, 20136 Milano , Italy alessandro.cipollini@db.com;4. Department of Mathematics and Applications , University of Milan – Bicocca , Via Cozzi 34, 20136 Milano , Italy |
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Abstract: | The Jarrow and Yildirim model for pricing inflation-indexed derivatives is still the main reference technique adopted in the inflation market. Despite its popularity it has some shortcomings, the most immediate of which is the difficulty of calibrating to market prices of options due to the large number of parameters involved. Since the market trades options on the inflation rate or index, we reformulate their model in terms of the notion of breakeven inflation. The first main advantage is the possibility of describing the prices of the most popular inflation derivatives as functions of just three parameters: breakeven volatility, the volatility of the CPI price index and the correlation between them. Secondly, the resulting Black–Scholes-implied volatilities are very straightforward to implement and the geometric interpretation of the model makes it intuitive to calibrate. Lastly, the model permits us to reproduce a realistic picture of the current state of the art of the derivatives market and, in particular, due to its simplicity, it is able to estimate the risk premium priced by the inflation market. |
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Keywords: | Inflation-indexed derivatives Jarrow and Yildirim model Implied volatility Calibration Inflation risk premium |
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