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I am trying to price an option on the Spanish CPI. The option is a European call with a single observation date. However, I am fairly new to inflation modelling, so there are two areas in which I would greatly appreciate any insights:

  1. Market data: I have already retrieved some data on Euro zone inflation swaps. However, I have not been able to recover any volatility information. Are you aware of any instruments that can be used to obtain expected inflation and implied volatilities for the Spanish market?

  2. Modelling framework: Given the simplicity of the option (and the potential lack of market data), my initial idea would be to keep things simple and employ a short rate model like Vasicek or Hull & White. However, I am not sure if I may be missing any relevant factors by using these models. Do you think this modelling framework could be appropriate in this particular case?

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In modelling inflation you absolutely have to take seasonalities into account. Usually inflation in summer is different from winter (it depends on the market and the role that traveling and heating play). If I remeber this correctly then this is take into account with inflation swaps. –  Richard Jan 17 at 10:09
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quantlib.org/slides/qlws13/acar.pdf This has an overview of some common approaches, including the Linear Gauss Markov with Jarrow-Yildirim dynamics. For volatility data, you should look for zero-coupon and year-on-year inflation caps and floors. –  experquisite Jan 17 at 14:35
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With respect to Richard's point, the European HICP inflation data all comes out NSA (non-seasonally adjusted). I checked and the Spanish data from INE is also NSA. You just have to be careful because other countries might provide the SA data (like the US does). Spanish prices are typically weak in winter before recovering in the spring. –  John Jan 17 at 15:43

1 Answer 1

One approach is to include the nominal rates, real rates and inflation in the model and then represent the inflation as a kind of exchange rate between nominal and real rates.

Jarrow and Yildrim presented such an approach in their paper "Pricing Treasury Inflation Protected Securities and Related Derivatives using an HJM Model" (2002). The definitive resource is "Interest Rate Models - Theory and Practice" by Brigo and Mercurio.

Belgrade and Ebenhamou discuss an extension to model the impact of seasonality in inflation derivatives pricing. Instead of changing the stochastic dynamics of the model, they reshape the forward curve of the CPI (i.e. they directly apply a static seasonal bump to the forward curve).

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