Modeling Inflation Derivatives with Nominal and Real Rates

Summary

The document addresses pricing a European call option on Spanish CPI and outlines a framework for modeling inflation derivatives. It describes jointly modeling nominal interest rates, real interest rates, and inflation, with inflation treated in a way analogous to an exchange rate linking nominal and real values. This approach is associated with the Jarrow–Yildirim framework.

It also summarizes a way to incorporate seasonal effects: adjust the CPI forward curve with a static seasonal shape rather than changing the model’s stochastic dynamics. The discussion points readers toward published references but gives no equations, calibration details, numerical example, or pricing evidence. It is therefore an orientation to modeling choices rather than a complete implementation guide, and it does not specify how to handle the option’s payoff conventions or market inputs.

Key ideas

• A joint model can represent nominal rates, real rates, and inflation in a common framework.
• Inflation can be viewed as analogous to an exchange rate between nominal and real quantities.
• Seasonality may be incorporated by reshaping the CPI forward curve.
• The document gives conceptual guidance but no calibration or pricing procedure.

Tags

# Inflation modelling


# Inflation modelling












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:





## Answer by user1157 (score 7, accepted)

https://quant.stackexchange.com/a/10020

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).

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.