Simple Inflation Option Modeling Linked to Nominal Rates

Summary

The document considers a simplified model for valuing inflation options embedded in inflation-indexed contracts with guarantees. The author already has a stochastic nominal interest-rate model, G2++, and wants inflation scenarios linked to it. One proposed route is to model real interest rates separately with a Ho-Lee short-rate model, calibrate it to real zero-coupon discount factors, and correlate the real and nominal models.

The main limitation raised is the scarcity of short-tenor real-rate data in Canada and the United States, which makes that calibration approach difficult. The author asks for simpler alternatives to more complex frameworks such as Jarrow-Yildirim that can connect inflation dynamics to the existing nominal model. No alternative method, valuation result, or supporting evidence is supplied, so the document identifies a modeling problem and constraints rather than resolving them.

Key ideas

• The modeling goal is to value inflation options in indexed contracts that include guarantees.
• The author wants inflation scenarios to connect with an existing G2++ nominal-rate model.
• A separate Ho-Lee real-rate model calibrated to real discount factors is proposed as an initial approach.
• Limited short-tenor real-rate data in Canada and the United States is identified as a calibration obstacle.
• The document requests simpler alternatives to complex inflation models but does not provide a solution.

Tags

# Inflation Option Modelling Approaches


# Inflation Option Modelling Approaches












I am trying to come up with a simplistic inflation option model to get a sense of the materiality of some inflation-indexed contracts containing inflation guarantees. I have a stochastic nominal IR model (G2++) and I would like to tie my inflation scenarios to this model. My initial idea: Set up a short rate model to independently model Real IR such as the Ho-Lee model and calibrate it Real ZCB Discount Factors. Then, I could specify a correlation to tie the real and nominal IR models. However, I don't think this approach is feasible since CAN/US Real IR data often isn't available for short tenors. Does anybody have any alternative approaches for valuing inflation options ? I know there are complicated models such as the Jarrow-Yildrim model, but I want to keep my model as simple as possible and I would like to tie it to my Nominal IR model. Given my constraints, any suggestions for alternative modelling approaches ? Any resources would be greatly appreciated as well. Cheers!

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