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Approximating an Inflation Bond Floor as a CPI Put

Article Quant Q&A · Author: sciencemonk
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Summary

The document proposes valuing the principal floor embedded in an inflation-linked bond by treating the consumer price index as an underlying asset and the floor as a put option. When traded inflation floor instruments are unavailable, it suggests estimating volatility from monthly observations of the non-seasonally-adjusted US CPI index, then using that estimate as an input to an option valuation framework.

The response reports historical CPI volatility of about two percent per year and suggests implied volatility may be higher. This is a rough proxy rather than a complete pricing recipe: it gives no option-pricing model, calibration procedure, or treatment of indexation lags and other contract details. Its volatility observation is specific to the cited US CPI series, so it should not be assumed to transfer directly to other inflation measures or markets.

Key ideas

  • A principal floor can be conceptualized as a put option on the relevant CPI index.
  • Monthly CPI observations can be used to estimate historical index volatility.
  • The cited US non-seasonally-adjusted CPI series is the proposed data source.
  • The response suggests implied volatility may exceed its historical estimate.
  • The approximation leaves model choice and contract-specific details unspecified.

Tags

Fixed incomeOptionsVolatilityDerivatives pricing
Full text
# Answer by dm63 (score 1)


# How to evaluate embedded floor option in inflation linked bonds if interbank inflation floor instruments cannot be used or do not exist












Suppose we consider simple case that only par is protected against base price index, so it is with zero coupon floor feature. How do we value this option given that there is no inflation floor instruments tradable?

## Answer by dm63 (score 1)

https://quant.stackexchange.com/a/54505

You can consider the CPI index like a stock, and treat the floor like a put option. You can measure the historical volatility of this index by looking at the monthly data. In the case of the US, we are talking about the non seasonally adjusted CPI index CPURNSA. You should find historical volatility around 2pct per annum, and like many markets I think the implied volatility is probably a bit higher than that.

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.