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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?

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  • $\begingroup$ You could use inflation options as a source of market implied volatility, which do trade for major markets. $\endgroup$
    – Bond wiz
    Commented May 29, 2020 at 1:04
  • $\begingroup$ OK, so I can get vol surface from inflation swap market. Then I should replace the discount from OIS/LIBOR with treasury discount to reflect the change of credit, correct? $\endgroup$ Commented Jun 1, 2020 at 18:56
  • $\begingroup$ That sounds right to me. Note that there are two types of inflation swaps trading, year over year (YoY) and zero-coupon. I believe swaptions trade on both in a variety of strikes but not sure on liquidity. There are also caps trading. $\endgroup$
    – Bond wiz
    Commented Jun 1, 2020 at 20:04
  • $\begingroup$ ZC swaps must be more liquid due to easier pricing. I think for par floor in linkers, only ZC floors should be used for put characteristic, although floors are far less liquid than swaps. Even bloomberg only shows quotes but not specific dealers I think. $\endgroup$ Commented Jun 1, 2020 at 20:26

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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.

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