a YOY inflation swaplet payoff is S2/S1 - 1 , where Si is the CPI at time i and a TRS (total return swaplet) asset leg payoff is also the same except the underlying is an asset.

So it seems to me that the modelling for both should be identical, assuming you use the same model for each.

but i understand that typically , in TRS modelling S is GBM , with drift and vol dependent on t so E(S2/S1) = E(S2)/E(S1)=F2/F1 (ie no convexity adj) whereas in inflation , there is or is NOT a convexity adjustment , dependent on the model used!

i do not understand this for inflation - surely it cannot be that there can be 2 answers!


You get a convexity adjustment from forward correlations only if you model separately the forwards and they are not perfectly correlated on the time interval $[0, T_1]$, as is the case in inflation market models where each forward CPI index is modelled separately from the others, with a global instantaneous correlation structure, not set to identity, similar to the correlation structure in the Libor Market Model.

The reason for using a market model approach for inflation is that the CPI itself is not a tradable asset anyway so we do not need a model that would start from the CPI as a state variable, and the market model provides a better fit to quoted derivatives.

In the case of a TRS swaplet where $S_1$ and $S_2$ represent the prices of the same asset on times $T_1$ and $T_2$, and assuming deterministic rates and dividends and a diffusion process for the asset price $S_t$, the forwards are perfectly correlated on the time interval $[0, T_1]$ so there is no convexity adjustment that would come from decorrelation.

There is of course another convexity adjustment that arises when rates are stochastic because the expectation is computed under the $T_2$ terminal measure and the first forward is a martingale only under the $T_1$ measure.

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  • $\begingroup$ Comments are not for extended discussion; this conversation has been moved to chat. $\endgroup$ – Bob Jansen May 22 '17 at 15:30
  • $\begingroup$ if i understand correct, you are saying that for a 1 factor model , one can use the tower law of expectations , and so there is no convexity adjustment. And also in a 1 factor model , correl(S1,S2)=100%. Can you show me how you prove mathematically that correl(S1,S2)=100% ? $\endgroup$ – Randor May 23 '17 at 11:17
  • $\begingroup$ In fact it seems that correl(s1,s2) is NOT 100% ! See stats.stackexchange.com/questions/6853/… $\endgroup$ – Randor May 23 '17 at 17:42
  • $\begingroup$ What do u mean by the statement "forwards are perfectly correlated on time interval 0 to T1" ? How do u write that mathematically? $\endgroup$ – Randor May 23 '17 at 17:44

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