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pj


Total Posts: 3649
Joined: Jun 2004
 
Posted: 2022-07-08 11:09
Is there an established way to
calibrate JY inflation model on LPI swaps?

I know I know the phorum is almost extinct and it is more of
a way of thinking aloud.

The older I grow, the more I distrust the familiar doctrine that age brings wisdom Henry L. Mencken

silverside


Total Posts: 1458
Joined: Jun 2004
 
Posted: 2022-07-08 15:06
Hi pj :)

i haven't worked as inflation quant in more than 10 years so the below is probably out of date, but anyway.
at the time, the big houses were coming to a realisation that simple (i.e. 1 factor for inflation short rate) models were inadequate and that the CPI vol needed to be included

(using a model similar to that used for PR/DC's)

even without using a multi factor model, calibrating to LPI swaps was notoriously difficult as it depended on the relative pricing of the 5% cap and 0% floor (which obviously depended on supply and demand i.e. inflation vol skew) which wasn't really observable. As short dated vanilla options might have been traded up until around 10y but LPI was a beast unto its own.
So it was a choice between hacking a simpler model (to account for skew) or having a lovely theoretical model (something like SABR LMM with FX vol) which would be really difficult to implement.

Presumably there are some big players still in that market (maybe HSBC or GS) who may be persuaded to give away their secrets.
Also would be interesting to see how far the Markov Functional model developed (Commerz were looking into it for rates more generally)

edit: if i had to work on it, i would start by trying to implement Mercurio's book/paper, i found his yellow and blue book invaluable when implementing LMM.

pj


Total Posts: 3649
Joined: Jun 2004
 
Posted: 2022-07-08 15:52
> calibrating to LPI swaps was notoriously difficult
true Sad

Well, we have sort of Inflation Market Model,
but to calibrate by brute force an LPI swap price
is, let us say, infeasible.
So I thought there were some simple things that even I could
apply.
Thank you for information!

The older I grow, the more I distrust the familiar doctrine that age brings wisdom Henry L. Mencken

getnewre3


Total Posts: 1
Joined: Jul 2022
 
Posted: 2022-07-11 05:53
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