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Every time I search calibration methods in short-rate models such as Hull-White, I always find information on how to do it with swaptions market data. Yet, I can't find anything about how to do it in markets without swaptions.

How can I calibrate Hull-White short rate model in a market without options? It is an overnight interbank rate with daily data and daily zero coupon curve (bootstrapped from swaps).

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    $\begingroup$ You cannot really calibrate the Hull-White model without options, or generally non-linear payoffs. You need some product whose price is dependent on volatility to be able to calibrate the model. I guess you might use CMS swaps which are vol dependent. $\endgroup$
    – Daneel Olivaw
    Sep 7, 2022 at 19:41
  • $\begingroup$ The only market that available is the daily overnight spot rate itself and OIS rates and zero coupon curves bootstrapped from those OIS. $\endgroup$
    – Oliver Mohr Bonometti
    Sep 7, 2022 at 20:22
  • $\begingroup$ What market exactly? Also, what is the use case of the model? $\endgroup$
    – AKdemy
    Sep 7, 2022 at 20:37
  • $\begingroup$ Chilean overnight interbank rate. Use case is to model a XVAs and probably XVAs distribution (to get XVA tails value). $\endgroup$
    – Oliver Mohr Bonometti
    Sep 7, 2022 at 20:55
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    $\begingroup$ CLP is tricky. Bloomberg for example only uses hard coded vols for all tenors and products because no one seems to quote swaptions, caps or floors. Usually you could proxy RFR (OIS) with IBOR if there is a market for IBOR derivatives. However, that is also not the case. I am not familiar with LATAM Rates markets so I cannot comment if there would be a way to get quotes from some local market makers. In the absence of all data, instead of simply hard coding some value like Bloomberg does, your best bet will be to proxy it with some other existing surface and potentially make some adjustments. $\endgroup$
    – AKdemy
    Sep 8, 2022 at 9:10

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To me there are some semantics involved here, I'd say you need to take a step back and think about a different adjoining question.

More than calibrate your parameters you need to estimate them since you have no points of reference for calibration i.e. no actively traded to Non-Linear / Vol products on this asset.

Calibration is simply trying to fit your model to market data by tweaking the parameters until you minimize some target function (like price difference) so that you're sure your model will match as closely as possible the observed market prices.... its a regression (using the term loosely) and your question is basically: how can I do a regression without a could of data points... you can't... but that doesn't mean you can't make educated/assumption driven guesses about your model parameters.

What I would do in this case, is I would look for proxy implied vols like:

  • USD/CLP
  • Copper
  • CLP RFR Historical Vols (per tenor ideally)
  • USD RFR Swaption Rates

And try to put together an estimated one based on correlation assumptions.

Another way is I would ask myself If I had a swaption position today, what would be my risk limits and how much would it cost me to hedge it? simulate different paths of the relevant state variables and get an idea my PnL Vol, do this for each tenor, that would be your market data.

Finish it all off by estimating the model to the above values or a function of them and adjusting for any trades you might do by using the traded vols as new market data.

See this question too for some reference: Options when there's no VolSurf - Emerging/Frontier Markets

Hope this helps.

M

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It all depends on the use case of your model. However, as the model has a volatility and mean reversion parameters, you will need to calibrate on non linear products, not necesserily swaptions but you can also use caps/floors or any type of non linear product...

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