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I am not as familiar with FX options as I am with equity index options.

For the purposes of numerical testing/experiments I'd appreciate if somebody could tell me what are typical parameter values for the Heston model calibrated to for instance USDEUR options for maturities 6M and 1YR in typical/average market conditions?

A typical range for the vol of vol, mean reversion, long term vol and correlation parameters would be great.

Sorry if the question is not more quantitative, but on the other hand this question and answers to this questions may also be useful to others in the future.

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    $\begingroup$ Do you have access to Bloomberg? If so, look at OVML, swap to Heston and go to model parameters (not next to a terminal ATM but it's definitely something like this). Alternatively, if you have BBA (own login), you can look at DLIB for a bit more details. Generally though, Heston in isolation wouldn't be used much in FX. Most pricing of exotics would use SLV. $\endgroup$
    – AKdemy
    Commented Jul 5, 2023 at 16:50
  • $\begingroup$ @AKdemy I don't have access to BBG, too expensive for a hobbyist. Not sure if the same info can be obtained from open BB? I'm aware SLV is market standard, but Heston (or SABR if that's easier) parameters would still be useful. $\endgroup$
    – Frido
    Commented Jul 5, 2023 at 16:54
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    $\begingroup$ Often libraries and universities have access, it would only be available via a terminal login. Maybe someone can share her/his data, if no one answers I'll see what I can do next week. $\endgroup$
    – AKdemy
    Commented Jul 5, 2023 at 16:57

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Since no one answered yet I'll provide a few numbers from Bloomberg's OVML as mentioned in a comment. The following logic is used by Bloomberg:

The Heston model parameters are calibrated to at-the-money and 25-delta options, with time-to-expiry between three months and one year. When calibrating the Heston model parameters to fit a volatility surface, mean reversion parameter is fixed to a typical value, due to an inherent interplay of opposing roles between mean reversion and volatility of volatility.

EURUSD for example looks like this at the moment. enter image description here

A few pretty much randomly selected values.

enter image description here

With regards to the sign of the correlation parameter, the Brownian motion that drives the variance process is correlated with the spot process – therefore, the correlation coefficient for the inverse spot will be the negative value of the original one.

In OVML, the Stochastic Vol model is a degenerated SLV model. However, it is not using using Heston dynamics because of the following explanation on the help page:

We have chosen a lognormal process for the volatility process, as opposed to the familiar squareroot process found, for example, in the Heston model. We get more realistic behavior for the paths of the volatility process and for the dynamics of the volatility surface.

Looking at SV, you will see the following (time dependent) values. enter image description here

Pretty much the same applies to DLIB, where typically short term correlation and vol of vol is higher and reduces with tenor.

Although it is just a few snapshots, I hope this helps a little bit.

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  • $\begingroup$ Thanks, quick question: the first table are calibrated Heston correls and vol of vols and the second table / screenshot are SABR params (for which fx pair?), correct? $\endgroup$
    – Frido
    Commented Jul 12, 2023 at 8:05
  • $\begingroup$ The First Screenshot is calibrated Heston from OVML. The second screenshot is from the calibrated Stochastic vol in OVML (which is not Heston but a lognormal vol process). Bloomberg does not offer SABR for FX - only for rates (VCUB). $\endgroup$
    – AKdemy
    Commented Jul 12, 2023 at 9:35

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