Interpreting Heston Parameters for Foreign Exchange Options
Summary
The document gives context for Heston model calibration in foreign exchange options. It describes a market-data provider’s approach of fitting to at-the-money and 25-delta options across expiries from several months to a year, while fixing mean reversion at a typical value. The stated rationale is interaction between mean reversion and volatility of volatility, which can make both difficult to identify freely from the same surface. The answer refers to selected parameter snapshots but does not include numerical values in the supplied text.
It explains that the sign of spot–variance correlation depends on whether the currency pair is quoted in its original or inverse form: inversion changes the sign. It also distinguishes the provider’s stochastic-volatility implementation from standard Heston dynamics, describing a lognormal volatility process chosen for path and surface behavior. The figures are characterized as a few snapshots rather than a broad empirical survey, so they do not establish universal typical parameter ranges. The discussion notes that short-term correlation and volatility of volatility can be higher and decline with tenor in the referenced implementations.
Key ideas
- The cited calibration fits at-the-money and 25-delta options across short-to-medium expiries.
- Mean reversion may be fixed because it interacts with volatility of volatility during calibration.
- Inverting a currency pair reverses the sign of spot–variance correlation.
- A stochastic-volatility implementation using lognormal volatility dynamics is distinct from standard Heston dynamics.
- The parameter observations are limited snapshots and should not be treated as universal FX calibration ranges.
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# Typical values Heston parameters for FX options # Typical values Heston parameters for FX options 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. ## Answer by AKdemy (score 3, accepted) https://quant.stackexchange.com/a/76097 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. A few pretty much randomly selected values. 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. 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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