Why Calibrate Option Models Across Multiple Dates?

Summary

The document asks why a study of a two-factor Double Heston model calibrates against option-market observations from many Wednesdays across a year, rather than conducting a separate calibration for each date. It contrasts that setup with research using repeated daily calibrations and asks whether pooling dates is appropriate when the stated goal is to explain the model's option-pricing performance.

The response suggests that multi-date calibration may serve a different empirical purpose: comparing parameter levels and variation over time with parameters estimated from historical returns. It cites an analogous Heston-Nandi analysis and reports that its risk-neutral estimates showed a stronger leverage effect, consistent with a skewness premium. The explanation is tentative, and the respondent acknowledges limited professional experience. It does not establish the exact objective or calibration design of the Double Heston paper, nor does it resolve when pooled or date-specific calibration is preferable. The main takeaway is to interpret calibration windows in light of the study's aim.

Key ideas

• Calibration across dates may be intended to study how model parameters vary over time.
• A multi-date option calibration can be compared with rolling estimates based on historical returns.
• The cited analogous analysis found a stronger leverage effect under the risk-neutral distribution.
• The response is tentative and does not verify the Double Heston paper's specific motivation.
• Calibration design should be interpreted in relation to the empirical question being studied.

Tags

# Answer by Mads Refer (score 1)


# Double Heston model calibration in Christoffersen's paper uses 52 sets of market data (each set as of a different date). Why?












In the paper on Double Heston model (2009) from Peter Christoffersen, they say: "Our focus is on explaining why a two-factor model works better than a one-factor model for the purpose of option pricing". However, they calibrate the model using market data from every Wednesday in a year period. So in the same calibration they include option (market) prices from 52 different dates. It seems strange to me that they are including historical data (1 year of data) to test a model for option pricing. If we have 52 sets of market data, I would expect 52 calibrations using market data only as of one date, similar to Bakshi's paper (1997), where they do daily calibrations for a period of 3 years. Any thoughts on this?

## Answer by Mads Refer (score 1)

https://quant.stackexchange.com/a/68608

I read a similar empirical analysis on the Heston-Nandi model where the model parameters were calibrated based on historical option data over a couple of years. For the same period, they also did a rolling estimation of the parameters (using historical log-returns). I believe the intention was to compare the parameter level and variance of the two methods over time. E.g. under risk-neutral distribution, they find that the leverage effect is stronger (consistent with the skewness premium).

I don't have professional experience with these types of models but my understanding is that you only use the most recent data when calibrating.

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