Choosing Historical Samples for Heston Parameter Estimation
Summary
The document addresses how to choose a historical sample when calibrating a Heston volatility model. The question reports accurate parameter estimates alongside wide confidence intervals for samples around a decade long, and asks whether a longer sample is preferable. The response focuses on a possible bias in the estimate of the mean-reversion parameter kappa, especially if shorter simulated samples appear more accurate despite coming from an unchanged data-generating process.
For practical market data, the recommendation is to use the longest period for which the underlying process can reasonably be treated as stable. A long history may reduce statistical uncertainty, but structural changes can make older observations inappropriate. The answer also suggests increasing observation frequency to gain information without relying on implausibly long histories. These are general diagnostics rather than a demonstrated sample-size selection procedure: the document provides no simulation results or formal test for bias, stability, or the tradeoff between estimation error and regime change.
Key ideas
- Unexpectedly better estimates from shorter simulated samples may indicate estimator bias.
- Check whether the estimate of kappa changes systematically with sample size.
- Use as much historical data as is credible under an assumption of a stable data-generating process.
- Higher-frequency observations may provide more information without extending the calendar history.
- Longer samples can be misleading when market dynamics have changed.
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# What tradeoff is there to using an accurate estimate with a large confidence interval? # What tradeoff is there to using an accurate estimate with a large confidence interval? I am working on calibrating a Heston model from simulated historical stock data. After obtaining an accurate estimate of the model parameters I found very large 95% confidence intervals for these estimations if the sample size is about 10-15 years. In view of the graph below, how would you choose the ideal sample size? A 5-10 years period seems small since a large confidence interval means that there is a large uncertainty about the estimation. On the other hand, it appears useless to accept a sample size for which the confidence interval is small (50 years) since shorter periods provides good enough estimates. I am a little confused as to how to interpret these results. ## Answer by Tal Fishman (score 2, accepted) https://quant.stackexchange.com/a/1803 Unless it is due to random chance, there seems to be a bias in your estimation method for $\kappa$, and this bias appears to depend on the size of the sample. This may be revealing a deeper underlying problem with your technique that will ultimately make it clearer what the tradeoff is between accuracy and sample size. I do not believe it should be the case that a shorter sample-size yields a more accurate estimate in a simulation where you can be certain the data generating process has not changed. In practice, though, you will want to use as long a sample as possible over which you can be reasonably sure the underlying DGP has not changed. I would also suggest trying to obtain higher frequency data. Unless your time scale here is arbitrary, it will be difficult to justify an estimate based on 20+ actual years of stock market data.
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