Stochastic volatility and the goodness-of-fit of the Heston model

Gilles Daniel, Nathan L. Joseph*, David S. Brée

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Recently, Drǎgulescu and Yakovenko proposed an analytical formula for computing the probability density function of stock log returns, based on the Heston model, which they tested empirically. Their research design inadvertently favourably biased the fit of the data to the Heston model, thus overstating their empirical results. Furthermore, Drǎgulescu and Yakovenko did not perform any goodness-of-fit statistical tests. This study employs a research design that facilitates statistical tests of the goodness-of-fit of the Heston model to empirical returns. Robustness checks are also performed. In brief, the Heston model outperformed the Gaussian model only at high frequencies and even so does not provide a statistically acceptable fit to the data. The Gaussian model performed (marginally) better at medium and low frequencies, at which points the extra parameters of the Heston model have adverse impacts on the test statistics. © 2005 Taylor & Francis Group Ltd.

Original languageEnglish
Pages (from-to)199-211
Number of pages13
JournalQuantitative Finance
Issue number2
Publication statusPublished - Apr 2005


  • probability density function
  • stock log returns
  • Heston model


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