  An analytical formula for the probability distribution of stock-market
returns, derived from the Heston model assuming a mean-reverting stochastic
volatility, was recently proposed by Dragulescu and Yakovenko in Quantitative
Finance 2002. While replicating their results, we found two significant
weaknesses in their method to pre-process the data, which cast a shadow over
the effective goodness-of-fit of the model. We propose a new method, more truly
capturing the market, and perform a Kolmogorov-Smirnov test and a Chi Square
test on the resulting probability distribution. The results raise some
significant questions for large time lags -- 40 to 250 days -- where the
smoothness of the data does not require such a complex model; nevertheless, we
also provide some statistical evidence in favour of the Heston model for small
time lags -- 1 and 5 days -- compared with the traditional Gaussian model
assuming constant volatility.
