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Comparison between the probability distribution of returns in the Heston model and empirical data for stock indexes

A. Christian Silva·Victor M. Yakovenko
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Abstract

We compare the probability distribution of returns for the three major stock-market indexes (Nasdaq, S&P500, and Dow-Jones) with an analytical formula recently derived by Dragulescu and Yakovenko for the Heston model with stochastic variance. For the period of 1982-1999, we find a very good agreement between the theory and the data for a wide range of time lags from 1 to 250 days. On the other hand, deviations start to appear when the data for 2000-2002 are included. We interpret this as a statistical evidence of the major change in the market from a positive growth rate in 1980s and 1990s to a negative rate in 2000s.

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A. Christian Silva, Victor M. Yakovenko. 2002-11-05. Comparison between the probability distribution of returns in the Heston model and empirical data for stock indexes. https://doi.org/10.1016/s0378-4371(02)01903-9

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