We propose a simple stochastic model for time series which is analytically tractable, easy to simulate and which captures some relevant stylized facts of financial indexes, including scaling properties. We show that the model fits the Dow Jones Industrial Average time series with a remarkable accuracy.
Despite its simplicity, the model has several interesting features. The volatility is not constant and displays high peaks. The empirical distribution of the log-returns is non-Gaussian and may exhibit heavy tails. Log-returns corresponding to disjoint time intervals are uncorrelated but not independent: the correlation of their absolute values decays exponentially fast in the distance between the time intervals for large distances, while it has a slowerdecay for moderate distances. Moreover, the distribution of the log-returns obeys scaling relations that are detected on real time series, but are notsatisfied by most available models.
Finally we show some result for pricing option with this model.