A contribution to the systematics of stochastic volatility models

Details A contribution to the systematics of stochastic volatility models A contribution to the systematics of stochastic volatility models

2010-09-14

arxiv.org/abs/1009.2696v1

Physica A, 389 (2010) 3230-3239

Economy

Quantitative Finance

Statistical Finance

15 pages, no figures

Scientific paper

10.1016/j.physa.2010.03.044

We compare systematically several classes of stochastic volatility models of stock market fluctuations. We show that the long-time return distribution is either Gaussian or develops a power-law tail, while the short-time return distribution has generically a stretched-exponential form, but can assume also an algebraic decay, in the family of models which we call ``GARCH''-type. The intermediate regime is found in the exponential Ornstein-Uhlenbeck process. We calculate also the decay of the autocorrelation function of volatility.

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