A contribution to the systematics of stochastic volatility models |
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Authors: | Franti&scaron ek Slanina |
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Affiliation: | Institute of Physics, Academy of Sciences of the Czech Republic, Na Slovance 2, CZ-18221 Praha, Czech Republic Center for Theoretical Study, Charles University in Prague / Academy of Sciences of the Czech Republic, Jilská 1, Praha, Czech Republic |
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Abstract: | We systematically compare 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 also assume 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 also calculate the decay of the autocorrelation function of volatility. |
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Keywords: | Fluctuations Econophysics Stochastic differential equations |
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