Extremes of stochastic volatility models

@article{Davis1998ExtremesOS,
  title={Extremes of stochastic volatility models},
  author={Richard A. Davis and Thomas Mikosch},
  journal={Annals of Applied Probability},
  year={1998},
  volume={8},
  pages={355-364}
}
We consider extreme value theory for stochastic volatility processes in both cases of light-tailed and heavy-tailed noise. First, the asymptotic behavior of the tails of the marginal distribution is described for the two cases when the noise distribution is Gaussian or heavy-tailed. The sequence of point processes, based on the locations of the suitable normalized observations from a stochastic volatility process, converges in distribution to a Poisson process. From the point process… 
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References

SHOWING 1-10 OF 35 REFERENCES
Bayesian Analysis of Stochastic Volatility Models
New techniques for the analysis of stochastic volatility models in which the logarithm of conditional variance follows an autoregressive model are developed. A cyclic Metropolis algorithm is used to
A Subordinated Stochastic Process Model with Finite Variance for Speculative Prices
S. Bochner's concept of a subordinate stochastic process is proposed as a model for speculative price series. A general class of finite-variance distributions for price changes is described, and a
Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation
Traditional econometric models assume a constant one-period forecast variance. To generalize this implausible assumption, a new class of stochastic processes called autoregressive conditional
Modelling of extremal events in insurance and finance
TLDR
The relevant theory which may also be used in the wider context of Operation Research is reviewed, various applications from the field of insurance and finance are discussed and an extensive list of references are guided towards further material.
The Variation of Certain Speculative Prices
My efforts to improve on Bachelier's Brownian model started with markets on which the dominant factor is the highly non Gaussian nature of the distribution's tails. In IBM Report NC-87, liThe
Generalized autoregressive conditional heteroskedasticity
THE PRICE VARIABILITY-VOLUME RELATIONSHIP ON SPECULATIVE MARKETS
This paper concerns the relationship between the variability of the daily price change and the daily volume of trading on the speculative markets. Our work extends the theory of speculative markets
...
...