Brownian Motions, Stochastic Volatility Models and Statistical Inferences

Start: 12/05/2012 - 1:15pm
End  : 12/05/2012 - 2:15pm

Applied Math Seminar

Qidi Peng (CGU)


Stochastic volatility models Z(t) are extensions of the well-known Black and Scholes model. Since several years, a number of authors have been interested in the statistical problem of the estimation of ?Z(t) starting from the observation of a discretized trajectory of the process Z(t). However, it does not always seem to be realistic to assume that such an observation is available, but only a corrupted version of it; therefore a natural question one can address is that whether it is still possible to estimate ?Z(t). To our knowledge, only a few number of articles in the literature deal with this problem and it has been studied only in a setting which basically remains to be that of Gaussian stationary increments processes; typically when the volatility X is a fractional Brownian motion. In such a setting, the pointwise Hôlder exponent is constant. The goal of this talk, is to study the statistical problem of the estimation of a hidden pointwise Hölder exponent in a new setting where this exponent has a rather complex structure since it is allowed to evolve over time.

KRV 164

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