Short-time near-the-money skew in rough fractional stochastic volatility models
Freitag, 28.4.17, 11:00-12:00, Raum 232, Eckerstr. 1
We consider rough stochastic volatility models where the driving noise of volatility\nhas fractional scaling, in the rough regime of Hurst parameter H < 1/2. This regime\nrecently attracted a lot of attention both from the statistical and option pricing\npoint of view. With focus on the latter, we sharpen the large deviation results of\nForde-Zhang (2017) in a way that allows us to zoom-in around the money while\nmaintaining full analytical tractability. More precisely, this amounts to proving\nhigher order moderate deviation estimates, only recently introduced in the option\npricing context. This in turn allows us to push the applicability range of known at-\nthe-money skew approximation formulae from CLT type log-moneyness deviations\nof order t1/2 (recent works of Alo‘s, Le ?on Vives and Fukasawa) to the wider\nmoderate deviations regime.\nThis is work in collaboration with C. Bayer, P. Friz, A. Gulsashvili and B. Stemper
A General Framework for Uncovering Dependence Networks
Freitag, 28.4.17, 12:00-13:00, Raum 404, Eckerstr. 1
Dependencies in multivariate observations are a unique gateway to uncovering relationships among processes. An approach that has proved particularly successful in modeling and visualizing such dependence structures is the use of graphical models. However, whereas graphical models have been formulated for finite count data and Gaussian-type data, many other data types prevalent in the sciences have not been accounted for. For example, it is believed that insights into microbial interactions in human habitats, such as the gut or the oral cavity, can be deduced\nfrom analyzing the dependencies in microbial abundance data, a data type that is not amenable to standard classes of graphical models. We present a novel framework that unifies existing classes of graphical models and provides other classes that extend the concept of graphical models to a broad variety of discrete and continuous data, both in low- and high-dimensional settings. Moreover, we present a corresponding set of statistical methods and theoretical guarantees that allows for efficient estimation and inference in the framework.