AG Stochastik und Finanzmathematik2 Items
Tapia, Nikolas ; Zambotti, Lorenzo (2020-03-18)
We construct an explicit transitive free action of a Banach space of Hölder functions on the space of branched rough paths, which yields in particular a bijection between these two spaces. This endows the space of branched rough paths with the structure of a principal homogeneous space over a Banach space and allows to characterize its automorphisms. The construction is based on the Baker–Campb...A regularity structure for rough volatility
Bayer, Christian ; Friz, Peter K. ; Gassiat, Paul ; Martin, Jorg ; Stemper, Benjamin (2019-11-19)
A new paradigm has emerged recently in financial modeling: rough (stochastic) volatility. First observed by Gatheral et al. in high‐frequency data, subsequently derived within market microstructure models, rough volatility captures parsimoniously key‐stylized facts of the entire implied volatility surface, including extreme skews (as observed earlier by Alòs et al.) that were thought to be outs...