Time: 14h00, Thursday, June 4, 2020

 Online via google meet meet.google.com/odg-dijq-dhs

Abstract: We develop a general mathematical framework, based on rough path theory, a recent important extension of the classical Itô calculus, that can incorporate the empirically observed nonlinear relation between the expected logarithmic return and its variance in a systematic manner.

Thus, we propose a stock price model driven by a Hölder continuous noise, understood in the sense of a rough differential equation. This model offers the possibility of additional noises hidden in the signatures of rough paths, hence supporting the idea of mixture of a standard Brownian noise and another source of long memory noise (a fractional Brownian motion for instance), and enabling to account for the multi-scaling phenomenon in financial data. The no-arbitrage principle is then satisfied under the assumption of transaction costs as long as the driving noise is a sticky process. We also discuss the potential risk of model uncertainty where the ambiguity comes from the signatures of rough paths. Our models are supported by the numerical data from stock indices.