I am new to quant finance - come from a mathematics background. I am starting stochastic calculus and have been particularly interested in some papers pathwise integration and rough calculus in general. At this time I struggle to see its applications in the world of quant finance? Does its utility come from the fact that we can then also model "rough paths" rather than just smooth ones?
Because Brownian motion has non zero quadratic variation (as opposed to continuous differentiable function which have 0). Quadratic variation is a defining characteristic of Brownian motion and Brownian motion is central to financial models of the evolution of prices/returns over time.