  Following a hedging based approach to model free financial mathematics, we
prove that it should be possible to make an arbitrarily large profit by
investing in those one-dimensional paths which do not possess local times. The
local time is constructed from discrete approximations, and it is shown that it
is $\alpha$-H\"older continuous for all $\alpha<1/2$. Additionally, we provide
various generalizations of F\"ollmer's pathwise It\^o formula.
