# Which models have non-smooth densities?

By smooth, I mean a density $$f$$ that lies in the space $$C^\infty$$, infinitely differentiable.

Are there, in the literature, some known models where the underlying density of the state process is non-smooth?

I have only been able to find one such example: the Variance Gamma model. Would love to hear if people know of more such examples.

The corresponding density is $$f_X(x) = p\zeta e^{-\zeta x}\mathbb{1}_{\{x\geq 0\}}+q\eta e^{\eta x}\mathbb{1}_{\{x<0\}},$$ where $$p+q=1$$ and $$\zeta,\eta>0$$ and $$p,q\geq0$$.