# Are densities used in finance square integrable?

Let $$f$$ be the density of the stock asset under some model (Heston, SABR, Black Scholes, Variance-Gamma, etc).

Is $$f$$ square-integrable in these models?

Yes, $$f$$ is square-integrate. This follows from the fact that the variance exists.
• Not sure of that: variance exists means that $S$ is square integrable, but that does not tell us for the density $f$. – siou0107 Dec 13 '19 at 16:39