Is the product of exponents of normal iid variables a martingale?

Question

I am told that $X_1,\:X_2,\:,\dots$ is a sequence of i.i.d random variables, where $X_i\sim N(\mu,\sigma^2)$ for $i=1,2,\dots$

and that $Y_N=e^{X_1}e^{X_2}\dots e^{X_N}$.

Is $Y_N$ a martingale?