Problem:
We have a framework of the Black and Scholes model.
I would like to find the price at $T=0$ of some asset. This asset pays $X_T=S^2_T/S_{T/2}$ at time $T$, where $S_T$ is a price of one share at time $T$.
My attempt
I don't really know from where to approach this question, but I suppose that I have to calculate $\mathbb{E}_*(exp(−rT)X_T)$, but that doesn't get me anywhere.