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Let $\sigma_J$ be the volatility of the index $J$. Assume that $J(0)\leq B$. Consider the following 2 extreme cases: $\sigma_J=0 \Rightarrow \forall x\in[0,T],J(x)=J(0)\leq B$: hence you will always be paid $I(T)$ at expiry. $\sigma_J=\infty \Rightarrow \exists\epsilon>0, J(\epsilon)>B$: hence you will almost immediately be paid \$I(0)\approx I(\...