Consider a non-tradable stock index $S$ which satisfies:
$dS_t=\mu S_tdt+\sigma S_tdW_t$
and a risk-free asset $B$.
I want to price an European Call option with the payoff $C_T=max(S_T-K,0)$. The No-Arbitrage condition tells us that if a portfolio consisting of underlyings $S$ and $B$ replicates the call option then the fair price of the call option is equal to the initial value of the portfolio. Now the problem is that the underlying $S$ is not tradable so that it's impossible to replicate (and hedge) the call option using $S$. We probably use futures based on the underlying $S$ to construct replicating portfolio. My question is how to price such index call option. I appreciate if you could share any reference. Thanks.