Assume you have a vanilla call on an underlying $S$ with strike price $K$ and expiry at time $T$.
Let's say that $S$ follows a GBM with volatility $\sigma$.
In general, one would use the Black-Scholes formula to price this option, but this relies on many assumptions and in particular that one can buy/sell the stock in continuous time.
What if we cannot trade the stock (for example, we're not allowed to). What are the different ways of valuing this options?
The only way I see is to estimate your own utility function given an expected payoff and a volatility, which is really hard, but I wanted to know if there was any other well-known approach?