# Option price of a future

This must be a dumb question. Consider a European option $V$ on a (stock) futures $F$. The hedging condition seems to be the same as that for a stock $$d\Big(V-\frac{\partial V}{\partial F}F\Big)=r\Big(V-\frac{\partial V}{\partial F}F\Big)dt$$ for the riskless short interest rate $r$, since the portfolio $\Pi:=V-\frac{\partial V}{\partial F}F$ is a riskless traded asset and thus should grow at the riskless interest rate. I will get the same PDE as that of a stock. However, one should obtain the risk-neutral growth rate of $F$ as $0$. What is the catch?

The catch is the future is an unfunded position (I’m disregarding the margin here) and as a result the term $r\frac{\partial{V}}{\partial{F}}Fdt$ does not exist. F is actually a contract worth 0.
• Could you please elucidate this point a bit more? Is the reason for excluding $F$ from the right-hand side of the hedging equation that the portfolio $\Pi$ cannot be considered to be self-financing? – Hans Sep 18 '18 at 22:33