What is the name of this call option ?

[Nguyen]

Dear all
Assume that
$$dS_t=\mu S_t dt+\sigma S_t dW_t, 0\leq t\leq T $$.
Consiser a call option with the payoff
$$
C=e^{-rT}E[(\int_0^T S_t dt-K)^+]
$$
C is not Asian call option for sure.
My question is : what is the name of the call option with the payoff defined above ?
If it is possible, could you please give some papers related to it ?
Thank you so much for your time.

 

[euroazn]

That doesn't look like a payoff, that looks like a price (as it seems to be a constant).

The payout component is presumably
$$
(\int_0^T S_t dt-K)^+
$$

In which case, yes, this looks like an Asian option. If you are concerned that there is no 1/T term before the integral, note that you would never exercise this early anyway, so it's consequently equivalent to T of the Asian.