Hedge fund interview question: down-and-out barrier option value

[cycbill]

I got a question from a hedge fund interview:
Assume a down-and-out call barrier option, with strike = 90 and barrier = 90. The current spot = 100. Interest rate and dividend are 0. What is the option value?

I didn't solve it out during the interview, but later know it = 10 (regardless of the vol), based on some online option calculator.
But can someone explain intuitively why it = 10?

barrieroptions

 

[ngnguyen]

Is the payoff of this product equal to [math]\Pi = (S_T-K)^+ \mathbf{1}_{\{\min_{0\le t \le T}S_t \ge B\}}[/math]with [imath]K = B = 90[/imath] and [imath]S_0 = 100[/imath]?

 

[cycbill]

Is the payoff of this product equal to [math]\Pi = (S_T-K)^+ \mathbf{1}_{\{\min_{0\le t \le T}S_t \ge B\}}[/math]with [imath]K = B = 90[/imath] and [imath]S_0 = 100[/imath]?

Yes correct.