Using a binomial tree, approximate the price of an up-and-out knock-out barrier call option given the following terms. This option is exotic, and therefore path dependent. A Knock-out barrier option only pays out if the underlying assets price does not reach or breach the predefined barrier. Once it is out, it's out for good.

S $100

K $100

50%

r 10.0%

T 2y

0.5y

Barrier $200