A binary (a.k.a. digital, all-or-nothing) call option has a strike price of $50. It also has a knock-out barrier of $61. If the option pays you at expiration, it pays you exactly $10. The risk-free rate is 2.2% per period. If the underlying asset goes up, it will go up 20% per period and if it goes down, it will go down 10% per period. The underlying asset currently costs $50. The option expires in 2 periods. How much is this option worth today?

Please show steps

Correct answer: $4.62

Note from professor: I'm asking you to do another binomial tree here. Just keep in mind the barrier. Good luck!