You invested in a European put option on the stock of TB12, Inc. (the Company), which is currently trading at $100. The strike price of the option is $105, and it matures in 6 months. The 10-year Treasury Bond has a yield of 5% p.a. compounded annually. Suppose the stock price only moves every two months: either goes up by 13.03% or goes down by 11.53%. Use a three-step binomial pricing model to estimate the value of the option.

1. What are the probabilities of stock price going up and down? (3 marks)
2. At which specific price the put is in the money? Please also indicate the time. (3 marks)
3. What is the current value of the put option? (3 marks)