C. Consider 6-month spot interest rates evolving in the following two-step binomial tree over 12 months, i.e., with 6 months in each of the next two steps. The current 12-month spot interest rate is 5.15% and the 18-month spot interest rate is 5.3%. Find the following by assuming monthly compounding.

12. The risk-neutral probability for the up move in the first step. 

13. The risk-neutral probability for the up move in the second step. 

14. The current fair value of a 6-month European call option with a strike price of $974 written on a 12-month zero coupon bond with a face value of $1000. 15. The current fair value of a 12-month European put option with a strike price of $994 written on an 18-month zero coupon bond with a face value of $1000.