From the spot rates, find the 1y1y, 2y1y forward rates and assume that interest rates follow a lognormal random walk, Given a volatility of 20%, construct the binomial interest rate tree. (Probability of high vs. low states are equal.)

years	spot rate
1	0.65%
2	0.876%
3	1.118%

Time 0 Time 1 Time 2 Time 3 13,HHH in,H 11,H 13,HHL io 12,HL ill 13,LLH 12,LL 13,LLL Time 0 Time 1 Time 2 Time 3 13,HHH in,H 11,H 13,HHL io 12,HL ill 13,LLH 12,LL 13,LLL