Evolution of short term interest rates (Construction of Tree in case of upward sloping curve)

[imran88]

I have a question related to the evolution of short term interest rates, in case of upward sloping curve i.e. r0,1 is 10% and E(r1,2) is 12% and E(r2,3) is 14% and volatility around the expectation of interest rates is 200bps. How would you construct the tree, what would be the values at t=1 for upper and lower node? The average of the upper and lower nodes should be 12% at t=1 and volatility around expected rates at 1 year for 1 year period is 200bps. I think that the interval should be between 10% and 14% which means interest rates at 1 year for 1 year will be at 10% for the lower node and 14% for the upper node. If that is the case what would be the values for t=2 for 0,1 and 2 nodes whose expected value at two years from now for 1 year should be 14%. I am assuming a risk-neutral probability of 0.5 as assumed in the example in Tuckman in the chapter the evolution of short term interest rates.