32. Question An analyst on the fixed-income desk of an investment bank is calculating the risk-neutral probabilities of upward or downward movements in interest rates at various nodes in a zero-coupon bond price tree. The analyst constructs an interest rate tree of semi-annual spot interest rates quoted on an annualized basis, and a price tree, both with semi-annual time steps, as shown below (t in years):

t = 0        t = 0.5         t = 1
              4.00%          4.50%
3.50%   0.70                 3.50%
        0.30   3.00%          2.50%

t = 0        t = 0.5        t = 1        t = 1.5
                         q           978.00      1000
945.80   P(1,1)            1-q         982.80      1000
                         P(1,0)      987.65      1000

t = 0        t = 0.5         t = 1
              4.00%          4.50%
3.50%   0.70                 3.50%
        0.30   3.00%          2.50%

t = 0        t = 0.5        t = 1        t = 1.5
                         q           978.00      1000
945.80   P(1,1)            1-q         982.80      1000
                         P(1,0)      987.65      1000

What is the risk-neutral probability of the upward movement labeled q?