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
                            4.50%
                            3.50%
                            2.50%

t = 0        t = 0.5        t = 1        t = 1.5
                            q    978.00        1000
                          1−q  982.80        1000
           P(1,1)

t = 0        t = 0.5        t = 1
                            4.50%
                            3.50%
                            2.50%

t = 0        t = 0.5        t = 1        t = 1.5
                            q    978.00        1000
                          1−q  982.80        1000
           P(1,1)

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