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An analyst on the fixed-income desk at Bank PNMS has been asked to complete the construction of a zero-coupon bond price tree that was started by another team member. The analyst is given an interest rate tree of semi-annual spot interest rates quoted on an annualized basis, and the partially completed price tree, both with semi-annual time steps, as shown below (time t in years and price P in USD):
t = 0 t = 0.5 t = 1
4.65% 5.10%
4.20% 0.72 4.20%
0.28 3.75% 3.30%
t = 0 t = 0.5 t = 1 t = 1.5
P(1,1) 975.13 1000
937.49 0.72 q
1-q 979.43 1000
0.28 P(1,0) 983.77 1000
t = 0 t = 0.5 t = 1
4.65% 5.10%
4.20% 0.72 4.20%
0.28 3.75% 3.30%
t = 0 t = 0.5 t = 1 t = 1.5
P(1,1) 975.13 1000
937.49 0.72 q
1-q 979.43 1000
0.28 P(1,0) 983.77 1000
When completing the price tree, which of the following is a correct estimate of price P(1,1)?
A
USD 954.15
B
USD 954.81
C
USD 956.25
D
USD 956.92