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Financial Risk Manager Part 2

Financial Risk Manager Part 2

Explanation:

D is correct. From the given rate tree and price tree, the equation for the price of a 1.5-year zero-coupon bond at t = 0 is:
Equation 1: (0.7∗P(1,1)+0.3∗P(1,0))/(1+0.035/2)=945.80(0.7 * P(1,1) + 0.3 * P(1,0)) / (1 + 0.035/2) = 945.80(0.7∗P(1,1)+0.3∗P(1,0))/(1+0.035/2)=945.80
and the prices for the then 1-year bond at t = 0.5 are:
Equation 2: P(1,1)=(978.00q+982.80(1−q))/(1+0.04/2)P(1,1) = (978.00q + 982.80(1-q)) / (1 + 0.04/2)P(1,1)=(978.00q+982.80(1−q))/(1+0.04/2)
Equation 3: P(1,0)=(982.80q+987.65(1−q))/(1+0.03/2)P(1,0) = (982.80q + 987.65(1-q)) / (1 + 0.03/2)P(1,0)=(982.80q+987.65(1−q))/(1+0.03/2)

Substituting Equations 2 and 3 into Equation 1 allows for q to be solved algebraically, resulting in q=0.85q = 0.85q=0.85.

A is incorrect. This is the risk-neutral probability of a downward movement.
B is incorrect. This incorrectly assumes that risk-neutrality indicates a probability of...

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  1. 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?

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UAnonymous
Last updated: July 5, 2026 at 07:28
0

    A

    0.15

    B

    0.50

    C

    0.70

    D

    0.85

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