
Explanation:
In the Ho-Lee model, the expected short-term interest rate at time t is given by:
E[r(t)] = r(0) + θ(1) + θ(2) + ... + θ(t)
Where:
Given:
Expected short-term interest rate in two periods: E[r(2)] = r(0) + θ(1) + θ(2) E[r(2)] = 5.4% + 0.25% + (-0.10%) E[r(2)] = 5.4% + 0.25% - 0.10% E[r(2)] = 5.55%
Note: The long-run mean reverting level (15.1%) and long-run true interest rate (12.6%) are not needed for this calculation in the Ho-Lee model, as the model uses the calibrated drift terms directly rather than mean reversion parameters.
Therefore, the expected short-term interest rate in two periods is 5.55%, which corresponds to option C.
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The trading desk at Big Bank is pricing an off-market swap. The quantitative analysis team has identified the interest rate drift in periods 1 and 2 to be 25 basis points and -10 basis points, respectively. These values were calibrated from liquid swap prices. The current short-term interest rate is 5.4% with a long-run mean reverting level of 15.1%. Additionally, the long-run true interest rate is 12.6%. The time steps is 1; i.e., dt=1. Using the HO-LEE Model, what is the expected short-term interest rate in two periods?
A
5.25%
B
5.4%
C
5.55%
D
5.75%