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Answer: 5.55%
## 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: - r(0) is the current short-term interest rate - θ(t) is the interest rate drift in period t Given: - Current short-term interest rate r(0) = 5.4% - Interest rate drift in period 1: θ(1) = 25 bps = 0.25% - Interest rate drift in period 2: θ(2) = -10 bps = -0.10% - Time step dt = 1 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%