FRM Part II · FRM Exam Part II · The Art of Term Structure Models: Drift
A risk analyst uses Model 1 (normal model with zero drift) for the short rate, dr = σ dw, with σ = 100 basis points per year and current r0 = 4.00%. Under this model, what is the expected value of the short rate in five years?
The expected short rate in five years is 4.00%. With zero drift, the mean of the short rate equals today's rate at every horizon, and volatility affects only the spread of outcomes around that mean, not the expected value.
- A4.00%Correct
- B4.50%
- C9.00%
- D2.00%
Explanation
In Model 1 the drift is zero, so E[r(t)] = r0 for all horizons. The expected rate in five years therefore remains 4.00%. Volatility only affects dispersion, not the mean. Choosing 4.50% or 9.00% wrongly adds a drift or volatility term.
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