In the Vasicek model, the risk premium (λ) affects the term structure by shifting the expected drift of the short-term interest rate. The observed long-run mean (θ′) in the real-world measure is adjusted to incorporate the risk premium:

$$\theta' = \theta + \frac{\lambda \sigma}{k}$$

Here:

• θ: Represents the long-run mean in the risk-neutral measure.
• λ: Risk premium, which scales with volatility (σ) and mean reversion (k).

This adjustment implies that the observed long-run mean (θ′) incorporates the risk premium and cannot be directly distinguished from θ when pricing securities.

A is incorrect. The risk premium affects the drift, not the volatility (σ).

C is incorrect. The risk premium affects the entire term structure, not just the short end.

D is incorrect. There's no inherent negative correlation implied by the risk premium.

Things to Remember

• The risk premium is incorporated into the risk-neutral drift.
• It makes it impossible to directly observe the true long-run value of the short-term rate from market prices alone.