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FRM Part II · FRM Exam Part II · The Art of Term Structure Models: Drift

A risk manager notes that in Model 1 (dr = σ dw), the model's zero drift is applied to the short rate while the model is also required to price bonds without arbitrage. Which statement about this model's implications for the term structure is correct?

Expected short rates are flat under zero drift, but spot rates decline with maturity because of convexity: bond prices are convex in rates, so volatility lowers yields. The yield reduction grows with maturity and with the square of volatility.

  1. AThe model implies a flat expected short rate, yet spot rates still fall with maturity because of a convexity effect from volatilityCorrect
  2. BThe model implies an upward-sloping expected short rate path because volatility adds positive drift
  3. CThe model implies that spot rates are constant across maturities regardless of volatility
  4. DThe model implies that bond prices are independent of σ

Explanation

With zero drift the expected short rate is flat, but bond prices are convex in rates, so Jensen's inequality raises prices and lowers yields as maturity grows. Spot rates are therefore r0 minus a term proportional to σ²T²/6, producing a downward-sloping curve. The other options ignore convexity.

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