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FRM Part II · FRM Exam Part II · Arbitrage Pricing with Term Structure Models

In a Vasicek model with k = 0.10 and σ = 1.2% per year, the short-rate drift in the risk-neutral measure is dr = k(θ − r)dt. The risk-neutral long-run mean θ is 6%. A risk manager notes the real-world long-run mean is 5%. Which interpretation of the difference is correct?

The difference reflects a risk premium. Arbitrage-free pricing uses the risk-neutral drift with θ of 6%, while real-world forecasting uses 5%. The two measures legitimately differ by the market price of risk times volatility, so no arbitrage or model error is implied.

  1. AThe 1% gap reflects a risk premium that is built into the risk-neutral drift, so pricing uses 6% while historical forecasting uses 5%Correct
  2. BThe model is arbitrageable because the two means differ
  3. CReal-world and risk-neutral means must be equal under no-arbitrage, so one is in error
  4. DThe gap means volatility is understated by 1% per year

Explanation

No-arbitrage pricing only fixes the risk-neutral drift; the real-world drift differs by the market price of risk times volatility. A gap between θ values is therefore expected and signals a risk premium, not an arbitrage or a volatility error.

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