Financial Risk Manager Part 2

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Explanation:

Option A is incorrect: The Ho-Lee model is an arbitrage-free model defined by $dr_t = \theta(t) dt + \sigma dz$ . It introduces a time-dependent drift $\theta(t)$ to perfectly fit the initial term structure, not a constant drift.
Option B is incorrect: The Ho-Lee model does not incorporate mean reversion. Models such as the Vasicek or Hull-White models have a drift component that incorporates mean reversion (pulling the rate toward a long-run equilibrium).
Option C is correct: The Cox-Ingersoll-Ross (CIR) model represents the dynamics of the short-term rate as $dr_t = k(\theta - r_t) dt + \sigma \sqrt{r_t} dz$ . Here, the basis-point volatility is determined by the term $\sigma \sqrt{r_t}$ , making it proportional to the square root of the short rate. This also guarantees that interest rates remain positive.
Option D is incorrect: The volatility in the CIR model does not decline exponentially to a constant level; it changes dynamically with the square root of the rate.

Explanation:

Option A is incorrect: The Ho-Lee model is an arbitrage-free model defined by $dr_t = \theta(t) dt + \sigma dz$ . It introduces a time-dependent drift $\theta(t)$ to perfectly fit the initial term structure, not a constant drift.
Option B is incorrect: The Ho-Lee model does not incorporate mean reversion. Models such as the Vasicek or Hull-White models have a drift component that incorporates mean reversion (pulling the rate toward a long-run equilibrium).
Option C is correct: The Cox-Ingersoll-Ross (CIR) model represents the dynamics of the short-term rate as $dr_t = k(\theta - r_t) dt + \sigma \sqrt{r_t} dz$ . Here, the basis-point volatility is determined by the term $\sigma \sqrt{r_t}$ , making it proportional to the square root of the short rate. This also guarantees that interest rates remain positive.
Option D is incorrect: The volatility in the CIR model does not decline exponentially to a constant level; it changes dynamically with the square root of the rate.

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UAnonymous

Last updated: July 5, 2026 at 07:29

In the Ho-Lee model, the drift of the interest rate process is presumed to be constant.

In the Ho-Lee model, when the short-term rate is above its long-run equilibrium value, the drift is presumed to be negative.

In the Cox-Ingersoll-Ross model, the basis-point volatility of the short-term rate is presumed to be proportional to the square root of the rate.

In the Cox-Ingersoll-Ross model, the volatility of the short-term rate is presumed to decline exponentially to a constant long-run level.