Answer-first summary for fast verification
Answer: In the Ho-Lee model the drift terms are additive, but in the lognormal model the drift terms are multiplicative.
## Explanation The correct answer is **D** because: - **Ho-Lee model** is an additive model where the drift terms are **additive**. In the Ho-Lee model, the short rate follows an arithmetic Brownian motion process with additive drift. - **Lognormal model** (such as Black-Karasinski or Black-Derman-Toy models) has **multiplicative** drift terms. In lognormal models, the short rate follows a geometric Brownian motion process where the drift term multiplies the current level of the rate. ### Key Differences: - **Ho-Lee Model**: Additive drift - r(t+Δt) = r(t) + μ(t)Δt + σΔW - **Lognormal Model**: Multiplicative drift - r(t+Δt) = r(t) * exp(μ(t)Δt + σΔW) This fundamental difference affects how interest rates evolve and the properties of the resulting term structure models.
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Which of the following statements best characterizes the differences between the Ho-Lee model with drift and the lognormal model with drift?
A
In the Ho-Lee model and the lognormal model the drift terms are multiplicative.
B
In the Ho-Lee model and the lognormal model the drift terms are additive
C
In the Ho-Lee model the drift terms are multiplicative, but in the lognormal model the drift terms are additive
D
In the Ho-Lee model the drift terms are additive, but in the lognormal model the drift terms are multiplicative.