Which single-factor model assumes that the short-term interest rate follows a normally distributed process?

• A. Black-Derman-Toy model
• B. Ho and Lee model
• C. KMV model
• D. P-Measure

Answer: (B)

The Ho and Lee model is a single-factor model that specifically assumes that the short-term interest rate follows a continuously compounded normal distribution. This model is formulated within the framework of interest rate derivatives and fixed-income securities, where it aims to characterize the dynamics of interest rates over time.

In the context of this model, the assumption of a normally distributed process allows for the analytical tractability of interest rate derivatives pricing, making it a popular choice for practitioners in the field. This characteristic enables the model to capture varying levels of interest rate volatility and provides a robust mechanism for forecasting rates.

The other models presented do not make this assumption about the short-term interest rate. The Black-Derman-Toy model, for instance, utilizes a geometric Brownian motion framework, which refers to log-normally distributed rates. The KMV model is primarily focused on credit risk and defaults rather than interest rate modeling. Finally, the P-Measure, or physical measure, relates to how probabilities are assigned to real-world outcomes but does not imply the assumption of a normally distributed process for interest rates. Therefore, the Ho and Lee model stands out as the correct answer because it specifically embodies the assumption of short-term interest rates following a normal distribution.