If the probability of default is assumed to have a normal distribution, which model is appropriate?

• A. Linear Probability Model
• B. Logit Model
• C. Probit Model
• D. Neural Network

Answer: (C)

When the underlying propensity to default is assumed to be normally distributed, a probit model is the natural choice. In a probit framework you think in terms of a latent variable Y* that represents this propensity: Y* = Xβ + ε, where ε follows a standard normal distribution. A default occurs when Y* exceeds zero, so the probability of default given X is P(default|X) = Φ(Xβ), with Φ being the standard normal cumulative distribution function. This setup directly ties the normal-distribution assumption to the link between predictors and observed outcomes, and it keeps predicted probabilities within the 0 to 1 range in a way that mirrors the assumed normal behavior of the latent propensity. The linear probability model, by contrast, can produce probabilities outside [0,1] and lacks a probabilistic foundation tied to a distribution. The logit model uses a logistic distribution for the error term, resulting in a logistic link rather than a normal one. A neural network is flexible and data-driven, not constrained to a specific distribution for the latent propensity.