Which modeling approach assumes that the probability of default has a cumulative normal distribution?

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

Answer: (C)

The probit model links the probability of default to a latent propensity through the standard normal distribution. Imagine an underlying score y* = Xβ + ε, where ε follows a standard normal distribution. Default occurs when this latent score exceeds a threshold, so the probability of default is P(default) = P(y* > threshold) = Φ(Xβ), with Φ being the standard normal CDF. This ensures the predicted probabilities stay between 0 and 1 and creates an S-shaped relationship between the predictors and the probability.

Other methods behave differently: the Linear Probability Model regresses probabilities directly on X, which can yield predictions outside [0,1]; the Logit Model uses a logistic CDF, p = 1/(1+exp(-Xβ)); and Neural Networks are flexible, nonparametric mappings that don’t impose a specific distribution for the error term. The question explicitly points to the cumulative normal distribution, which is the hallmark of the probit approach.