In credit scoring, the probit model theory is described as assuming what distribution for the probability of default?

• A. It assumes the probability of default follows a logistic distribution.
• B. It assumes the probability of default has a cumulative normal distribution.
• C. It assumes the probability of default is linear with factors.
• D. It assumes the probability of default is independent of factors.

Answer: (B)

Probit modeling in credit scoring assumes there is an unobserved propensity to default that is normally distributed. We link this latent tendency to observed factors with a linear index, and the probability of default is the probability that this latent propensity crosses a threshold. With a standard normal distribution, that probability becomes the cumulative normal distribution evaluated at the linear index: P(default|X) = Φ(Xβ). In practical terms, Φ maps any real-valued score into a probability between 0 and 1, and the shape of Φ gives the S-shaped curve used to model how risk grows with the predictor.

This differs from the logistic approach, which uses a logistic function, and it avoids the issues of a linear probability model, which can yield probabilities outside [0,1] and ignores the probabilistic framing. So the probit model is grounded in assuming the latent propensity is normally distributed, causing the default probability to follow a cumulative normal distribution.