title: Jarrow–Turnbull model
text: # Jarrow–Turnbull model
  
  The Jarrow–Turnbull model is a widely used "reduced-form" credit risk model. It was published in 1995 by Robert A. Jarrow and Stuart Turnbull. Under the model, which returns the corporate's probability of default, bankruptcy is modeled as a statistical process. The model extends the reduced-form model of Merton (1976) to a random interest rates framework.
  
  Reduced-form models are an approach to credit risk modeling that contrasts sharply with "structural credit models", the best known of which is the Merton model of 1974. Reduced-form models focus on modeling the probability of default as a statistical process, whereas structural-models inhere a microeconomic model of the firm's capital structure, deriving the (single-period) probability of default from the random variation in the (unobservable) value of the firm's assets.
  
  Large financial institutions employ default models of both the structural and reduced-form types. The Merton structural default probabilities were first offered by KMV LLC in the early 1990s. KMV LLC was acquired by Moody's Investors Service in 2002.
  
  