Jarrow–Turnbull model

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The Jarrow–Turnbull model was the first "reduced-form" credit risk model. It was published in 1995 by Robert A. Jarrow of Kamakura Corporation and Cornell University and Stuart Turnbull, currently at the University of Houston.[1] 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 the "structural credit models".[2]

  • The structural or "Merton" credit models are single-period models which derive the probability of default from the random variation in the unobservable value of the firm's assets. Two years after the development of the structural credit model, Robert Merton modeled bankruptcy as a continuous probability of default.[3] Upon the random occurrence of default, the stock price of the defaulting company is assumed to go to zero. Merton derived the value of options for a company that can default.
  • Under a "reduced form" model bankruptcy is modeled as a statistical process, rather than as a microeconomic model of the firm's capital structure.[citation needed] Reduced form credit risk models focus on modeling the probability of default rather than trying to explain default in terms of the firm's asset value.

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. Kamakura Corporation, where Robert Jarrow serves as director of research, has offered both structural and reduced form default probabilities on public companies since 2002.[citation needed]

See also[edit]


  1. ^ Robert A. Jarrow and Stuart Turnbull, "Pricing Derivatives on Financial Securities Subject to Credit Risk" Journal of Finance, vol. 50, March, 1995
  2. ^ Robert C. Merton “On the Pricing of Corporate Debt: The Risk Structure of Interest Rates,” Journal of Finance 29, 1974, pp. 449–470
  3. ^ Robert Merton, “Option Pricing When Underlying Stock Returns are Discontinuous” Journal of Financial Economics, 3, January–March, 1976, pp. 125–44.

Further reading[edit]

  • Duffie, Darrell; Kenneth J. Singleton (2003). Credit Risk: Pricing, Measurement, and Management. Princeton University Press.
  • Jarrow, Robert, Donald R. van Deventer, Li Li, and Mark Mesler (2006). Kamakura Risk Information Services Technical Guide, Version 4.1. Kamakura Corporation.CS1 maint: multiple names: authors list (link)
  • Lando, David (2004). Credit Risk Modeling: Theory and Applications. Princeton University Press. ISBN 978-0-691-08929-4.
  • van Deventer; Donald R.; Kenji Imai; Mark Mesler (2004). Advanced Financial Risk Management: Tools & Techniques for Integrated Credit Risk and Interest Rate Risk Modeling. John Wiley. ISBN 978-0-470-82126-8.