Jarrow Turnbull Model The Jarrow Turnbull credit risk model was published by Robert A. Jarrow of Kamakura Corporation and Cornell University and Stuart Turnbull, currently at the University of Houston, in March, 1995. The article "Pricing Derivatives on Financial Securities Subject to Credit Risk," appeared in the Journal of Finance, volume 50. Many experts in financial theory label the Jarrow Turnbull model as the first "reduced form" credit model. Reduced form models are an approach to credit risk modeling that contrasts sharply with the "structural credit models" developed by Robert C. Merton in the article “On the Pricing of Corporate Debt: The Risk Structure of Interest Rates,” Journal of Finance 29, 1974, pp. 449-470. The structural or "Merton" credit models are single period models which derive the default probability 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 published “Option Pricing When Underlying Stock Returns are Discontinuous,” Journal of Financial Economics, 3, January-March, 1976, pp. 125-44. In this publication, he modeled bankruptcy as a continuous probability of default. 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. This was in fact the first "reduced form" model where bankruptcy is modeled as a statistical process, rather than a micoreconomic model of the firm's capital structure. Credit risk is the risk of loss due to a debtors non-payment of a loan or other line of credit (either the principal or interest (coupon) or both). ... Robert C. Merton (born July 31, 1944), a leading scholar in the field of finance, was one of three men who, in the early 1970s, developed the mathematics of the stock options markets. ...

The Jarrow-Turnbull model extends the reduced form model of Merton (1976) to a random interest rates framework. For a more detailed explanation of the reduced form model, see Duffie and Singleton (2003), Lando (2004), van Deventer and Imai (2003), and van Deventer, Imai and Mesler (2004).

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. An example of the derivation of the Jarrow Turnbull default probabilities is described in detail in Jarrow, van Deventer, Li and Mesler (2006).

See also

• Credit derivatives
• Credit default swap
• Credit risk
• Default probabilities
• Robert A. Jarrow

A Credit Derivative is a contract to transfer the risk of the total return on a credit asset falling below an agreed level, without transfer of the underlying asset. ... A credit default swap (CDS) is a swap designed to transfer the credit exposure of fixed income products between parties. ... Credit risk is the risk of loss due to a debtors non-payment of a loan or other line of credit (either the principal or interest (coupon) or both). ...

References

• Duffie, Darrell and 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. 
• Lando, David (2004). Credit Risk Modeling: Theory and Applications. Princeton University Press. ISBN13 978-0691089294. 
• van Deventer, Donald R., Kenji Imai and Mark Mesler (2004). Advanced Financial Risk Management: Tools & Techniques for Integrated Credit Risk and Interest Rate Risk Modeling. John Wiley. ISBN13 978-0470821268. 

External links

• Facts and Figures about Credit loss risks in Europe
• The Risk Management Association - leading industry organisation for credit risk professionals
• http://bis2information.org: Practical articles, on BIS2 and risk modelling, submitted by professionals to help create an industry standard.
• http://www.defaultrisk.com: Large library of recent articles on credit risk.
• http://www.moodyskmv.com: Major credit rating agency and vendor of a variant on the Merton structural model default probabilities.
• http://www.kamakuraco.com: Extensive research section with many Robert Jarrow publications. First vendor of reduced form default models descended from the Jarrow Turnbull Model.