## DEFINITION of 'Jarrow Turnbull Model'

The Jarrow Turnbull credit risk model is one of the first reduced-form models for pricing credit risk. Developed by Robert Jarrow and Stuart Turnbull, the model utilizes multi-factor and dynamic analysis of interest rates to calculate the probability of default. Reduced-form models are one of two approaches to credit risk modeling, the other being structural.

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## BREAKING DOWN 'Jarrow Turnbull Model'

Structural models like the Jarrow Turnbull model assume that the modeler — like a company's managers — has complete knowledge of its assets and liabilities, leading to a predictable default time. Reduced-form models assume that the modeler — like the market — has incomplete knowledge about the company's condition, leading to an inaccessible default time. Structural models, often called "Merton" models, after the Nobel Laureate academic Robert C. Merton, are single-period models which derive their probability of default from the random variations in the unobservable value of a firm's assets. Because structural models are rather sensitive to the many assumptions underlying their design, Jarrow concluded that for pricing and hedging, reduced-form models are the preferred methodology.

In reality, credit risk scoring is a highly advanced field, involving both complex math and high octane computing. Most banks and credit rating agencies will use a combination of structural and reduced-form models, as well as proprietary variants, to assess credit risk. Structural models offer the built-in advantage of offering a link between the credit quality of a firm and the firm’s economic and financial conditions established Merton’s model. The Jarrow Turnbull reduced-form models utilize some of the same information but account for certain market parameters, as well as knowledge of a firm’s financial condition at a point in time.

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