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.

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.