What Is the Jarrow Turnbull Model?

What Is the Jarrow Turnbull Model?

Let me explain the Jarrow Turnbull model to you directly—it's one of the first reduced-form models designed for pricing credit risk. Created by Robert Jarrow and Stuart Turnbull, this model uses multi-factor and dynamic analysis of interest rates to figure out the probability of default.

Key Takeaways

You should know that the Jarrow Turnbull Model is essentially a credit risk tool that gauges how likely a borrower is to default on a loan. It was put together by finance professors Robert Jarrow and Stuart Turnbull back in the 1990s. As a reduced-form model, it stands out from others by factoring in the effects of changing interest rates, which is basically the cost of borrowing. Remember, reduced-form models are different from structural ones, which base default probability on a firm's asset values.

Understanding the Jarrow Turnbull Model

Determining credit risk—the chance of loss when a borrower fails to repay a loan or meet obligations—is a sophisticated area that involves complex math and powerful computing. Various models help financial institutions assess if a company might not meet its financial duties. In the past, tools focused mainly on a company's capital structure for default risk.

But the Jarrow Turnbull model, which came out in 1995, changed that by introducing a method to measure default likelihood that includes the impact of fluctuating interest rates, or the cost of borrowing. Importantly, Jarrow and Turnbull’s model demonstrates how credit investments behave under different interest rate conditions.

Structural Models vs. Reduced-Form Models

There are two main approaches to credit risk modeling: reduced-form and structural. Structural models assume you have full knowledge of a company’s assets and liabilities, leading to a predictable default time. These are often called 'Merton' models, named after Nobel Laureate Robert C. Merton; they're single-period models that calculate default probability from random changes in a firm's unobservable asset values. Default happens at maturity if assets fall below outstanding debt.

Here's a fast fact: Merton's structural credit model was first provided by KMV LLC, which Moody's Investors Service acquired in 2002, in the early 1990s.

In contrast, reduced-form models assume you're unaware of the company's financial details. They see default as a surprise event driven by various market factors. Since structural models rely heavily on their assumptions, Jarrow argued that reduced-form models are better for pricing and hedging.

Special Considerations

Most banks and credit rating agencies use a mix of structural and reduced-form models, along with their own versions, to evaluate credit risk. Structural models link credit quality to a firm’s economic and financial conditions, as in Merton’s approach. On the other hand, the Jarrow Turnbull reduced-form models use similar info but incorporate market parameters and a snapshot of the firm’s financial state.