Jarrow Turnbull Model

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What is the Jarrow Turnbull model?

The Jarrow Turnbull model is one of the first reduced-form models for pricing credit risk. Developed by Robert Jarrow and Stuart Turnbull, the model uses a multifactorial and dynamic analysis of interest rates to calculate the probability of default.

Key points to remember

  • The Jarrow Turnbull model is one of the first reduced-form models for pricing credit risk.
  • The model, developed by Robert Jarrow and Stuart Turnbull, uses a multifactorial and dynamic analysis of interest rates to calculate the probability of default.
  • Reduced-form models differ from modeling structural credit risk, which derives the probability of default in the value of a company’s assets.
  • Since structural models are quite sensitive to the many assumptions underlying their design, Jarrow concluded that reduced-form models are the preferred methodology for pricing and coverage.

Understanding the Jarrow Turnbull model

Determining credit risk, the possibility of a loss resulting from a borrower’s failure to repay a loan or meet its contractual obligations, is a very advanced field, involving both complex mathematics and an index-based calculation ‘high octane.

Various models exist to help financial institutions (FIs) better understand whether or not a company can meet its financial obligations. Previously, it was common to use tools that examine the risk of default mainly by examining the capital structure of a business.

The Jarrow Turnbull model, introduced in the early 1990s, offered a new way of measuring the probability of default taking into account the impact of fluctuating interest rates, also known as cost of borrowing.

Jarrow and Turnbull’s model shows how credit investments would behave with different interest rates.

Structural models and reduced form models

Reduced-form models are one of two approaches to modeling credit risk, the other being structural. Structural models assume that the modeler has complete knowledge of the assets and liabilities of a business, which leads to a predictable default time.

Structural models, often called “Merton” models, according to Nobel laureate Robert C. Merton, are single-period models that derive their probability of default from random variations in the unobservable value of a firm’s assets . According to this model, the risks of default occurring on the due date if, at this stage, the value of a company’s assets falls below its outstanding debt.

Merton’s structural credit model was first proposed by the provider of quantitative credit analysis tools KMV LLC, which was acquired by Moody’s Investors Service in 2002, in the early 1990s.

Reduced-form models, on the other hand, consider that the modeller is in ignorance of the company’s financial situation. These models treat failure as an unexpected event that can be governed by a multitude of different factors that occur in the market.

Since structural models are quite sensitive to the many assumptions underlying their design, Jarrow concluded that for prices and hedges, reduced-form models are the preferred methodology.

Special considerations

Most banks and credit rating agencies use a combination of structural and reduced form models, as well as proprietary variants, to assess credit risk. Structural models have the intrinsic advantage of providing a link between the credit quality of a business and the economic and financial conditions of the business established in the Merton model.

At the same time, the Jarrow Turnbull models in reduced form use some of the same information but take into account certain market parameters, as well as the knowledge of the financial situation of a company at a given time.

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