What is the Jarrow Turnbull Model?
The Jarrow Turnbull Model revolutionizes how we price credit risk. Developed by Robert Jarrow and Stuart Turnbull in the mid-’90s, this model utilizes multi-factor and dynamic interest rate analysis to calculate the probability of default.
Key Takeaways
- The Jarrow Turnbull Model assesses the likelihood of a borrower defaulting on a loan.
- Pioneered by Robert Jarrow and Stuart Turnbull.
- This reduced-form model uniquely incorporates changing interest rates.
- It stands apart from structural models that derive default probability from a firm’s asset values.
Understanding the Jarrow Turnbull Model
Credit risk, the chance of a borrower failing to repay loan obligations, involves robust calculations and advanced technologies. Various models assist financial institutions in evaluating a firm’s risk of default. Traditionally, default risk assessments focused on a company’s capital structure. The Jarrow Turnbull Model takes it further by accounting for fluctuating interest rates, known as the cost of borrowing.
Introduced in 1995, the model enables investors to predict the performance of credit investments under different interest rates, providing a more dynamic risk analysis.
Structural Models vs. Reduced-Form Models
Credit risk modeling employs either structural or reduced-form models. Structural models assume visibility into a company’s assets and liabilities, leading to predictable default times. Often referred to as Merton models—named after Nobel Laureate Robert C. Merton—these derived the default probability from random variations in a firm’s asset values, with defaults occurring if the asset value falls below outstanding debt at maturity.
By contrast, reduced-form models do not require detailed insights into a company’s finances. Instead, they treat default events as sudden occurrences influenced by numerous market factors. Due to their design flexibility, Robert Jarrow favored reduced-form models for pricing and hedging over structural models, which are highly sensitive to underlying assumptions.
Special Considerations
Most banks and credit rating agencies combine structural and reduced-form models, enhanced by proprietary variants, for comprehensive credit risk assessment. Structural models link credit quality with a firm’s economic and financial conditions as estbalished in Merton’s framework. Conversely, the Jarrow Turnbull Model integrates market parameters with temporal insights into a firm’s financial status, making it an invaluable tool for modern financial risk assessment.
Related Terms: Credit Risk, Interest Rates, Default Probability, Reduced-Form Models, Structural Models.
References
- Journal of Finance. “Pricing Derivatives on Financial Securities Subject to Credit Risk”.
- Journal of Finance. “On the Pricing of Corporate Debt: the Risk Structure of Interest Rates”.
