The Jarrow–Turnbull credit risk model was published by Robert A. Jarrow of Kamakura Corporation and Cornell University and Stuart Turnbull, currently at the University of Houston. Many experts in financial theory label the Jarrow–Turnbull model as the first “reduced-form” credit model. Reduced-form models are an approach to credit risk modeling that contrasts sharply with the “structural credit models”. The structural or “Merton” credit models are single-period models which derive the probability of default from the random variation in the unobservable value of the firm’s assets. Two years after the development of the structural credit model, Robert Merton modeled bankruptcy as a continuous probability of default. Upon the random occurrence of default, the stock price of the defaulting company is assumed to go to zero. Merton derived the value of options for a company that can default.
Jarrow Turnbull Model
What is ‘Jarrow Turnbull Model’
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.
Explaining ‘Jarrow Turnbull Model’
Structural models 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. Jarrow concludes that for pricing and hedging, reduced-form models are the preferred methodology.
- The Jarrow/Turnbull default risk model—Evidence from the German market – www.tandfonline.com [PDF]
- Pricing derivatives on financial securities subject to credit risk – onlinelibrary.wiley.com [PDF]
- A Markov model for the term structure of credit risk spreads – academic.oup.com [PDF]
- The intersection of market and credit risk – www.sciencedirect.com [PDF]
- A Stochastic Model for Credit Spreads Under a Risk-Neutral Framework Through the Use of an Extended Version of the Jarrow, Lando and Turnbull Model – papers.ssrn.com [PDF]
- The subprime credit crisis of 2007 – jod.pm-research.com [PDF]
- Credit market equilibrium theory and evidence: Revisiting the structural versus reduced form credit risk model debate – www.sciencedirect.com [PDF]