# Jarrow-Turnbull model

The

**Jarrow-Turnbull credit risk model**was published byRobert A. Jarrow ofKamakura Corporation andCornell University andStuart Turnbull , currently at theUniversity of Houston [*Robert A. Jarrow and Stuart Turnbull, "Pricing Derivatives on Financial Securities Subject to*] . 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" [Credit Risk " "Journal of Finance", vol. 50, March, 1995] . The structural or "Merton" credit models are single-period models which derive theRobert C. Merton “On the Pricing of Corporate Debt: The Risk Structure of Interest Rates,” "Journal of Finance" 29, 1974, pp. 449-470default probability 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 [*Robert Merton, “Option Pricing When Underlying Stock Returns are Discontinuous” "Journal of Financial Economics", 3, January-March, 1976, pp. 125-44.*] . Upon therandom 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. This was in fact the first "reduced form" model where bankruptcy is modeled as a statistical process, rather than as a microeconomic model of the firm's capital structure.Fact|date=October 2007The Jarrow-Turnbull model extends the reduced-form model of Merton (1976) to a random interest rates framework.

Large financial institutions employ default models of both the structural and reduced form types. The Merton structural default probabilities were first offered by

KMV LLC in the early 1990s. KMV LLC was acquired byMoody's Investors Service in 2002.Kamakura Corporation , where Robert Jarrow serves as director of research, has offered both structural and reduced form default probabilities on public companies since 2002.Fact|date=October 2007**See also***

Credit derivatives

*Credit default swap

*Credit risk

*Default probability

*Merton Model

*Robert A. Jarrow **References****Further reading***

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