How do the Jarrow-Turnbull and Duffie-Singleton reduced-form models differ?
What will be an ideal response?
The Jarrow-Turnbull reduced-form model assumes that the recovery payment can occur only at maturity (rather than when default actually occurs) and the recovery amount can fluctuate randomly over time.On the contrary, the model offered by Duffie and Singleton permits the recovery payment to occur at any time and restricts the amount of recovery to be a fixed fraction of the non-default bond price at the time of default. More details are given below.
The assumption that the recovery payment can occur only at maturity rather than when default actually occurs (or soon after) in the Jarrow-Turnbull model so that a closed-form solution can be derived is not realistic. This is one of two major drawbacks of that model. The second drawback is that the recovery amount can fluctuate randomly over time. The recovery amount fluctuates because it depends on the corporation's liquidation value at the time of default. As a result, it is possible to have scenarios for the Jarrow-Turnbull model wherein the recovery payment may exceed the price of the bond at the time of default because the recovery rate is an exogenously specified percentage of the risk-free bonds.
In contrast, the model proposed by Duffie and Singleton (1) allows the recovery payment to occur at any time and (2) restricts the amount of recovery to be a fixed fraction of the non-default bond price at the time of default. Because of this second assumption, the Duffie-Singleton model is referred to as a fractional recovery model or fractional recovery of predefault market value model. The rationale for this assumption is as a corporate bond's credit quality deteriorates, its price falls. At the time of default, the recovery price will be some fraction of the final price that prevailed prior to default, and, as a result, one does not encounter the shortcoming of the Jarrow-Turnbull model that price can be greater than the price prior to default.
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