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Bond and CDS Pricing via the Stochastic Recovery Black-Cox Model

by Albert Cohen 1,* and Nick Costanzino 2,*
1
Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA
2
Quantitative Analytics, Barclays Capital, 745 7th Ave, New York, NY 10019, USA
*
Authors to whom correspondence should be addressed.
Risks 2017, 5(2), 26; https://doi.org/10.3390/risks5020026
Received: 18 January 2017 / Revised: 4 April 2017 / Accepted: 10 April 2017 / Published: 19 April 2017
Building on recent work incorporating recovery risk into structural models by Cohen & Costanzino (2015), we consider the Black-Cox model with an added recovery risk driver. The recovery risk driver arises naturally in the context of imperfect information implicit in the structural framework. This leads to a two-factor structural model we call the Stochastic Recovery Black-Cox model, whereby the asset risk driver At defines the default trigger and the recovery risk driver Rt defines the amount recovered in the event of default. We then price zero-coupon bonds and credit default swaps under the Stochastic Recovery Black-Cox model. Finally, we compare our results with the classic Black-Cox model, give explicit expressions for the recovery risk premium in the Stochastic Recovery Black-Cox model, and detail how the introduction of separate but correlated risk drivers leads to a decoupling of the default and recovery risk premiums in the credit spread. We conclude this work by computing the effect of adding coupons that are paid continuously until default, and price perpetual (consol bonds) in our two-factor firm value model, extending calculations in the seminal paper by Leland (1994). View Full-Text
MDPI and ACS Style

Cohen, A.; Costanzino, N. Bond and CDS Pricing via the Stochastic Recovery Black-Cox Model. Risks 2017, 5, 26.

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