## Pricing the risks of default (1998)

Venue: | Review of Derivatives Research |

Citations: | 126 - 6 self |

### BibTeX

@ARTICLE{Madan98pricingthe,

author = {Dilip B. Madan and Haluk Unal and Anthony M. Santomero},

title = {Pricing the risks of default},

journal = {Review of Derivatives Research},

year = {1998},

pages = {121--160}

}

### Years of Citing Articles

### OpenURL

### Abstract

the problems and opportunities facing the financial services industry in its search for competitive excellence. The Center's research focuses on the issues related to managing risk at the firm level as well as ways to improve productivity and performance. The Center fosters the development of a community of faculty, visiting scholars and Ph.D. candidates whose research interests complement and support the mission of the Center. The Center works closely with industry executives and practitioners to ensure that its research is informed by the operating realities and competitive demands facing industry participants as they pursue competitive excellence. Copies of the working papers summarized here are available from the Center. If you would like to learn more about the Center or become a member of our research community, please let us know of your interest.

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Citation Context ...lled hazard rate models that focus their attention directly on event probabilities and their su±cient statistics, leaving the precise event unde¯ned. We shall cover in section 3, the models of Merto=-=n [14], -=-Longsta®-Schwartz [9], and an application of the model by Madan, Carr and Chang [11]. Section 4 surveys the models by Du±e and Singleton [3], Madan and Unal 1 [12], Jarrow, Lando and Turnbull [8], a... |

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Citation Context ...constructed to be a vector of positive random variables through time. We suppose that these state variable follow a vector stochastic di®erential equation that generalizes the Cox, Ingersoll and Ross=-= [2] -=-model for the instantaneous spot rate to the vector case. Let K denote a diagonal matrix of speeds of mean reversion while £ is a vector of long term levels to which the state variables are reverting... |

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Citation Context ...nt characteristic function at an appropriate point. The result is a closed form model for defaultable bonds that may be empirically evaluated. 4.2.2 Defaultable HJM models The Heath Jarrow and Morton =-=[5] m-=-odels, for the purposes of pricing ¯xed income claims, require a speci¯cation of the dynamics of the forward rates under the risk neutral measure associated with the money market discounting process... |

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Citation Context ...n [14], Longsta®-Schwartz [9], and an application of the model by Madan, Carr and Chang [11]. Section 4 surveys the models by Du±e and Singleton [3], Madan and Unal 1 [12], Jarrow, Lando and Turnbul=-=l [8],-=- and Madan and Unal 2 [13]. 2 State Contingent Zero Coupon Bonds For each name that is an individual or a legal entity empowered to write ¯nancial contracts in our economies with similar counterparti... |

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Citation Context ...s some constant write down of the face and creditors receive (1 ¡ w)F: In pricing the defaultable claim one may account for correlation between interest rates and asset values by following Jamshidian=-= [6]-=- and Geman, El Karoui and Rochet [4] and expressing the dynamic evolution of asset values and interest rates using the price of the risk-free bond, p(t; T ); as the numeriare. Hence we let Q T be the ... |

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Citation Context ...ies are obtained from a study of S&P default rates reported by Lucas [10]. The prices are inferred from rates of return earned on managing portfolios of bonds by rating category as reported in Altman =-=[1]-=-. Probability, Prices and Risk Premia for No Default on Bonds by Rating and Maturity in Basis Points Maturity Rating Item 1 3 5 8 10 AAA Probability 1 1 1 .9922 .9861 AAA Price .9955 .9835 .9656 .9228... |

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Citation Context ...[9], and an application of the model by Madan, Carr and Chang [11]. Section 4 surveys the models by Du±e and Singleton [3], Madan and Unal 1 [12], Jarrow, Lando and Turnbull [8], and Madan and Unal 2=-= [13].-=- 2 State Contingent Zero Coupon Bonds For each name that is an individual or a legal entity empowered to write ¯nancial contracts in our economies with similar counterparties we are interested in the... |

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Citation Context ...that focus their attention directly on event probabilities and their su±cient statistics, leaving the precise event unde¯ned. We shall cover in section 3, the models of Merton [14], Longsta®-Schwar=-=tz [9],-=- and an application of the model by Madan, Carr and Chang [11]. Section 4 surveys the models by Du±e and Singleton [3], Madan and Unal 1 [12], Jarrow, Lando and Turnbull [8], and Madan and Unal 2 [13... |

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Citation Context ... their su±cient statistics, leaving the precise event unde¯ned. We shall cover in section 3, the models of Merton [14], Longsta®-Schwartz [9], and an application of the model by Madan, Carr and Cha=-=ng [11].-=- Section 4 surveys the models by Du±e and Singleton [3], Madan and Unal 1 [12], Jarrow, Lando and Turnbull [8], and Madan and Unal 2 [13]. 2 State Contingent Zero Coupon Bonds For each name that is a... |

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Citation Context ...e¯ned. We shall cover in section 3, the models of Merton [14], Longsta®-Schwartz [9], and an application of the model by Madan, Carr and Chang [11]. Section 4 surveys the models by Du±e and Singlet=-=on [3],-=- Madan and Unal 1 [12], Jarrow, Lando and Turnbull [8], and Madan and Unal 2 [13]. 2 State Contingent Zero Coupon Bonds For each name that is an individual or a legal entity empowered to write ¯nanci... |

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Citation Context ...ce and creditors receive (1 ¡ w)F: In pricing the defaultable claim one may account for correlation between interest rates and asset values by following Jamshidian [6] and Geman, El Karoui and Rochet=-= [4]-=- and expressing the dynamic evolution of asset values and interest rates using the price of the risk-free bond, p(t; T ); as the numeriare. Hence we let Q T be the probability under which asset prices... |

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Citation Context ...and implied risk premia in basis points on the event of no default for n yearsby¯rmsintheratingcategories AAA and B: The probabilities are obtained from a study of S&P default rates reported by Lucas=-= [10]-=-. The prices are inferred from rates of return earned on managing portfolios of bonds by rating category as reported in Altman [1]. Probability, Prices and Risk Premia for No Default on Bonds by Ratin... |

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