Pricing the risks of default

Madan, Dilip B.; Ünal, Haluk

doi:10.1007/bf01531333

Cited by 322 publications

(181 citation statements)

References 18 publications

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“…Reduced-form models are more commonly used in practice on account of their tractability and because fewer assumptions are required about the nature of the debt obligations involved and the circumstances that might lead to default (see, e.g., Flesaker et al [14], Jarrow & Turnbull [22], Duffie et al [10], Jarrow et al [20], Lando [28], Madan & Unal [31], Duffie & Singleton 1999, Madan & Unal [32], Jarrow & Yu [24]). Most reduced-form models are based on the introduction of a random time of default, modelled as the time at which the integral of a random intensity process first hits a certain critical level, this level itself being an independent random variable.…”

Section: Introductionmentioning

confidence: 99%

Beyond Hazard Rates: A New Framework for Credit-Risk Modelling

Brody

Hughston

Macrina

2007

Applied and Numerical Harmonic Analysis

134

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Summary.A new approach to credit risk modelling is introduced that avoids the use of inaccessible stopping times. Default events are associated directly with the failure of obligors to make contractually agreed payments. Noisy information about impending cash flows is available to market participants. In this framework the market filtration is modelled explicitly, and is assumed to be generated by one or more independent market information processes. Each such information process carries partial information about the values of the market factors that determine future cash flows. For each market factor, the rate at which true information is provided to market participants concerning the eventual value of the factor is a parameter of the model. Analytical expressions that can be readily used for simulation are presented for the price processes of defaultable bonds with stochastic recovery. Similar expressions can be formulated for other debt instruments, including multi-name products. An explicit formula is derived for the value of an option on a defaultable discount bond. It is shown that the value of such an option is an increasing function of the rate at which true information is provided about the terminal payoff of the bond. One notable feature of the framework is that it satisfies an overall dynamic consistency condition that makes it suitable as a basis for practical modelling situations where frequent recalibration may be necessary.

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Section: Introductionmentioning

confidence: 99%

Beyond Hazard Rates: A New Framework for Credit-Risk Modelling

Brody

Hughston

Macrina

2007

Applied and Numerical Harmonic Analysis

134

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“…A default event associated with a single firm occurs as in intensity-based models introduced by, among others, Artzner and Delbaen [1] , Madan and Unal [26], Lando [24] and Jarrow and Turnbull [21]. However our valuation mechanism incorporates information from the firm's stock price.…”

Section: General Modelmentioning

confidence: 99%

Utility valuation of multi-name credit derivatives and application to CDOs

Sircar

Zariphopoulou

2009

Quantitative Finance

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We study the impact of risk-aversion on the valuation of credit derivatives. Using the technology of utility-indifference pricing in intensity-based models of default risk, we analyze resulting yield spreads in multiname credit derivatives, particularly CDOs. We study first the idealized problem with constant intensities where solutions are essentially explicit. We also give the large portfolio asymptotics for this problem. We then analyze the case where the firms have stochastic default intensities driven by a common factor, which can be viewed as another extreme from the independent case. This involves the numerical solution of a system of reaction-diffusion PDEs. We observe that the nonlinearity of the utility-indifference valuation mechanism enhances the effective correlation between the times of the credit events of the various firms leading to non-trivial senior tranche spreads, as often seen from market data.

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“…Next, we start with a brief description of a Merton's type of which the univariate case was introduced, for the VG process, in Madan [21]. We will model in this context n firms; the risk-neutral firm's value are modelled by (2).…”

Section: Credit Risk Modellingmentioning

confidence: 99%

A Multivariate Jump-Driven Financial Asset Model

Luciano

Schoutens

2005

SSRN Journal

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We discuss a Lévy multivariate model for financial assets which incorporates jumps, skewness, kurtosis and stochastic volatility. We use it to describe the behavior of a series of stocks or indexes and to study a multi-firm, value-based default model.Starting from an independent Brownian world, we introduce jumps and other deviations from normality, including non-Gaussian dependence. We use a stochastic time-change technique and provide the details for a Gamma change.The main feature of the model is the fact that -opposite to other, non jointly Gaussian settings -its risk neutral dependence can be calibrated from univariate derivative prices, providing a surprisingly good fit. JEL classification numbers: G12, G10.

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Pricing the risks of default

Cited by 322 publications

References 18 publications

Beyond Hazard Rates: A New Framework for Credit-Risk Modelling

Beyond Hazard Rates: A New Framework for Credit-Risk Modelling

Utility valuation of multi-name credit derivatives and application to CDOs

A Multivariate Jump-Driven Financial Asset Model

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