A Two-Factor Hazard Rate Model for Pricing Risky Debt and the Term Structure of Credit Spreads

Madan, Dilip B.; Ünal, Haluk

doi:10.2307/2676238

Cited by 151 publications

(73 citation statements)

References 32 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…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

View full text Add to dashboard Cite

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.

show abstract

Section: Introductionmentioning

confidence: 99%

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

Brody

Hughston

Macrina

2007

Applied and Numerical Harmonic Analysis

134

View full text Add to dashboard Cite

show abstract

“…Therefore, criticism of the models based on low credit spreads at short maturities is that of the underlying assumptions. Zhou (1997) and Madan and Unal (2000) derive models in which the short-term credit spreads are non-trivial.…”

Section: A R T T P a R T Fq R T S ( ) Ln ( ) ( )mentioning

confidence: 99%

Pricing corporate bonds with dynamic default barriers

Hui¹,

Lo²,

Tsang³

2003

JOR

View full text Add to dashboard Cite

Merton-type models of pricing corporate bonds based on relatively simple default processes cannot generate credit spreads which replicate empirically observed spreads. This article presents an analytical valuation model of corporate discount bond prices to address this problem. The main feature of the model is a dynamic default barrier. Different default scenarios can be incorporated into the valuation model through adjusting the default barrier's dynamics. We derive a closed-form solution of the corporate bond price based on the model as a function of the firm value and short-term interest rate, with time-dependent model parameters. The numerical results calculated from the solution show that the model is capable of producing term structures of credit spreads that are consistent with some empirical findings. This model could provide new insight for future research on corporate bond analysis and credit risk modeling.

show abstract

“…4 The pricing of corporate debt subject to credit risk has been extensively studied in the literature. We refer to Duffie and Singleton [6], Jarrow and Turnbull [11] and Madan and Unal [20] for the recovery rate is exogenously given and related to no firm-specific variables. In contrast, our model assumes that the recovery rate depends on the value of a collateral asset, 5 whence it is also a stochastic process.…”

Section: Introductionmentioning

confidence: 99%

“…(19) 0 Hence, the cumulative default process H(t) is normally distributed with mean µH(t) = mht + (h(0) -mh) 1 -e-ah t ah and variance _ v2 r 1 -e -ah t 1 -e-2ahtS = ah I t -2 ah + 2ahIn particular, the risk-adjusted discount process M(t) = R(t)+H(t) is also normally distributed with mean µR (t) + µH (t) and variance SR (t) + SH (t) + 2CRH (t), where O'r ah rt -1 -e -a,t -1 -e-ah t + 1 -é ia r+ah)t^ ( 20 ). …”

mentioning

confidence: 99%

On the term structure of lending interest rates when a fraction of collateral is recovered upon default

Kijima

Miyake

2004

Japan J. Indust. Appl. Math.

View full text Add to dashboard Cite

This article provides an arbitrage-free model to evaluate the term structure of lending interest rates when a fraction of collateral is recovered upon default of the borrower. Unlike the previous literature, we assume that the value of the collateral asset fluctuates over time with certain correlation to the risk-free interest rate as well as the default hazard rate of the borrower. It is shown that the bank loan is a sum of holding a coupon-bearing bond and selling a put option, both being callable upon default. A Gaussian model is considered, as a special case, to derive an analytic expression of the appropriate lending interest rates, and some numerical example is given to demonstrate that bank loans exhibit different properties from corporate bonds.

show abstract

A Two-Factor Hazard Rate Model for Pricing Risky Debt and the Term Structure of Credit Spreads

Cited by 151 publications

References 32 publications

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

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

Pricing corporate bonds with dynamic default barriers

On the term structure of lending interest rates when a fraction of collateral is recovered upon default

Contact Info

Product

Resources

About