Term structure modelling of defaultable bonds

In this paper we present a model of the development of the term structure of defaultable interest rates that is based on a multiple-defaults model. Instead of modelling a cash payoff in default we assume that defaulted debt is restructured and continues to be traded. The model allows for loss quotas that are not predictable while maintaining a very close link to the modelling of default-free interest rate modelling. We use the Heath-Jarrow-Morton (HJM) [21] approach to represent the terms structure of defaultable bond prices in terms of forward rates and concentrate on modelling the development of the term structure of the defaultable bonds and give conditions under which these dynamics are arbitrage-free. These conditions are a drift restriction that is closely related to the HJM drift restriction for risk-free bonds, and the restriction that the defaultable short rate must always be not below the risk-free short rate. By keeping the mechanism that triggers the defaults as general as possible, it is shown that the HJM-drift conditions must also be satisfied by bond prices derived from firm's value models with predictable times of default, and not only by bond prices derived from intensity based models. In its most general version the model is set in a marked point process framework, to allow for jumps in the defaultable rates at times of default

Evaluation of Tranche in Securitization and Long-range Ising Model

This econophysics work studies the long-range Ising model of a finite system with $N$ spins and the exchange interaction $\frac{J}{N}$ and the external field $H$ as a modely for homogeneous credit portfolio of assets with default probability $P_{d}$ and default correlation $\rho_{d}$. Based on the discussion on the $(J,H)$ phase diagram, we develop a perturbative calculation method for the model and obtain explicit expressions for $P_{d},\rho_{d}$ and the normalization factor $Z$ in terms of the model parameters $N$ and $J,H$. The effect of the default correlation $\rho_{d}$ on the probabilities $P(N_{d},\rho_{d})$ for $N_{d}$ defaults and on the cumulative distribution function $D(i,\rho_{d})$ are discussed. The latter means the average loss rate of the``tranche'' (layered structure) of the securities (e.g. CDO), which are synthesized from a pool of many assets. We show that the expected loss rate of the subordinated tranche decreases with $\rho_{d}$ and that of the senior tranche increases linearly, which are important in their pricing and ratings.Comment: 21 pages, 9 figure

Early childhood development of boys with genital anomalies

Male genital anomalies often require surgery in early life to address functional and cosmetic consequences. However, there has been little assessment of developmental outcomes of affected boys

Team Structure Modelling of Defaultable Bonds

In this paper we present a model of the development of the term structure of defaultable interest rates that is based on a multiple-defaults model. Instead of modelling a cash payoff in default we assume that defaulted debt is restructured and continues to be traded. The model allows for loss quotas that are not predictable while maintaining a very close link to the modelling of default-free interest rate modelling. We use the Heath-Jarrow-Morton (HJM) [21] approach to represent the terms structure of defaultable bond prices in terms of forward rates and concentrate on modelling the development of the term structure of the defaultable bonds and give conditions under which these dynamics are arbitrage-free. These conditions are drift restriction that is closely related to the HJM drift restriction for risk-free bonds, and the restriction that the defaultable short rate must always be not below the risk-free short rate. By keeping mechanism that triggers the defaults as general as possible, it is shown that the HJM-drift conditions must also be satisfied by bond prices derived from firms value models with predictable times of default, and not only by bond prices derived from intensity based models. In its most general version the model is set in a marked point process framework, to allow for jumps in the defaultable rates at times of default.

Copula-Dependent Default Risk in Intensity Models

In this paper we present a new approach to incorporate dynamic default dependency in intensity-based default risk models. The model uses an arbitrary default dependency structure which is specified by the Copula of the times of default, this is combined with individual intensity-based models for the defaults of the obligors without loss of the calibration of the individual default-intensity models. The dynamics of the survival probabilities and credit spreads of individual obligors are derived and it is shown that in situations with positive dependence, the default of one obligor causes the credit spreads of the other obligors to jump upwards, as it is experienced empirically in situations with credit contagion. For th

Pricing Interest Rate-SensitiveCredit Portfolio Derivatives

In this paper we present a modelling framework for portfolio credit risk which incorporates the dependence between risk-free interest-rates and the default loss process. The contribution in this approach is that { besides the traditional diffusion based covariation between loss intensities and interest-rates { a direct dependence between interest-rates and the loss process is allowed, in particular default-free interest-rates can also depend on the loss history of the credit portfolio. Amongst other things this enables us to capture the effect that economy-wide default events are likely to have on government bond markets and/or central banks' interest-rate policies. Similar to Schonbucher (2005), the model is set up using a set of losscontingent forward interest-rates fn(t; T) and loss-contingent forward credit protection rates Fn(t; T) to parameterize the market prices of default-free bonds and credit-sensitive assets such as CDOs. We show that (up to weak regularity conditions), existence of such a parametrization is necessary and sufficient for the absence of static arbitrage opportunities in the underlying assets. We also give necessary conditions and sucient conditions on the dynamics of the parametrization which ensure absence of dynamic arbitrage opportunities in the model. Similar to the HJM drift restrictions for default-free interest-rates, these conditions take the form of restrictions on the drifts of fn(t; T) and Fn(t; T), together with a set of regularity conditions.AP, MI, Credit Portfolio Risk, Top-Down, Forward Model, Contagion, Collateralized Debt Obligations