Common Failings: How Corporate Defaults are Correlated

We develop, and apply to data on U.S. corporations from 1979-2004, tests of the standard doubly-stochastic assumption under which firms'default times are correlated only as implied by the correlation of factors determining their default intensities. This assumption is violated in the presence of contagion or "frailty" (unobservable explanatory variables that are correlated across firms). Our tests do not depend on the time-series properties of default intensities. The data do not support the joint hypothesis of well specified default intensities and the doubly-stochastic assumption. There is also some evidence of default clustering in excess of that implied by the doubly-stochastic model with the given intensities.

A Simple Model for Pricing Securities with Equity, Interest-Rate, and Default Risk

We develop a model for pricing derivative and hybrid securities whose value may depend on different sources of risk, namely, equity, interest-rate, and default risks. In addition to valuing such securities the framework is also useful for extracting probabilities of default (PD) functions from market data. Our model is not based on the stochastic process for the value of the firm [which is unobservable], but on the stochastic process for interest rates and the equity price, which are observable. The model comprises a risk-neutral setting in which the joint process of interest rates and equity are modeled together with the default conditions for security payoffs. The model is embedded on a recombining lattice which makes implementation of the pricing scheme feasible with polynomial complexity. We present a simple approach to calibration of the model to market observable data. The framework is shown to nest many familiar models as special cases. The model is extensible to handling correlated default risk and may be used to value distressed convertible bonds, debt-equity swaps, and credit portfolio products such as CDOs. We present several numerical and calibration examples to demonstrate the applicability and implementation of our approach

A Direct Approach to Arbitrage-Free Pricing of Credit Derivatives1

This paper develops a framework for modelling risky debt and valuing credit derivatives that is exible and simple to implement, and that is, to the maximum extent possible, based on observables. Our approach is based on expanding the Heath-Jarrow-Morton term-structure model to allow for defaultable debt. We do not follow the procedure of implying out the behavior of spreads from assumptions concerning the default process, instead working directly with the evolution of spreads. We show that risk-neutral drifts in the resulting model possess a recursive representation that particularly facilitates implementation and makes it possible to handle path-dependence and early exercise features without difficulty. The framework permits embedding a variety of specifications for default; we present an empirical example of a default structure which provides promising calibration results

Average Interest

We develop analytic pricing models for options on averages by means of a state-space expansion method. These models augment the class of Asian options to markets where the underlying traded variable follows a mean-reverting process. The approach builds from the digital Asian option on the average and enables pricing of standard Asian calls and puts, caps and floors, as well as other exotica. The models may be used (i) to hedge long period interest rate risk cheaply, (ii) to hedge event risk (regime based risk), (iii) to manage long term foreign exchange risk by hedging through the average interest differential, (iv) managing credit risk exposures, and (v) for pricing specialized options like range-Asians. The techniques in the paper provide several advantages over existing numerical approaches.

Polishing diamonds in the rough: the sources of syndicated venture performance

Using an effort-sharing framework for VC syndicates, we assess how syndication impacts investment returns, chances of successful exit, and the time taken to exit. With data from 1980-2003, and applying apposite econometrics for endogeneity to these different performance measures, we are able to ascribe much of the better return to selection, with the value-addition by monitoring role significantly impacting the likelihood and time of exit. While the extant literature on Venture Capital (VC) syndication is divided about the relative importance of the selection and value-add hypotheses, we find that their roles are complementary

A Direct Approach to Arbitrage-Free Pricing of Credit Derivatives

This paper develops a model for the pricing of credit derivatives using observables. The model (i) is arbitrage-free, (ii) accommodates path-dependence, and (iii) handles a range of securities, even with American features. The computer implementation uses a recursive scheme that is convenient and seamlessly processes forward induction and backward recursion, needed to compute more complicated derivative securities.

Poisson-Guassian Processes and the Bond Markets

That interest rates move in a discontinuous manner is no surprise to participants in the bond markets. This paper proposes and estimates a class of Poisson-Gaussian processes that allow for jumps in interest rates. Estimation is undertaken using exact continuous-time and discrete-time estimators. Analytical derivations of the characteristic functions, moments and density functions of jump-diffusion stochastic process are developed and employed in empirical estimation. These derivations are general enough to accommodate any jump distribution. We find that jump processes capture empirical features of the data which would not be captured by diffusion models. The models in the paper enable an assessment of the impact of Fed activity and day-of-week effects on the stochastic process for interest rates. There is strong evidence that existing diffusion models would be well-enhanced by jump processes.

An Efficient Generalized Discrete-Time Approach to Poisson-Gaussian Bond Option Pricing in the Heath-Jarrow-Morton Model

Term structure models employing Poisson-Gaussian processes may be used to accommodate the observed skewness and kurtosis of interest rates. This paper extends the discrete-time, pure-Gaussian version of the Heath-Jarrow-Morton model to the pricing" of American-type bond options when the underlying term structure of interest rates follows a Poisson-Gaussian process. The Poisson-Gaussian process is specified using a hexanomial tree (six nodes emanating from each node), and the tree is shown to be recombining. The scheme is parsimonious and convergent. This model extends the class of HJM models by (i) introducing a more generalized volatility specification than has been used so far, and (ii) inducting jumps, yet retaining lattice recombination, thus making the model useful for practical applications.