This paper estimates recent default risk premia for U.S. corporate debt, based on a close relationship between default probabilities, as estimated by Moody's KMV EDFs, and default swap (CDS) market rates. The default-swap data, obtained through CIBC from 22 banks and specialty dealers, allow us to establish a strong link between actual and risk-neutral default probabilities for the 69 firms in the three sectors that we analyze: broadcasting and entertainment, healthcare, and oil and gas. We find dramatic variation over time in risk premia, from peaks in the thrid quarter of 2002, dropping by roughly 50% to late 2003.

Abstract. This paper gives a brief overview of the nonparametric techniques that are useful for financial econometric problems. The problems include estimation and inference for instantaneous returns and volatility functions of time-homogeneous and time-dependent diffusion processes, and estimation of transition densities and state price densities. We first briefly describe the problems and then outline the main techniques and main results. Some useful probabilistic aspects of diffusion processes are also briefly summarized to facilitate our presentation and applications.

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We provide maximum likelihood estimators of term structures of conditional probabilities of bankruptcy over relatively long time horizons, incorporating the dynamics of firm-specific and macroeconomic covariates. We find evidence in the U.S. industrial machinery and instruments sector, based on over 28,000 firm-quarters of data spanning 1971 to 2001, of significant dependence of the level and shape of the term structure of conditional future bankruptcy probabilities on a firm's distance to default (a volatility-adjusted measure of leverage) and on U.S. personal income growth, among other covariates. Variation in a firm's distance to default has a greater relative e#ect on the term structure of future failure hazard rates than does a comparatively sized change in U.S. personal income growth, especially at dates more than a year into the future.

In recent years, credit derivatives have become the main tool for transferring and hedging credit risk. The credit derivatives market has grown rapidly both in volume and in the breadth of the instruments it offers. Among the most complicated of these instruments are the multiname ones. These are instruments with payoffs that are contingent on the default realization in a portfolio of names. The modeling of dependent defaults is difficult because there is very little historical data available about joint defaults and because the prices of those instruments are not quoted. Therefore, the models cannot be calibrated, neither to defaults nor to prices. In this paper, we present a methodology for the estimation, simulation, and pricing of multiname contingent instruments. Our model is a hybrid of the well-known structural and reduced form approaches for modeling defaults. The dependence structure of our model is of a t-copula that possesses non-trivial tail dependence. The t-copula allows for more joint extreme events, which have a big impact on the prices of multiname instruments, e.g. n th-todefault baskets and CDOs. We demonstrate this impact with n th-to-default baskets. J.E.L. Subject Classification: G13.

An American option grants the holder the right to select the time at which to exercise the option, so pricing an American option entails solving an optimal stopping problem. Difficulties in applying standard numerical methods to complex pricing problems have motivated the development of techniques that combine Monte Carlo simulation with dynamic programming. One class of methods approximates the option value at each time using a linear combination of basis functions, and combines Monte Carlo with backward induction to estimate optimal coefficients in each approximation. We analyze the convergence of such a method as both the number of basis functions and the number of simulated paths increase. We get explicit results when the basis functions are polynomials and the underlying process is either Brownian motion or geometric Brownian motion. We show that the number of paths required for worst-case convergence grows exponentially in the degree of the approximating polynomials in the case of Brownian motion and faster in the case of geometric Brownian motion. 1. Introduction. An American

An Information-Based Framework for Asset Pricing: X-Factor Theory and its Applications. This thesis presents a new framework for asset pricing based on modelling the information available to market participants. Each asset is characterised by the cash flows it generates. Each cash flow is expressed as a function of one or more independent random variables called market factors or “X-factors”. Each X-factor is associated with a “market information process”, the values of which become available to market participants. In addition to true information about the X-factor, the in-formation process contains an independent “noise ” term modelled here by a Brownian bridge. The information process thus gives partial information about the X-factor, and the value of the market factor is only revealed at the termination of the process. The market filtration is assumed to be generated by the information processes associated with the X-factors. The price of an asset is given by the risk-neutral expectation of the sum of the discounted cash flows, conditional on the information available from the filtration. The thesis develops the theory in some detail, with a variety of applica-

In all the existing literature on survival in heterogeneous economies, the rate at which an agent vanishes in the long run relative to another agent can be characterized by the difference of the so-called survival indices, where each survival index only depends on the preferences of the corresponding agent and the properties of the aggregate endowment. In particular, one agent experiences extinction relative to another (that is, the wealth ratio of the two agents goes to zero) if and only if she has a smaller survival index. We consider a simple complete market model and show that the survival index is more complex if there are more than two agents in the economy. In fact, the following phenomenon may take place: even if agent one experiences extinction relative to agent two, adding a third agent to the economy may reverse the situation and force the agent two to experience extinction relative to agent one. We also calculate the rates of convergence.

We present an introduction to mathematical Finance Theory, covering

During the past couple of years much research effort has been devoted to explaining the spread of corporate bonds over Treasuries. On the other hand, relatively little is known about the spread components of structured credit products. This paper shows that such securities compensate investors for expected losses due to defaults, pure jump-to-default risk, correlation risk, as well as the risk of firm-specific and market-wide adverse changes in credit conditions. We provide a framework that allows a decomposition of ”structured ” credit spreads, and we apply this decomposition to CDX index tranches.