Securities Pricing with Information-Sensitive Discounting

In this paper incomplete-information models are developed for the pricing of securities in a stochastic interest rate setting. In particu- lar we consider credit-risky assets that may include random recovery upon default. The market filtration is generated by a collection of information processes associated with economic factors, on which in- terest rates depend, and information processes associated with mar- ket factors used to model the cash flows of the securities. We use information-sensitive pricing kernels to give rise to stochastic interest rates. Semi-analytical expressions for the price of credit-risky bonds are derived, and a number of recovery models are constructed which take into account the perceived state of the economy at the time of default. The price of European-style call bond options is deduced, and it is shown how examples of hybrid securities, like inflation-linked credit-risky bonds, can be valued. Finally, a cumulative information process is employed to develop pricing kernels that respond to the amount of aggregate debt of an economy.Asset pricing, incomplete information, stochastic interest rates, credit risk, recovery models, credit-inflation hybrid securities, information-sensitive pricing kernels

Corporate Security Prices in Structural Credit Risk Models with Incomplete Information

The paper studies structural credit risk models with incomplete information of the asset value. It is shown that the pricing of typical corporate securities such as equity, corporate bonds or CDSs leads to a nonlinear filtering problem. This problem cannot be tackled with standard techniques as the default time does not have an intensity under full information. We therefore transform the problem to a standard filtering problem for a stopped diffusion process. This problem is analyzed via SPDE results from the filtering literature. In particular we are able to characterize the default intensity under incomplete information in terms of the conditional density of the asset value process. Moreover, we give an explicit description of the dynamics of corporate security prices. Finally, we explain how the model can be applied to the pricing of bond and equity options and we present results from a number of numerical experiments

Mathematical models of credit management and credit derivatives

>Magister Scientiae - MScThe first two chapters give the background, history and overview of the dissertation, together with the necessary mathematical preliminaries. Thereafter, the next four chapters deal with credit risk and credit derivatives.The final part of the dissertation is devoted to the Basel II bank regulatory framework and the mathematical modeling of asset allocation in bank management, pertaining to credit risk.Credit risk models can be categorized into two groups known as structural models and reduced form models. These models are used in pricing and hedging credit risk. In this thesis we review a variety of credit risk instruments described by models of the said types. One of the strategies utilized by companies to mitigate credit risk is by using credit derivatives.In this thesis, five main types of risk derivatives have been considered: credit swaps, credit linked notes, credit spreads, total return swaps and collaterized debt obligations. Valuation models for the first three derivatives that are mentioned above, are also presented in this dissertation.The material presented include some of the most recent developments in the literature. Our methods range from single-period modeling to application of stochastic optimal control theory. We expand on the material presented from the literature by way of simplifying or clarifying proofs, and by adding illustrative examples in the form of calculations, tables and simulations.Also, the entire Chapter 6 is a new original contribution to the existing literature on mathematical modeling of credit risk. Key words: credit risk; default risk; structural approach; reduced form approach; incomplete information approach; investment strategy; Basel II regulatory framewor

Empirical Pricing of Chinese Defaultable Corporate Bonds Based on the Incomplete Information Model

The default of Suntech Power made the year 2013 in China “the first year of default” of bond markets. People are also clearly aware of the default risk of corporate bonds and find that fair pricing for defaultable corporate bonds is very important. In this paper we first give the pricing model based on incomplete information, then empirically price the Chinese corporate bond “11 super JGBS” from Merton’s model, reduced-form model, and incomplete information model, respectively, and then compare the obtained prices with the real prices. Results show that all the three models can reflect the trend of bond prices, but the incomplete information model fits the real prices best. In addition, the default probability obtained from the incomplete information model can discriminate the credit quality of listed companies

Forecasting Bankruptcy with Incomplete Information

We propose new specifications that explicitly account for information noise in the input data of bankruptcy hazard models. The specifications are motivated by a theory of modeling credit risk with incomplete information (Duffie and Lando [2001]). Based on over 2 million firm-months of data during 1979-2012, we demonstrate that our proposed specifications significantly improve both in-sample model fit and out-of-sample forecasting accuracy. The improvements in forecasting accuracy are persistent throughout the 10-year holdout periods. The improvements are also robust to empirical setup, and are more substantial in cases where information quality is a more serious problem. Our findings provide strong empirical support for using our proposed hazard specifications in credit risk research and industry applications. They also reconcile conflicting empirical results in the literature

Forecasting Bankruptcy with Incomplete Information

We propose new specifications that explicitly account for information noise in the input data of bankruptcy hazard models. The specifications are motivated by a theory of modeling credit risk with incomplete information (Duffie and Lando [2001]). Based on over 2 million firm-months of data during 1979-2012, we demonstrate that our proposed specifications significantly improve both in-sample model fit and out-of-sample forecasting accuracy. The improvements in forecasting accuracy are persistent throughout the 10-year holdout periods. The improvements are also robust to empirical setup, and are more substantial in cases where information quality is a more serious problem. Our findings provide strong empirical support for using our proposed hazard specifications in credit risk research and industry applications. They also reconcile conflicting empirical results in the literature

Essays on Debt in Macroeconomics

My dissertation consists of three chapters, where the common theme among them is debt and saving. My work contributes to our understanding of how debt markets function for entrepreneurs, large corporations and households. The first chapter studies how entrepreneurs used personal borrowing to fund their businesses during the Great Recession. One of the defining characteristics of this period was a “credit crunch” during which the supply of credit dropped for all borrowers. I show that changes in the finances of entrepreneurs between 2007 and 2009 are consistent with entrepreneurs using personal assets to secure lending for their businesses and overcome this credit crunch. In particular, I find that home equity loan balances increased by 10%, despite a 12% drop in the value of aggregate housing stock. Entrepreneurs were responsible for 76% of the increase in home equity loan balances, while they only represent 13% of the population. In the second chapter, I study the use of credit ratings by large corporations in the bond market. Over the last 25 years, there has been a drastic change in the distribution of corporate bond ratings: between 1985 and 2010 the number of firms issuing AAA or AA-rated debt dropped by 70%, while the number of firms issuing debt with lower ratings increased. I propose a mechanism whereby investors learn about firms through credit ratings and publicly available financial information and develop a model that incorporates this mechanism such that firms must devote resources to improving their rating. Under general conditions, the number of high-rated firms decreases in response to an increase in public signal accuracy. The third chapter explores the role of financial market access on household consumption inequality. The standard macroeconomic models of consumption and saving with stochastic income processes have failed to match the rise in consumption inequality between 1980 and 2004. I present a model with idiosyncratic earnings risk and endogenous market segmentation between incomplete and complete markets for financial assets. This model improves upon the qualitative predictions regarding between-group and within-group consumption inequality of a standard incomplete markets model and a standard complete markets model with limited commitment

Dynamic Defaultable Term Structure Modelling beyond the Intensity Paradigm

The two main approaches in credit risk are the structural approach pioneered in Merton (1974) and the reduced-form framework proposed in Jarrow & Turnbull (1995) and in Artzner & Delbaen (1995). The goal of this article is to provide a unified view on both approaches. This is achieved by studying reduced-form approaches under weak assumptions. In particular we do not assume the global existence of a default intensity and allow default at fixed or predictable times with positive probability, such as coupon payment dates. In this generalized framework we study dynamic term structures prone to default risk following the forward-rate approach proposed in Heath-Jarrow-Morton (1992). It turns out, that previously considered models lead to arbitrage possibilities when default may happen at a predictable time with positive probability. A suitable generalization of the forward-rate approach contains an additional stochastic integral with atoms at predictable times and necessary and sufficient conditions for a suitable no-arbitrage condition (NAFL) are given. In the view of efficient implementations we develop a new class of affine models which do not satisfy the standard assumption of stochastic continuity. The chosen approach is intimately related to the theory of enlargement of filtrations, to which we provide a small example by means of filtering theory where the Azema supermartingale contains upward and downward jumps, both at predictable and totally inaccessible stopping times

Where do we stand in the theory of finance? : a selective overview with reference to Erich Gutenberg

For the past 20 years, financial markets research has concerned itself with issues related to the evaluation and management of financial securities in efficient capital markets and with issues of management control in incomplete markets. The following selective overview focuses on key aspects of the theory and empirical experience of management control under conditions of asymmetric information. The objective is examine the validity of the recently advanced hypothesis on the myths of corporate control. The present overview is based on Gutenberg's position that there exists a discrete corporate interest, as distinct from and separate from the interests of the shareholders or other stakeholders. In the third volume of Grundlagen der BWL: Die Finanzen, published in 1969, this position of Gutenberg's is coupled with an appeal for a so-called financial equilibrium to be maintained. Not until recently have models grounded in capital market theory been developed which also allow for a firm's management to exercise autonomy vis-à-vis its stakeholder. This paper was prepared for the Erich Gutenberg centenary conference on December 12 and 13, 1997 in Cologne