An Examination of the Effects of Parameter Misspecification

It is well-known that Gaussian hedging strategies are robust in the sense that they always lead to a cost process of bounded variation and that a superhedge is possible if upper bounds on the volatility of the relevant processes are available, cf. El Karoui, Jeanblanc-Picque and Shreve (1998) and in particular for applications to fixed income derivatives Dudenhausen, Schlögl and Schlögl (1998). These results crucially depend on the choice of certain ``natural'' hedge instruments which are not always available in the market and fail to hold otherwise. In this paper, the problem of optimally selecting hedging instruments from a given set of traded assets, in particular of zero coupon bonds, is studied. Misspecified hedging strategies lead to a non-vanishing cost process, which in turn depends on the particular choice of instruments. The effect of this choice on the cost process is analyzed. Referring to bond markets, a thorough study of the implications of volatility mismatching is made and explicit results are stated for a broad range of volatility scenarios.Model misspecification, duplication of bonds, volatility mismatch, optimal selection of hedging instruments

Credit dynamics in a first passage time model with jumps

The payoff of many credit derivatives depends on the level of credit spreads. In particular, the payoff of credit derivatives with a leverage component is sensitive to jumps in the underlying credit spreads. In the framework of first passage time models we extend the model introduced in [Overbeck and Schmidt, 2005] to address these issues. In the extended a model, a credit quality process is driven by an Itô integral with respect to a Brownian motion with stochastic volatility. Using a representation of the credit quality process as a time-changed Brownian motion, we derive formulas for conditional default probabilities and credit spreads. An example for a volatility process is the square root of a Lévy-driven Ornstein-Uhlenbeck process. We show that jumps in the volatility translate into jumps in credit spreads. We examine the dynamics of the OS-model and the extended model and provide examples. --gap risk,credit spreads,credit dynamics,first passage time models,Lévy processes,general Ornstein-Uhlenbeck processes

Credit gap risk in a first passage time model with jumps

The payoff of many credit derivatives depends on the level of credit spreads. In particular, credit derivatives with a leverage component are subject to gap risk, a risk associated with the occurrence of jumps in the underlying credit default swaps. In the framework of first passage time models, we consider a model that addresses these issues. The principal idea is to model a credit quality process as an Itô integral with respect to a Brownian motion with a stochastic volatility. Using a representation of the credit quality process as a time-changed Brownian motion, one can derive formulas for conditional default probabilities and credit spreads. An example for a volatility process is the square root of a Lévy-driven Ornstein-Uhlenbeck process. The model can be implemented efficiently using a technique called Panjer recursion. Calibration to a wide range of dynamics is supported. We illustrate the effectiveness of the model by valuing a leveraged credit-linked note. --gap risk,credit spreads,credit dynamics,first passage time models,stochastic volatility,general Ornstein-Uhlenbeck processes

Recent advances in modeling and analysis of bioelectric and biomagnetic sources

Determining the centers of electrical activity in the human body and the connectivity between different centers of activity in the brain is an active area of research. To understand brain function and the nature of cardiovascular diseases requires sophisticated methods applicable to non-invasively measured bioelectric and biomagnetic data. As it is difficult to solve for all unknown parameters at once, several strains of data analysis have been developed, each trying to solve a different part of the problem and each requiring a different set of assumptions. Current trends and results from major topics of electro- and magnetoencephalographic data analysis are presented here together with the aim of stimulating research into the unification of the different approaches. The following topics are discussed: source reconstruction using detailed finite element modeling to locate sources deep in cthe brain; connectivity analysis for the quantification of strength and direction of information flow between activity centers, preferably incorporating an inverse solution; the conflict between the statistical independence assumption of sources and a possible connectivity; the verification and validation of results derived from non-invasively measured data through animal studies and phantom measurements. This list already indicates the benefits of a unified view