In this survey we discuss models with level-dependent and stochastic volatility from the viewpoint of derivative asset analysis. Both classes of models are generalisations of the classical Black-Scholes model; they have been developed in an effort to build models that are flexible enough to cope...

Binomial models, which rebuild the continuous setup in the limit, serve for approximative valuation of options, especially where formulas cannot be derived mathematically. Even with the valuation of European call options distorting irregularities occur. For this case, sources of convergence...

Starting with observable annually compounded forward rates we derive a term structure model of interest rates. The model relies upon the assumption that a specific set of annually compounded forward rates is log-normally distributed. We derive solutions for interest rate caps and floors as well...

The forward measure in the discrete time Ho/Lee model is derived and passages to the continuous time limit are carried out under this measure. In particular the continuous time valuation formula for call options on zero coupon bonds is obtained as a limit of its discrete time equivalent as well...

In this paper we present a new approach to incorporate 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...

This paper gives a simple introduction to portfolio credit risk models of the factor model type. In factor models, the dependence between the individual defaults is driven by a small number of systematic factors. When conditioning on the realisation of these factors the defaults become...

In this paper we present a tree model for defaultable bond prices which can be used for the pricing of credit derivatives. The model is based upon the two-factor Hull-White (1994) model for default-free interest rates, where one of the factors is taken to be the credit spread of the defaultable...

In this paper we examine the problem of partially hedging a given credit risk exposure. We derive hedges which satisfy certain optimality criteria: For a given investment into the hedge they minimize the remaining risk, or vice versa. This is motivated by the fact that it is a core business of...

We develop a new approach to pricing and hedging contingent claims in incomplete markets framework the no-arbitrage arguments that have been developed in complete markets leads us to defining the concept we are able to extend the no-arbitrage ideo to a world of incomplete markets in such a way...

The aim of this paper is the valuation and hedging of defaultable bonds and options on defaultable bonds. The Heath/Jarrow/Morton-framework is used to model the interest rate risk, and the time of default is determined by the first jump time of a point process. (...)