We demonstrate that in a CAPM economy Walras Law and the Tobin Separation Property characterize market demand in finite sets of prices. Consequently, for any number n there exist CAPM economies which have at least n equilibria and hence have n different beta pricing fomulas. It is shown that the...

We develop a new approach to pricing and hedging contingent claims in incomplete markets. Mimicking as closely as possible in an incomplete markets framework the no--arbitrage arguments that have been developed in complete markets leads us to defining the concept of pseudo--arbitrage. Building...

In this survey we discuss models with level-dependent and stochastic volatility from the viewpoint of erivative 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...

This paper constructs a model for the evolution of a risky security that is consistent with a set of observed call option prices. It explicitly treats the fact that only a discrete data set can be observed in practice. The framework is general and allows for state dependent volatility and jumps....

This paper discusses the pitfalls in the pricing of barrier options a pproximations of the underlying continuous processes via discrete lattice models. These problems are studied first in a Black-Scholes model. Improvements result from a trinomial model and a further modified model where price...

We deal with the valuration and hedging of non path-dependent European options on one or several underlyings in a model of an international economy which allows for both interest rate and exchange rate risk. Using martingale theory we provide a unified and easily applicable approach to pricing...

In this paper, the effects of so-called model misspecification and the effects of dropping the assumption that continuous rebalancing is possible are examined. Strategies which are robust if applied continuously fail to be robust if applied in discrete time. Therefore, the hedging bias which...

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)...

The basic model of financial economics is the Samuelson model of geometric Brownian motion because of the celebrated Black-Scholes formula for pricing the call option. The asset's volatility is a linear function of the asset value and the model garantees positive asset prices. In this paper it...

The effect of model and parameter misspecification on the effectiveness of Gaussian hedging strategies for derivative financial instruments is analyzed, showing that Gaussian hedges in the `natural'' hedging instruments are particularly robust. This is true for all models that imply...