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 study a model of local evolution. Players are located on a network and play games agains their neighbors. Players are characterized by three properties: (1) The stage game strategies they use agains their neighbors. (2) The repeated game strategy that determines the former. (3) A learning...

This paper applies the idea of evolution to a spatial model. We assume that prisoners' dilemmas or coordination games are played repeatedly within neighborhoods where players do not optimize but instead copy successful strategies. Discriminatory behavior of players is introduced representing...

The finding of clustered volatility and ARCH effects is ubiquitous in financial data. This paper presents a possible explanation of this phenomenon within a multi-agent framework of speculative activity. In the model, both chartist and fundamentalist strategies are considered with agents...

This paper reports statistical analyses performed on simulated data from a stochastic multi-agent model of speculative behaviour in a financial market. The price dynamics resulting from this artificial market process exhibits the same type of scaling laws as do empirical data from stock markets...

In this paper it is shown that the space of stochastic integrals w.r. to a special semimartingal is closed and hence every square integrable random variable admits a best approximation in this space. In terms of financial economics this means that for every contingent claim there exists a...

pagehe problem of term structure of interest rates modelling is considered in a continuous-time framework. The emphasis is on the bond prices, forward bond prices or LIBOR rates, rather than on the instantaneous rates as in the traditional models. Forward and spot probability measures are...

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...

In the framework of the classical Black and Scholes model of security market we present the explicit formulas of the minimal hedging portfolios for a number of reward processes of the ``classical'', lookback and Asian type. These results complement the solutions previously received by Mc~Kean,...

A term structure model with lognormal type volatility structure is proposed. The Heath, Jarrow and Morton (HJM) framework, coupled with the theory of stochastic evolution equations in infinite dimensions, is used to show that the resulting rates are well defined (they do not explode) and remain...