International Journal of Theoretical and Applied Finance

An exact solution is presented to a model that mimics the crowding effect in financial markets which arises when groups of agents share information. We show that the size distribution of groups of agents has a power law tail with an exponential cut-off. As the size of these groups determines the supply and demand balance, this implies heavy tails in the distribution of price variation. The moments of the distribution are calculated, as well as the kurtosis. We find that the kurtosis is large for all model parameter values and that the model is not self-organizing.

We propose a new framework to measure the risk of a single asset and of a portfolio of financial assets which takes the agent's investment horizon into account. The methodology is based on the moderate and large deviations theory in its simplest form. We show how it can be used to select optimal portfolios given investors' planning horizons and preferences for fatter right or left tails. For practical purposes, we introduce a new parameter, the "dilation exponent" α to characterize asset returns' distributions beyond the information contained in the mean-variance framework. We estimate α for Swiss individual stocks and for MSCI country and sector stock market indices. Finally, we show how to use the dilation exponent in conjunction with Sharpe's ratio for portfolio allocation purposes.

This paper uses the enlargement of filtrations to analyze the financial strategy of an insider trader in a discontinuous time market where prices are driven by a Brownian motion and a compound Poisson process. We compare this strategy with that of a non-insider trader. The market is a chosen viable and complete; we can give an explicit expression of the optimal portfolio of the insider trader.

On considère un marché financier dont les prix sont dirigés par un mouvement brownien et un processus de Poisson multivarié. Dans ce cadre le marché peut être complet et viable. Nous étudions la stratégie financière d'un agent qui a une information anticipant l'évolution du marché et nous la comparons un agent qui n'a pas cette information. La complétude du marché permet d'expliciter le portefeuille optimal de l'agent initié. Le grossissement de filtration permet de replacer une équation anticipante dans un cadre adapté.

This paper provides a method for pricing options in the constant elasticity of variance (CEV) model environment using the Lie-algebraic technique when the model parameters are time-dependent. Analytical solutions for the option values incorporating time-dependent model parameters are obtained in various CEV processes with different elasticity factors. The numerical results indicate that option values are sensitive to volatility term structures. It is also possible to generate further results using various functional forms for interest rate and dividend term structures. Furthermore, the Lie-algebraic approach is very simple and can be easily extended to other option pricing models with well-defined algebraic structures.

The finding of clustered volatility and ARCH effects is ubiquitous in financial data. This paper presents a possible explanation for this phenomenon within a multi-agent framework of speculative activity. In the model, both chartist and fundamentalist strategies are considered with agents switching between both behavioural variants according to observed differences in pay-offs. Price changes are brought about by a market maker reacting to imbalances between demand and supply. Most of the time, a stable and efficient market results. However, its usual tranquil performance is interspersed by sudden transient phases of destabilisation. An outbreak of volatility occurs if the fraction of agents using chartist techniques surpasses a certain threshold value, but such phases are quickly brought to an end by stabilising tendencies. Formally, this pattern can be understood as an example of a new type of dynamic behaviour known as "on-off intermittency" in physics literature. Statistical analysis of simulated time series shows that the main stylised facts (unit roots in levels together with heteroscedasticity and leptokurtosis of returns) can be found in this "artificial" market.

In this paper we study empirically the Forward Rate Curve (FRC) of 5 different currencies. We confirm and extend the findings of a previous investigation of the U.S. FRC. In particular, the average FRC follows a square-root law, with a prefactor related to the spot volatility, suggesting a Value-at-Risk-like pricing. We find a striking correlation between the instantaneous FRC and the past spot trend over a certain time horizon, in agreement with the idea of an extrapolated trend effect. We present a model which can be adequately calibrated to account for these effects.