Following is a list of past Occasional Lectures for 2005.

Speaker:	Professor Thomas Lux, University of Kiel, Germany
Title:	"The Markov-Switching Multi-Fractal Model of Asset Returns: GMM Estimation and Linear Forecasting of Volatility"
Date:	29 November, 2005
Abstract:	Multi-fractal processes have recently been proposed as a new formalism for modelling the time series of returns in finance. The major attraction of these processes is their ability to generate various degrees of long memory in different powers of returns - a feature that has been found in virtually all financial data. Initial difficulties stemming from non-stationarity and the combinatorial nature of the original model have been overcome by the introduction of an iterative Markov-switching multi-fractal model in Calvet and Fisher (2001) which allows for estimation of its parameters via maximum likelihood and Bayesian forecasting of volatility. However, applicability of MLE is restricted to cases with a discrete distribution of volatility components. From a practical point of view, ML also becomes computationally unfeasible for large numbers of components even if they are drawn from a discrete distribution. Here we propose an alternative GMM estimator together with linear forecasts which in principle is applicable for any continuous distribution with any number of volatility components. Monte Carlo studies show that GMM performs reasonably well for the popular Binomial and Lognormal models and that the loss incurred with linear compared to optimal forecasts is small. Extending the number of volatility components beyond what is feasible with MLE leads to gains in forecasting accuracy for some time series.

Speaker:	Professor Ernst Eberlein, University of Freiburg, Germany
Title:	"Lévy Driven Models in Mathematical Finance "
Date:	06 December, 2005
Abstract:	Most of the models implemented in the financial industry are still diffusion based, i.e. they are driven by Brownian motions. A number of empirical studies of financial time series shows however that with the normal distributions underlying these processes only a poor approximation of the real return distributions can be obtained. As a consequence the classical approach produces a significant model risk. In this talk we survey the development of more powerful models which are driven by Lévy processes or more general by semimartingales. Among the processes considered are hyperbolic, variance gamma as well as normal inverse Gaussian processes. Due to the flexibility of the underlying distributions more accurate results can be obtained in risk management and derivative pricing. Besides of equity models we consider in particular models for fixed income and credit markets. Implementation issues are discussed as well. From the mathematical point of view a basic knowledge of modern stochastic analysis is required.