Professor Dilip Madan, University of Maryland, USA

Title: FIRN supported seminar: "Stochastic Volatility for Lévy Processes"
Date: Tuesday, 09 October 2007
Time: 4:00-6:00 pm
Audience: This Lecture is open to the public
Location:
University of Technology, Sydney
School of Finance & Economics
Seminar Room
Level 3, D Block, Room 3.01
Haymarket

Please RSVP to Michelle Manion for catering purposes.

Abstract: Three processes reflecting persistence of volatility are initially formulated by evaluating three Lévy processes at a time change given by the integral of a mean reverting square root process. The model for the mean reverting time change is then generalized to include Non-Gaussian models that are solutions to OU (Ornstein-Uhlenbeck) equations driven by one sided discontinuous Lévy processes permitting correlation with the stock. Positive stock price processes are obtained by exponentiating and mean correcting these processes, or alternatively by stochastically exponentiating these processes. The characteristic functions for the log price can be used to yield option prices via the fast Fourier transform. In general, mean corrected exponentiation performs better than employing the stochastic exponential. It is observed that the mean corrected exponential model is not a martingale in the filtration in which it is originally defined. This leads us to formulate and investigate the important property of martingale marginals where we seek martingales in altered filtrations consistent with the one dimensional marginal distributions of the level of the process at each future date.

Volker Böhm, Bielefeld University, Germany

Title: "The Dynamics of Random Asset Prices in the Generalized CAPM: Some Recent Results"
Date: Wednesday, 14 March, 2007
Time: 4:00-6:00 pm
Audience: This Lecture is open to the public
Location:
University of Technology, Sydney
School of Finance & Economics
Seminar Room
Level 3, D Block, Room 3.01
Haymarket

Abstract:

Recent results of the theory of endogenous asset pricing of the generalized CAPM reveal that some of the traditional concepts and results of the two period model with homogeneous consumers have natural extensions to situations when they are heterogeneous with respect to their preferences, their beliefs, and their behavior. In addition, heterogeneity induces additional dynamic and stochastic features not present in the standard model. Results are given for arbitrary preferences and beliefs and their impact on asset demand, existence and multiplicity of equilibria in economies of overlapping cohorts of consumers. Extensions of the concepts of an efficient market portfolio under heterogeneous forecasting are given. With arbitrary multi-period planning horizons separation properties of asset demand are derived and an extension of a generalized fund separation theorem can be deduced under rational expectations. Finally, the role of different forecasting rules is investigated. In such cases switching behavior or bounded rationality often leads to non-ergodic asset prices.