More realistic modelling in finance

Ernst Eberlein

Abstract: The need for sound risk management is not only a consequence of enforced legislation, it has become a competitive factor for financial institutions. The talk surveys a new approach, the hyperbolic model, which results in a considerable increase in accuracy in risk measurement. The model is based on Lévy processes generated by generalized hyperbolic distributions as driving processes. This class, which replaces classical Brownian motion, is flexible enough to fit almost perfectly empirical distributions from financial time series. Due to the properties of Lévy processes, the excellent fit of empirical distributions is not only obtained for a fixed time scale, it is consistent on various time scales such as daily, hourly, or weekly data. We discuss statistical estimation, derivative pricing, term structure modelling, and market risk in this new model world.

References:

E. Eberlein (2001), Application of generalized hyperbolic Lévy motions to finance. In: Lévy Processes: Theory and Applications, O.E. Barndorff-Nielsen, T. Mikosch, and S. Resnick (eds.), Birkhäuser, 319--337

E. Eberlein (2001), Recent advances in more realistic risk management: The hyperbolic model. In: Mastering Risk, Volume 2: Applications, Carol Alexander (ed.), Prentice Hall -- Financial Times, 56--72

E. Eberlein and U. Keller (1995), Hyperbolic Distributions in Finance. Bernoulli 1, 281--299

E. Eberlein and J. Jacod (1997), On the range of options prices. Finance and Stochastics 1, 131--140

E. Eberlein, U. Keller, and K. Prause (1998, New insights into smile, mispricing and value at risk: the hyperbolic model. Journal of Business 71, 371--406

E. Eberlein and S. Raible (1999), Term structure models driven by general Lévy processes. Mathematical Finance 9, 31--53

E. Eberlein and K. Prause (2001), The generalized hyperbolic model: financial derivatives and risk measures. In: Mathematical Finance -- Bachelier Congress 2000; H. Geman, D. Madan, S. Pliska, and T. Vorst (eds.), Springer Verlag, 245--267

E. Eberlein and S. Raible (2000), Some analytic facts on the generalized hyperbolic model. In: Proceedings of the 3rd European Conference of Mathematics, Progress in Mathematics, Birkhäuser, 367--378

E. Eberlein, J. Kallsen, and J. Kristen (2003), Risk management based on stochastic volatility. Journal of Risk

E. Eberlein and F. Özkan (2003), The defaultable Lévy term structure: ratings and restructuring. Mathematical Finance 13, 277--300

E. Eberlein and F. Özkan (2003), Time consistency of Lévy models. Quantitative Finance 3.

E. Eberlein and E.A. von Hammerstein (2002), Generalized hyperbolic and inverse Gaussian distributions: limiting cases and approximation of processes. FDM-Preprint 80, University of Freiburg

E. Eberlein and F. Özkan (2002), The Lévy Libor model. FDM-Preprint 82, University of Freiburg