Regensburg 2000 – scientific programme

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DY: Dynamik und Statistische Physik

DY 53: Interdisziplin
äre Anwendungen

DY 53.1: Talk

Friday, March 31, 2000, 11:00–11:15, H3

Intermediate arbitrage opportunities in derivatives markets as a non-equilibrium phenomenon in econophysics: consequences for option pricing — •Matthias Otto — Institut für Theoretische Physik, Universität Göttingen, Bunsenstr. 9, 37073 Göttingen

Non-equilibrium phenomena occur not only in the physical world, but also in finance. In this work, stochastic relaxational dynamics (together with path integrals) is applied to option pricing theory. Equilibrium in financial markets is defined as the absence of arbitrage, i.e. profits “for nothing”. A recently proposed model (by Ilinski et al.) considers fluctuations around this equilibrium state by introducing a relaxational dynamics with random noise for intermediate deviations called “virtual” arbitrage returns. In this work, the model is incorporated within a martingale pricing method for derivatives on securities (e.g. stocks) in incomplete markets using a mapping to option pricing theory with stochastic interest rates. Numerical examples are given which underline the fact that an additional positive risk premium (with respect to the Black-Scholes values) is found reflecting extra hedging costs due to intermediate deviations from economic equilibrium.