Geometric Arbitrage Theory and Calibration of a Generator of Consistent Economic Scenarios

54 Pages Posted: 2 Apr 2008 Last revised: 11 Dec 2008

Date Written: December 2008

Abstract

On the theoretical side: we introduced the differential geometric framework to translate any market model into a principal fibre bundle allowing to interpret arbitrage as curvature, parameterizing arbitrage opportunities with the Lie Algebra of the holonomy group. The no arbitrage condition is equivalent to a continuity equation.

On the practical side: we propose a methodology to simulate the future evolution of asset values such that:

- the dimension of risk factors can be reduced. - the no arbitrage condition is satisfied. - the simulated moments of asset returns match the empirical ones.

Keywords: Geometric Arbitrage Theory, Asset Pricing Theory, Risk Management

Suggested Citation

Farinelli, Simone, Geometric Arbitrage Theory and Calibration of a Generator of Consistent Economic Scenarios (December 2008). Available at SSRN: https://ssrn.com/abstract=1115860 or http://dx.doi.org/10.2139/ssrn.1115860

Simone Farinelli (Contact Author)

Core Dynamics GmbH ( email )

Scheuzerstrasse 43
Zurich, 8006
Switzerland

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