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
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