Noncommutative Geometry and Stochastic Calculus: Applications in Mathematical Finance

Abstract:     
The present report contains an introduction to some elementary concepts in noncommutative differential geometry. The material extends upon ideas first presented by Dimakis and Mueller-Hoissen. In particular, stochastic calculus and the Ito formula are shown to arise naturally from introducing noncommutativity of functions (0-forms) and differentials (1-forms). The abstract construction allows for the straightforward generalization to lattice theories for the direct implementation of numerical models. As an elementary demonstration of the formalism, the standard Black-Scholes model for option pricing is reformulated.

Number of Pages in PDF File: 15

Keywords: Mathematical Finance, Black-Scholes Model, Stochastic Calculus, Noncommutative Geometry

working papers series