A Path Integral Approach to Derivative Security Pricing: I. Formalism and Analytical Results

TL;DR

This paper introduces a path integral framework for pricing derivative securities, demonstrating its equivalence to traditional methods and applying it to models with analytical solutions for financial quantities.

Contribution

It develops a covariant path integral formalism for derivative pricing, extending to multi-dimensional cases with variable coefficients, and provides analytical solutions for economic models.

Findings

Path integral approach is equivalent to SDE and PDE methods.

The formalism handles multi-dimensional models with variable coefficients.

Analytical solutions are obtained for specific economic models.

Abstract

We use a path integral approach for solving the stochastic equations underlying the financial markets, and we show the equivalence between the path integral and the usual SDE and PDE methods. We analyze both the one-dimensional and the multi-dimensional cases, with point dependent drift and volatility, and describe a covariant formulation which allows general changes of variables. Finally we apply the method to some economic models with analytical solutions. In particular, we evaluate the expectation value of functionals which correspond to quantities of financial interest.