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

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

1999-01-26

arxiv.org/abs/cond-mat/9901277v1

Physics

Condensed Matter

Statistical Mechanics

20 pages, no figures, to be published in International Journal of Theoretical and Applied Finance

Scientific paper

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.

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