Article1999

A PATH INTEGRAL APPROACH TO DERIVATIVE SECURITY PRICING I: FORMALISM AND ANALYTICAL RESULTS

ELEONORA BENNATI · M. Rosa-Clot · Stefano Taddei

54 citations0/0 files storedInternational Journal of Theoretical and Applied Finance

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Stochastic processes and financial applications Financial Markets and Investment Strategies Economic theories and models

Abstract

We use a path integral approach for solving the stochastic equations underlying the financial markets, and 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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References

1993A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options 1985A Theory of the Term Structure of Interest Rates 1990Options, Futures, and Other Derivative Securities.1989An Exact Bond Option Formula 1988Introduction to stochastic differential equations

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