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

Eleonora Bennati, Marco Rosa-Clot and Stefano Taddei
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Eleonora Bennati: Dipartimento di Scienze, Economiche dell'Università di Pisa, Via Curtatone e Montanara, 14 56100 Pisa, Italy
Marco Rosa-Clot: Dipartimento di Fisica, Università degli Studi di Firenze and Istituto Nazionale di Fisica Nucleare, Sezione di Firenze, Largo Enrico Fermi 2, I-50125, Firenze, Italy
Stefano Taddei: Dipartimento di Fisica, Università degli Studi di Firenze and Istituto Nazionale di Fisica Nucleare, Sezione di Firenze, Largo Enrico Fermi 2, I-50125, Firenze, Italy

International Journal of Theoretical and Applied Finance (IJTAF), 1999, vol. 02, issue 04, 381-407

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.

Date: 1999
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DOI: 10.1142/S0219024999000200

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