Physica a-statistical mechanics and its applications vol:342 issue:3-4 pages:677-692
In the recent econophysics literature, the use of functional integrals is widespread for the calculation of option prices. In this paper, we extend this approach in several directions by means of delta-function perturbations. First, we show that results about infinitely repulsive delta-function are applicable to the pricing of barrier options. We also introduce functional integrals over skew paths that give rise to a new European option formula when combined with delta-function potential. We propose accurate closed-form approximations based on the theory of comonotonic risks in case the functional integrals are not analytically computable. (C) 2004 Elsevier B.V. All rights reserved.