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hal-00003773, version 1

Applications of delta-function perturbation to the pricing of derivative securities

Marc Decamps () 1, Ann De Scheppe, Marc Goovaerts

Physica A 342 (2004) 677-692

Résumé : 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.

  • 1 :  Accounting-Finance-Insurance research group (AFI)
  • Université Catholique de Louvain (UCL) - Belgique
  • Domaine : Physique/Physique mathématique
  • Mots-clés : functional integrals – local time – comonotonicity – skew Brownian motion – option pricing – delta-function perturbation
 
  • hal-00003773, version 1
  • http://hal.archives-ouvertes.fr/hal-00003773
  • oai:hal.archives-ouvertes.fr:hal-00003773
  • Contributeur : Marc Decamps <>
  • Soumis le : Mardi 4 Janvier 2005, 15:44:58
  • Dernière modification le : Mardi 4 Janvier 2005, 16:12:38